diff --git a/dnscrypt-proxy/crypto.go b/dnscrypt-proxy/crypto.go index 9db36d0c..d7335d66 100644 --- a/dnscrypt-proxy/crypto.go +++ b/dnscrypt-proxy/crypto.go @@ -7,9 +7,9 @@ import ( "errors" "math/rand" + "github.com/cloudflare/circl/dh/x25519" "github.com/jedisct1/dlog" "github.com/jedisct1/xsecretbox" - "golang.org/x/crypto/curve25519" "golang.org/x/crypto/nacl/box" "golang.org/x/crypto/nacl/secretbox" ) @@ -70,7 +70,12 @@ func (proxy *Proxy) Encrypt(serverInfo *ServerInfo, packet []byte, proto string) var ephSk [32]byte h.Sum(ephSk[:0]) var xPublicKey [PublicKeySize]byte - curve25519.ScalarBaseMult(&xPublicKey, &ephSk) + + var cfxPublicKey, cfephSk x25519.Key + copy(cfephSk[:], ephSk[:]) + x25519.KeyGen(&cfxPublicKey, &cfephSk) + copy(xPublicKey[:], cfxPublicKey[:]) + publicKey = &xPublicKey xsharedKey := ComputeSharedKey(serverInfo.CryptoConstruction, &ephSk, &serverInfo.ServerPk, nil) sharedKey = &xsharedKey diff --git a/dnscrypt-proxy/proxy.go b/dnscrypt-proxy/proxy.go index 97f1700b..9cf97add 100644 --- a/dnscrypt-proxy/proxy.go +++ b/dnscrypt-proxy/proxy.go @@ -9,10 +9,10 @@ import ( "sync/atomic" "time" + "github.com/cloudflare/circl/dh/x25519" "github.com/jedisct1/dlog" clocksmith "github.com/jedisct1/go-clocksmith" stamps "github.com/jedisct1/go-dnsstamps" - "golang.org/x/crypto/curve25519" ) type Proxy struct { @@ -72,7 +72,12 @@ func (proxy *Proxy) StartProxy() { if _, err := crypto_rand.Read(proxy.proxySecretKey[:]); err != nil { dlog.Fatal(err) } - curve25519.ScalarBaseMult(&proxy.proxyPublicKey, &proxy.proxySecretKey) + + var cfProxyPublicKey, cfProxySecretKey x25519.Key + copy(cfProxySecretKey[:], proxy.proxySecretKey[:]) + x25519.KeyGen(&cfProxyPublicKey, &cfProxySecretKey) + copy(proxy.proxyPublicKey[:], cfProxyPublicKey[:]) + for _, registeredServer := range proxy.registeredServers { proxy.serversInfo.registerServer(proxy, registeredServer.name, registeredServer.stamp) } diff --git a/go.mod b/go.mod index cd11c428..f052b837 100644 --- a/go.mod +++ b/go.mod @@ -8,6 +8,7 @@ require ( github.com/aead/chacha20 v0.0.0-20180709150244-8b13a72661da // indirect github.com/aead/poly1305 v0.0.0-20180717145839-3fee0db0b635 // indirect github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412 + github.com/cloudflare/circl v0.0.0-20190621185434-0ba9a9382e8b github.com/coreos/go-systemd v0.0.0-20190321100706-95778dfbb74e github.com/dchest/safefile v0.0.0-20151022103144-855e8d98f185 github.com/facebookgo/atomicfile v0.0.0-20151019160806-2de1f203e7d5 // indirect diff --git a/go.sum b/go.sum index ffdafc51..e46c2e54 100644 --- a/go.sum +++ b/go.sum @@ -8,6 +8,8 @@ github.com/aead/poly1305 v0.0.0-20180717145839-3fee0db0b635 h1:52m0LGchQBBVqJRyY github.com/aead/poly1305 v0.0.0-20180717145839-3fee0db0b635/go.mod h1:lmLxL+FV291OopO93Bwf9fQLQeLyt33VJRUg5VJ30us= github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412 h1:w1UutsfOrms1J05zt7ISrnJIXKzwaspym5BTKGx93EI= github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412/go.mod h1:WPjqKcmVOxf0XSf3YxCJs6N6AOSrOx3obionmG7T0y0= +github.com/cloudflare/circl v0.0.0-20190621185434-0ba9a9382e8b h1:yGcUL49UXXtIcd8FIkrxCZ7N96l16UM1C0VcA4UOVH4= +github.com/cloudflare/circl v0.0.0-20190621185434-0ba9a9382e8b/go.mod h1:MhjB3NEEhJbTOdLLq964NIUisXDxaE1WkQPUxtgZXiY= github.com/coreos/go-systemd v0.0.0-20190321100706-95778dfbb74e h1:Wf6HqHfScWJN9/ZjdUKyjop4mf3Qdd+1TvvltAvM3m8= github.com/coreos/go-systemd v0.0.0-20190321100706-95778dfbb74e/go.mod h1:F5haX7vjVVG0kc13fIWeqUViNPyEJxv/OmvnBo0Yme4= github.com/dchest/safefile v0.0.0-20151022103144-855e8d98f185 h1:3T8ZyTDp5QxTx3NU48JVb2u+75xc040fofcBaN+6jPA= diff --git a/vendor/github.com/cloudflare/circl/LICENSE b/vendor/github.com/cloudflare/circl/LICENSE new file mode 100644 index 00000000..67edaa90 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/LICENSE @@ -0,0 +1,57 @@ +Copyright (c) 2019 Cloudflare. All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + * Redistributions of source code must retain the above copyright +notice, this list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above +copyright notice, this list of conditions and the following disclaimer +in the documentation and/or other materials provided with the +distribution. + * Neither the name of Cloudflare nor the names of its +contributors may be used to endorse or promote products derived from +this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +======================================================================== + +Copyright (c) 2009 The Go Authors. All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + * Redistributions of source code must retain the above copyright +notice, this list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above +copyright notice, this list of conditions and the following disclaimer +in the documentation and/or other materials provided with the +distribution. + * Neither the name of Google Inc. nor the names of its +contributors may be used to endorse or promote products derived from +this software without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve.go b/vendor/github.com/cloudflare/circl/dh/x25519/curve.go new file mode 100644 index 00000000..0527f801 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve.go @@ -0,0 +1,96 @@ +package x25519 + +import ( + fp "github.com/cloudflare/circl/math/fp25519" +) + +// ladderJoye calculates a fixed-point multiplication with the generator point. +// The algorithm is the right-to-left Joye's ladder as described +// in "How to precompute a ladder" in SAC'2017. +func ladderJoye(k *Key) { + w := [5]fp.Elt{} // [mu,x1,z1,x2,z2] order must be preserved. + fp.SetOne(&w[1]) // x1 = 1 + fp.SetOne(&w[2]) // z1 = 1 + w[3] = fp.Elt{ // x2 = G-S + 0xbd, 0xaa, 0x2f, 0xc8, 0xfe, 0xe1, 0x94, 0x7e, + 0xf8, 0xed, 0xb2, 0x14, 0xae, 0x95, 0xf0, 0xbb, + 0xe2, 0x48, 0x5d, 0x23, 0xb9, 0xa0, 0xc7, 0xad, + 0x34, 0xab, 0x7c, 0xe2, 0xee, 0xcd, 0xae, 0x1e, + } + fp.SetOne(&w[4]) // z2 = 1 + + const n = 255 + const h = 3 + swap := uint(1) + for s := 0; s < n-h; s++ { + i := (s + h) / 8 + j := (s + h) % 8 + bit := uint((k[i] >> uint(j)) & 1) + copy(w[0][:], tableGenerator[s*Size:(s+1)*Size]) + diffAdd(&w, swap^bit) + swap = bit + } + for s := 0; s < h; s++ { + double(&w[1], &w[2]) + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +// ladderMontgomery calculates a generic scalar point multiplication +// The algorithm implemented is the left-to-right Montgomery's ladder. +func ladderMontgomery(k, xP *Key) { + w := [5]fp.Elt{} // [x1, x2, z2, x3, z3] order must be preserved. + w[0] = *(*fp.Elt)(xP) // x1 = xP + fp.SetOne(&w[1]) // x2 = 1 + w[3] = *(*fp.Elt)(xP) // x3 = xP + fp.SetOne(&w[4]) // z3 = 1 + + move := uint(0) + for s := 255 - 1; s >= 0; s-- { + i := s / 8 + j := s % 8 + bit := uint((k[i] >> uint(j)) & 1) + ladderStep(&w, move^bit) + move = bit + } + toAffine((*[fp.Size]byte)(k), &w[1], &w[2]) +} + +func toAffine(k *[fp.Size]byte, x, z *fp.Elt) { + fp.Inv(z, z) + fp.Mul(x, x, z) + fp.ToBytes(k[:], x) +} + +var lowOrderPoints = [5]fp.Elt{ + { /* (0,_,1) point of order 2 on Curve25519 */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (1,_,1) point of order 4 on Curve25519 */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + }, + { /* (x,_,1) first point of order 8 on Curve25519 */ + 0xe0, 0xeb, 0x7a, 0x7c, 0x3b, 0x41, 0xb8, 0xae, + 0x16, 0x56, 0xe3, 0xfa, 0xf1, 0x9f, 0xc4, 0x6a, + 0xda, 0x09, 0x8d, 0xeb, 0x9c, 0x32, 0xb1, 0xfd, + 0x86, 0x62, 0x05, 0x16, 0x5f, 0x49, 0xb8, 0x00, + }, + { /* (x,_,1) second point of order 8 on Curve25519 */ + 0x5f, 0x9c, 0x95, 0xbc, 0xa3, 0x50, 0x8c, 0x24, + 0xb1, 0xd0, 0xb1, 0x55, 0x9c, 0x83, 0xef, 0x5b, + 0x04, 0x44, 0x5c, 0xc4, 0x58, 0x1c, 0x8e, 0x86, + 0xd8, 0x22, 0x4e, 0xdd, 0xd0, 0x9f, 0x11, 0x57, + }, + { /* (-1,_,1) a point of order 4 on the twist of Curve25519 */ + 0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, + }, +} diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.go b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.go new file mode 100644 index 00000000..ab7bf38d --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.go @@ -0,0 +1,30 @@ +// +build amd64,!purego + +package x25519 + +import ( + "golang.org/x/sys/cpu" + + fp "github.com/cloudflare/circl/math/fp25519" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func double(x, z *fp.Elt) { doubleAmd64(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddAmd64(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepAmd64(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Amd64(z, x) } + +//go:noescape +func ladderStepAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func diffAddAmd64(w *[5]fp.Elt, b uint) + +//go:noescape +func doubleAmd64(x, z *fp.Elt) + +//go:noescape +func mulA24Amd64(z, x *fp.Elt) diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.h b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.h new file mode 100644 index 00000000..8c1ae4d0 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.h @@ -0,0 +1,111 @@ +#define ladderStepLeg \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulLeg(b0,x2,z3) \ + integerMulLeg(b1,x3,z2) \ + reduceFromDoubleLeg(t0,b0) \ + reduceFromDoubleLeg(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrLeg(b0,t0) \ + integerSqrLeg(b1,t1) \ + reduceFromDoubleLeg(x3,b0) \ + reduceFromDoubleLeg(z3,b1) \ + integerMulLeg(b0,x1,z3) \ + reduceFromDoubleLeg(z3,b0) \ + integerSqrLeg(b0,x2) \ + integerSqrLeg(b1,z2) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z2) \ + integerMulLeg(b0,x2,z2) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x2,b0) \ + reduceFromDoubleLeg(z2,b1) + +#define ladderStepBmi2Adx \ + addSub(x2,z2) \ + addSub(x3,z3) \ + integerMulAdx(b0,x2,z3) \ + integerMulAdx(b1,x3,z2) \ + reduceFromDoubleAdx(t0,b0) \ + reduceFromDoubleAdx(t1,b1) \ + addSub(t0,t1) \ + cselect(x2,x3,regMove) \ + cselect(z2,z3,regMove) \ + integerSqrAdx(b0,t0) \ + integerSqrAdx(b1,t1) \ + reduceFromDoubleAdx(x3,b0) \ + reduceFromDoubleAdx(z3,b1) \ + integerMulAdx(b0,x1,z3) \ + reduceFromDoubleAdx(z3,b0) \ + integerSqrAdx(b0,x2) \ + integerSqrAdx(b1,z2) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) \ + subtraction(t0,x2,z2) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z2) \ + integerMulAdx(b0,x2,z2) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x2,b0) \ + reduceFromDoubleAdx(z2,b1) + +#define difAddLeg \ + addSub(x1,z1) \ + integerMulLeg(b0,z1,ui) \ + reduceFromDoubleLeg(z1,b0) \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + integerMulLeg(b0,x1,z2) \ + integerMulLeg(b1,z1,x2) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define difAddBmi2Adx \ + addSub(x1,z1) \ + integerMulAdx(b0,z1,ui) \ + reduceFromDoubleAdx(z1,b0) \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + integerMulAdx(b0,x1,z2) \ + integerMulAdx(b1,z1,x2) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) + +#define doubleLeg \ + addSub(x1,z1) \ + integerSqrLeg(b0,x1) \ + integerSqrLeg(b1,z1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Leg(t1,t0) \ + additionLeg(t1,t1,z1) \ + integerMulLeg(b0,x1,z1) \ + integerMulLeg(b1,t0,t1) \ + reduceFromDoubleLeg(x1,b0) \ + reduceFromDoubleLeg(z1,b1) + +#define doubleBmi2Adx \ + addSub(x1,z1) \ + integerSqrAdx(b0,x1) \ + integerSqrAdx(b1,z1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) \ + subtraction(t0,x1,z1) \ + multiplyA24Adx(t1,t0) \ + additionAdx(t1,t1,z1) \ + integerMulAdx(b0,x1,z1) \ + integerMulAdx(b1,t0,t1) \ + reduceFromDoubleAdx(x1,b0) \ + reduceFromDoubleAdx(z1,b1) diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.s b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.s new file mode 100644 index 00000000..b7723185 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_amd64.s @@ -0,0 +1,156 @@ +// +build amd64 + +#include "textflag.h" + +// Depends on circl/math/fp25519 package +#include "../../math/fp25519/fp_amd64.h" +#include "curve_amd64.h" + +// CTE_A24 is (A+2)/4 from Curve25519 +#define CTE_A24 121666 + +#define Size 32 + +// multiplyA24Leg multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R13, FLAGS +// Instr: x86_64, cmov +#define multiplyA24Leg(z,x) \ + MOVL $CTE_A24, AX; MULQ 0+x; MOVQ AX, R8; MOVQ DX, R9; \ + MOVL $CTE_A24, AX; MULQ 8+x; MOVQ AX, R12; MOVQ DX, R10; \ + MOVL $CTE_A24, AX; MULQ 16+x; MOVQ AX, R13; MOVQ DX, R11; \ + MOVL $CTE_A24, AX; MULQ 24+x; \ + ADDQ R12, R9; \ + ADCQ R13, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + MOVL $38, AX; /* 2*C = 38 = 2^256 MOD 2^255-19*/ \ + IMULQ AX, DX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ $0, R11; MOVQ R11, 24+z; \ + MOVQ $0, DX; \ + CMOVQCS AX, DX; \ + ADDQ DX, R8; MOVQ R8, 0+z; + +// multiplyA24Adx multiplies x times CTE_A24 and stores in z +// Uses: AX, DX, R8-R12, FLAGS +// Instr: x86_64, cmov, bmi2 +#define multiplyA24Adx(z,x) \ + MOVQ $CTE_A24, DX; \ + MULXQ 0+x, R8, R10; \ + MULXQ 8+x, R9, R11; ADDQ R10, R9; \ + MULXQ 16+x, R10, AX; ADCQ R11, R10; \ + MULXQ 24+x, R11, R12; ADCQ AX, R11; \ + ;;;;;;;;;;;;;;;;;;;;; ADCQ $0, R12; \ + MOVL $38, DX; /* 2*C = 38 = 2^256 MOD 2^255-19*/ \ + IMULQ DX, R12; \ + ADDQ R12, R8; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ $0, R11; MOVQ R11, 24+z; \ + MOVQ $0, R12; \ + CMOVQCS DX, R12; \ + ADDQ R12, R8; MOVQ R8, 0+z; + +#define mulA24Legacy \ + multiplyA24Leg(0(DI),0(SI)) +#define mulA24Bmi2Adx \ + multiplyA24Adx(0(DI),0(SI)) + +// func mulA24Amd64(z, x *fp255.Elt) +TEXT ·mulA24Amd64(SB),NOSPLIT,$0-16 + MOVQ z+0(FP), DI + MOVQ x+8(FP), SI + CHECK_BMI2ADX(LMA24, mulA24Legacy, mulA24Bmi2Adx) + + +// func ladderStepAmd64(w *[5]fp255.Elt, b uint) +// ladderStepAmd64 calculates a point addition and doubling as follows: +// (x2,z2) = 2*(x2,z2) and (x3,z3) = (x2,z2)+(x3,z3) using as a difference (x1,-). +// work = (x1,x2,z2,x3,z3) are five fp255.Elt of 32 bytes. +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·ladderStepAmd64(SB),NOSPLIT,$192-16 + // Parameters + #define regWork DI + #define regMove SI + #define x1 0*Size(regWork) + #define x2 1*Size(regWork) + #define z2 2*Size(regWork) + #define x3 3*Size(regWork) + #define z3 4*Size(regWork) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regMove + CHECK_BMI2ADX(LLADSTEP, ladderStepLeg, ladderStepBmi2Adx) + #undef regWork + #undef regMove + #undef x1 + #undef x2 + #undef z2 + #undef x3 + #undef z3 + #undef t0 + #undef t1 + #undef b0 + #undef b1 + +// func diffAddAmd64(w *[5]fp255.Elt, b uint) +// diffAddAmd64 calculates a differential point addition using a precomputed point. +// (x1,z1) = (x1,z1)+(mu) using a difference point (x2,z2) +// w = (mu,x1,z1,x2,z2) are five fp.Elt, and +// stack = (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·diffAddAmd64(SB),NOSPLIT,$128-16 + // Parameters + #define regWork DI + #define regSwap SI + #define ui 0*Size(regWork) + #define x1 1*Size(regWork) + #define z1 2*Size(regWork) + #define x2 3*Size(regWork) + #define z2 4*Size(regWork) + // Local variables + #define b0 0*Size(SP) + #define b1 2*Size(SP) + MOVQ w+0(FP), regWork + MOVQ b+8(FP), regSwap + cswap(x1,x2,regSwap) + cswap(z1,z2,regSwap) + CHECK_BMI2ADX(LDIFADD, difAddLeg, difAddBmi2Adx) + #undef regWork + #undef regSwap + #undef ui + #undef x1 + #undef z1 + #undef x2 + #undef z2 + #undef b0 + #undef b1 + +// func doubleAmd64(x, z *fp255.Elt) +// doubleAmd64 calculates a point doubling (x1,z1) = 2*(x1,z1). +// stack = (t0,t1) are two fp.Elt of fp.Size bytes, and +// (b0,b1) are two-double precision fp.Elt of 2*fp.Size bytes. +TEXT ·doubleAmd64(SB),NOSPLIT,$192-16 + // Parameters + #define x1 0(DI) + #define z1 0(SI) + // Local variables + #define t0 0*Size(SP) + #define t1 1*Size(SP) + #define b0 2*Size(SP) + #define b1 4*Size(SP) + MOVQ x+0(FP), DI + MOVQ z+8(FP), SI + CHECK_BMI2ADX(LDOUB,doubleLeg,doubleBmi2Adx) + #undef x1 + #undef z1 + #undef t0 + #undef t1 + #undef b0 + #undef b1 diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_generic.go b/vendor/github.com/cloudflare/circl/dh/x25519/curve_generic.go new file mode 100644 index 00000000..dae67ea3 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_generic.go @@ -0,0 +1,85 @@ +package x25519 + +import ( + "encoding/binary" + "math/bits" + + fp "github.com/cloudflare/circl/math/fp25519" +) + +func doubleGeneric(x, z *fp.Elt) { + t0, t1 := &fp.Elt{}, &fp.Elt{} + fp.AddSub(x, z) + fp.Sqr(x, x) + fp.Sqr(z, z) + fp.Sub(t0, x, z) + mulA24Generic(t1, t0) + fp.Add(t1, t1, z) + fp.Mul(x, x, z) + fp.Mul(z, t0, t1) +} + +func diffAddGeneric(w *[5]fp.Elt, b uint) { + mu, x1, z1, x2, z2 := &w[0], &w[1], &w[2], &w[3], &w[4] + fp.Cswap(x1, x2, b) + fp.Cswap(z1, z2, b) + fp.AddSub(x1, z1) + fp.Mul(z1, z1, mu) + fp.AddSub(x1, z1) + fp.Sqr(x1, x1) + fp.Sqr(z1, z1) + fp.Mul(x1, x1, z2) + fp.Mul(z1, z1, x2) +} + +func ladderStepGeneric(w *[5]fp.Elt, b uint) { + x1, x2, z2, x3, z3 := &w[0], &w[1], &w[2], &w[3], &w[4] + t0 := &fp.Elt{} + t1 := &fp.Elt{} + fp.AddSub(x2, z2) + fp.AddSub(x3, z3) + fp.Mul(t0, x2, z3) + fp.Mul(t1, x3, z2) + fp.AddSub(t0, t1) + fp.Cmov(x2, x3, b) + fp.Cmov(z2, z3, b) + fp.Sqr(x3, t0) + fp.Sqr(z3, t1) + fp.Mul(z3, x1, z3) + fp.Sqr(x2, x2) + fp.Sqr(z2, z2) + fp.Sub(t0, x2, z2) + mulA24Generic(t1, t0) + fp.Add(t1, t1, z2) + fp.Mul(x2, x2, z2) + fp.Mul(z2, t0, t1) +} + +func mulA24Generic(z, x *fp.Elt) { + const A24 = 121666 + const n = 8 + var xx [4]uint64 + for i := range xx { + xx[i] = binary.LittleEndian.Uint64(x[i*n : (i+1)*n]) + } + + h0, l0 := bits.Mul64(xx[0], A24) + h1, l1 := bits.Mul64(xx[1], A24) + h2, l2 := bits.Mul64(xx[2], A24) + h3, l3 := bits.Mul64(xx[3], A24) + + var c3 uint64 + l1, c0 := bits.Add64(h0, l1, 0) + l2, c1 := bits.Add64(h1, l2, c0) + l3, c2 := bits.Add64(h2, l3, c1) + l4, _ := bits.Add64(h3, 0, c2) + _, l4 = bits.Mul64(l4, 38) + l0, c0 = bits.Add64(l0, l4, 0) + xx[1], c1 = bits.Add64(l1, 0, c0) + xx[2], c2 = bits.Add64(l2, 0, c1) + xx[3], c3 = bits.Add64(l3, 0, c2) + xx[0], _ = bits.Add64(l0, (-c3)&38, 0) + for i := range xx { + binary.LittleEndian.PutUint64(z[i*n:(i+1)*n], xx[i]) + } +} diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/curve_noasm.go b/vendor/github.com/cloudflare/circl/dh/x25519/curve_noasm.go new file mode 100644 index 00000000..ccddab2e --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/curve_noasm.go @@ -0,0 +1,10 @@ +// +build !amd64 purego + +package x25519 + +import fp "github.com/cloudflare/circl/math/fp25519" + +func double(x, z *fp.Elt) { doubleGeneric(x, z) } +func diffAdd(w *[5]fp.Elt, b uint) { diffAddGeneric(w, b) } +func ladderStep(w *[5]fp.Elt, b uint) { ladderStepGeneric(w, b) } +func mulA24(z, x *fp.Elt) { mulA24Generic(z, x) } diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/doc.go b/vendor/github.com/cloudflare/circl/dh/x25519/doc.go new file mode 100644 index 00000000..e8feed56 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/doc.go @@ -0,0 +1,20 @@ +/* +Package x25519 provides Diffie-Hellman functions as specified in RFC-7748. + +Validation of public keys. + +The Diffie-Hellman function, as described in RFC-7748 [1], works for any +public key. However, if a different protocol requires contributory +behaviour [2,3], then the public keys must be validated against low-order +points [3,4]. To do that, the Shared function performs this validation +internally and returns false when the public key is invalid (i.e., it +is a low-order point). + +References: + - [1] RFC7748 by Langley, Hamburg, Turner (https://rfc-editor.org/rfc/rfc7748.txt) + - [2] Curve25519 by Bernstein (https://cr.yp.to/ecdh.html) + - [3] Bernstein (https://cr.yp.to/ecdh.html#validate) + - [4] Cremers&Jackson (https://eprint.iacr.org/2019/526) + +*/ +package x25519 diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/key.go b/vendor/github.com/cloudflare/circl/dh/x25519/key.go new file mode 100644 index 00000000..bbd37ddd --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/key.go @@ -0,0 +1,47 @@ +package x25519 + +import ( + "crypto/subtle" + + fp "github.com/cloudflare/circl/math/fp25519" +) + +// Size is the length in bytes of a X25519 key. +const Size = 32 + +// Key represents a X25519 key. +type Key [Size]byte + +func (k *Key) clamp(in *Key) *Key { + *k = *in + k[0] &= 248 + k[31] = (k[31] & 127) | 64 + return k +} + +// isValidPubKey verifies if the public key is not a low-order point. +func (k *Key) isValidPubKey() bool { + fp.Modp((*fp.Elt)(k)) + isLowOrder := false + for _, P := range lowOrderPoints { + isLowOrder = isLowOrder || subtle.ConstantTimeCompare(P[:], k[:]) != 0 + } + return !isLowOrder +} + +// KeyGen obtains a public key given a secret key. +func KeyGen(public, secret *Key) { + ladderJoye(public.clamp(secret)) +} + +// Shared calculates Alice's shared key from Alice's secret key and Bob's +// public key returning true on success. A failure case happens when the public +// key is a low-order point, thus the shared key is all-zeros and the function +// returns false. +func Shared(shared, secret, public *Key) bool { + validPk := *public + validPk[31] &= (1 << (255 % 8)) - 1 + ok := validPk.isValidPubKey() + ladderMontgomery(shared.clamp(secret), &validPk) + return ok +} diff --git a/vendor/github.com/cloudflare/circl/dh/x25519/table.go b/vendor/github.com/cloudflare/circl/dh/x25519/table.go new file mode 100644 index 00000000..30927e7b --- /dev/null +++ b/vendor/github.com/cloudflare/circl/dh/x25519/table.go @@ -0,0 +1,266 @@ +package x25519 + +import "github.com/cloudflare/circl/math/fp25519" + +// tableGenerator contains the set of points: +// t[i] = (xi+1)/(xi-1), +// where (xi,yi) = 2^iG and G is the generator point +// Size = (256)*(256/8) = 8192 bytes. +var tableGenerator = [256 * fp25519.Size]byte{ + /* (2^ 0)P */ 0xf3, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x5f, + /* (2^ 1)P */ 0x96, 0xfe, 0xaa, 0x16, 0xf4, 0x20, 0x82, 0x6b, 0x34, 0x6a, 0x56, 0x4f, 0x2b, 0xeb, 0xeb, 0x82, 0x0f, 0x95, 0xa5, 0x75, 0xb0, 0xa5, 0xa9, 0xd5, 0xf4, 0x88, 0x24, 0x4b, 0xcf, 0xb2, 0x42, 0x51, + /* (2^ 2)P */ 0x0c, 0x68, 0x69, 0x00, 0x75, 0xbc, 0xae, 0x6a, 0x41, 0x9c, 0xf9, 0xa0, 0x20, 0x78, 0xcf, 0x89, 0xf4, 0xd0, 0x56, 0x3b, 0x18, 0xd9, 0x58, 0x2a, 0xa4, 0x11, 0x60, 0xe3, 0x80, 0xca, 0x5a, 0x4b, + /* (2^ 3)P */ 0x5d, 0x74, 0x29, 0x8c, 0x34, 0x32, 0x91, 0x32, 0xd7, 0x2f, 0x64, 0xe1, 0x16, 0xe6, 0xa2, 0xf4, 0x34, 0xbc, 0x67, 0xff, 0x03, 0xbb, 0x45, 0x1e, 0x4a, 0x9b, 0x2a, 0xf4, 0xd0, 0x12, 0x69, 0x30, + /* (2^ 4)P */ 0x54, 0x71, 0xaf, 0xe6, 0x07, 0x65, 0x88, 0xff, 0x2f, 0xc8, 0xee, 0xdf, 0x13, 0x0e, 0xf5, 0x04, 0xce, 0xb5, 0xba, 0x2a, 0xe8, 0x2f, 0x51, 0xaa, 0x22, 0xf2, 0xd5, 0x68, 0x1a, 0x25, 0x4e, 0x17, + /* (2^ 5)P */ 0x98, 0x88, 0x02, 0x82, 0x0d, 0x70, 0x96, 0xcf, 0xc5, 0x02, 0x2c, 0x0a, 0x37, 0xe3, 0x43, 0x17, 0xaa, 0x6e, 0xe8, 0xb4, 0x98, 0xec, 0x9e, 0x37, 0x2e, 0x48, 0xe0, 0x51, 0x8a, 0x88, 0x59, 0x0c, + /* (2^ 6)P */ 0x89, 0xd1, 0xb5, 0x99, 0xd6, 0xf1, 0xcb, 0xfb, 0x84, 0xdc, 0x9f, 0x8e, 0xd5, 0xf0, 0xae, 0xac, 0x14, 0x76, 0x1f, 0x23, 0x06, 0x0d, 0xc2, 0xc1, 0x72, 0xf9, 0x74, 0xa2, 0x8d, 0x21, 0x38, 0x29, + /* (2^ 7)P */ 0x18, 0x7f, 0x1d, 0xff, 0xbe, 0x49, 0xaf, 0xf6, 0xc2, 0xc9, 0x7a, 0x38, 0x22, 0x1c, 0x54, 0xcc, 0x6b, 0xc5, 0x15, 0x40, 0xef, 0xc9, 0xfc, 0x96, 0xa9, 0x13, 0x09, 0x69, 0x7c, 0x62, 0xc1, 0x69, + /* (2^ 8)P */ 0x0e, 0xdb, 0x33, 0x47, 0x2f, 0xfd, 0x86, 0x7a, 0xe9, 0x7d, 0x08, 0x9e, 0xf2, 0xc4, 0xb8, 0xfd, 0x29, 0xa2, 0xa2, 0x8e, 0x1a, 0x4b, 0x5e, 0x09, 0x79, 0x7a, 0xb3, 0x29, 0xc8, 0xa7, 0xd7, 0x1a, + /* (2^ 9)P */ 0xc0, 0xa0, 0x7e, 0xd1, 0xca, 0x89, 0x2d, 0x34, 0x51, 0x20, 0xed, 0xcc, 0xa6, 0xdd, 0xbe, 0x67, 0x74, 0x2f, 0xb4, 0x2b, 0xbf, 0x31, 0xca, 0x19, 0xbb, 0xac, 0x80, 0x49, 0xc8, 0xb4, 0xf7, 0x3d, + /* (2^ 10)P */ 0x83, 0xd8, 0x0a, 0xc8, 0x4d, 0x44, 0xc6, 0xa8, 0x85, 0xab, 0xe3, 0x66, 0x03, 0x44, 0x1e, 0xb9, 0xd8, 0xf6, 0x64, 0x01, 0xa0, 0xcd, 0x15, 0xc2, 0x68, 0xe6, 0x47, 0xf2, 0x6e, 0x7c, 0x86, 0x3d, + /* (2^ 11)P */ 0x8c, 0x65, 0x3e, 0xcc, 0x2b, 0x58, 0xdd, 0xc7, 0x28, 0x55, 0x0e, 0xee, 0x48, 0x47, 0x2c, 0xfd, 0x71, 0x4f, 0x9f, 0xcc, 0x95, 0x9b, 0xfd, 0xa0, 0xdf, 0x5d, 0x67, 0xb0, 0x71, 0xd8, 0x29, 0x75, + /* (2^ 12)P */ 0x78, 0xbd, 0x3c, 0x2d, 0xb4, 0x68, 0xf5, 0xb8, 0x82, 0xda, 0xf3, 0x91, 0x1b, 0x01, 0x33, 0x12, 0x62, 0x3b, 0x7c, 0x4a, 0xcd, 0x6c, 0xce, 0x2d, 0x03, 0x86, 0x49, 0x9e, 0x8e, 0xfc, 0xe7, 0x75, + /* (2^ 13)P */ 0xec, 0xb6, 0xd0, 0xfc, 0xf1, 0x13, 0x4f, 0x2f, 0x45, 0x7a, 0xff, 0x29, 0x1f, 0xca, 0xa8, 0xf1, 0x9b, 0xe2, 0x81, 0x29, 0xa7, 0xc1, 0x49, 0xc2, 0x6a, 0xb5, 0x83, 0x8c, 0xbb, 0x0d, 0xbe, 0x6e, + /* (2^ 14)P */ 0x22, 0xb2, 0x0b, 0x17, 0x8d, 0xfa, 0x14, 0x71, 0x5f, 0x93, 0x93, 0xbf, 0xd5, 0xdc, 0xa2, 0x65, 0x9a, 0x97, 0x9c, 0xb5, 0x68, 0x1f, 0xc4, 0xbd, 0x89, 0x92, 0xce, 0xa2, 0x79, 0xef, 0x0e, 0x2f, + /* (2^ 15)P */ 0xce, 0x37, 0x3c, 0x08, 0x0c, 0xbf, 0xec, 0x42, 0x22, 0x63, 0x49, 0xec, 0x09, 0xbc, 0x30, 0x29, 0x0d, 0xac, 0xfe, 0x9c, 0xc1, 0xb0, 0x94, 0xf2, 0x80, 0xbb, 0xfa, 0xed, 0x4b, 0xaa, 0x80, 0x37, + /* (2^ 16)P */ 0x29, 0xd9, 0xea, 0x7c, 0x3e, 0x7d, 0xc1, 0x56, 0xc5, 0x22, 0x57, 0x2e, 0xeb, 0x4b, 0xcb, 0xe7, 0x5a, 0xe1, 0xbf, 0x2d, 0x73, 0x31, 0xe9, 0x0c, 0xf8, 0x52, 0x10, 0x62, 0xc7, 0x83, 0xb8, 0x41, + /* (2^ 17)P */ 0x50, 0x53, 0xd2, 0xc3, 0xa0, 0x5c, 0xf7, 0xdb, 0x51, 0xe3, 0xb1, 0x6e, 0x08, 0xbe, 0x36, 0x29, 0x12, 0xb2, 0xa9, 0xb4, 0x3c, 0xe0, 0x36, 0xc9, 0xaa, 0x25, 0x22, 0x32, 0x82, 0xbf, 0x45, 0x1d, + /* (2^ 18)P */ 0xc5, 0x4c, 0x02, 0x6a, 0x03, 0xb1, 0x1a, 0xe8, 0x72, 0x9a, 0x4c, 0x30, 0x1c, 0x20, 0x12, 0xe2, 0xfc, 0xb1, 0x32, 0x68, 0xba, 0x3f, 0xd7, 0xc5, 0x81, 0x95, 0x83, 0x4d, 0x5a, 0xdb, 0xff, 0x20, + /* (2^ 19)P */ 0xad, 0x0f, 0x5d, 0xbe, 0x67, 0xd3, 0x83, 0xa2, 0x75, 0x44, 0x16, 0x8b, 0xca, 0x25, 0x2b, 0x6c, 0x2e, 0xf2, 0xaa, 0x7c, 0x46, 0x35, 0x49, 0x9d, 0x49, 0xff, 0x85, 0xee, 0x8e, 0x40, 0x66, 0x51, + /* (2^ 20)P */ 0x61, 0xe3, 0xb4, 0xfa, 0xa2, 0xba, 0x67, 0x3c, 0xef, 0x5c, 0xf3, 0x7e, 0xc6, 0x33, 0xe4, 0xb3, 0x1c, 0x9b, 0x15, 0x41, 0x92, 0x72, 0x59, 0x52, 0x33, 0xab, 0xb0, 0xd5, 0x92, 0x18, 0x62, 0x6a, + /* (2^ 21)P */ 0xcb, 0xcd, 0x55, 0x75, 0x38, 0x4a, 0xb7, 0x20, 0x3f, 0x92, 0x08, 0x12, 0x0e, 0xa1, 0x2a, 0x53, 0xd1, 0x1d, 0x28, 0x62, 0x77, 0x7b, 0xa1, 0xea, 0xbf, 0x44, 0x5c, 0xf0, 0x43, 0x34, 0xab, 0x61, + /* (2^ 22)P */ 0xf8, 0xde, 0x24, 0x23, 0x42, 0x6c, 0x7a, 0x25, 0x7f, 0xcf, 0xe3, 0x17, 0x10, 0x6c, 0x1c, 0x13, 0x57, 0xa2, 0x30, 0xf6, 0x39, 0x87, 0x75, 0x23, 0x80, 0x85, 0xa7, 0x01, 0x7a, 0x40, 0x5a, 0x29, + /* (2^ 23)P */ 0xd9, 0xa8, 0x5d, 0x6d, 0x24, 0x43, 0xc4, 0xf8, 0x5d, 0xfa, 0x52, 0x0c, 0x45, 0x75, 0xd7, 0x19, 0x3d, 0xf8, 0x1b, 0x73, 0x92, 0xfc, 0xfc, 0x2a, 0x00, 0x47, 0x2b, 0x1b, 0xe8, 0xc8, 0x10, 0x7d, + /* (2^ 24)P */ 0x0b, 0xa2, 0xba, 0x70, 0x1f, 0x27, 0xe0, 0xc8, 0x57, 0x39, 0xa6, 0x7c, 0x86, 0x48, 0x37, 0x99, 0xbb, 0xd4, 0x7e, 0xcb, 0xb3, 0xef, 0x12, 0x54, 0x75, 0x29, 0xe6, 0x73, 0x61, 0xd3, 0x96, 0x31, + /* (2^ 25)P */ 0xfc, 0xdf, 0xc7, 0x41, 0xd1, 0xca, 0x5b, 0xde, 0x48, 0xc8, 0x95, 0xb3, 0xd2, 0x8c, 0xcc, 0x47, 0xcb, 0xf3, 0x1a, 0xe1, 0x42, 0xd9, 0x4c, 0xa3, 0xc2, 0xce, 0x4e, 0xd0, 0xf2, 0xdb, 0x56, 0x02, + /* (2^ 26)P */ 0x7f, 0x66, 0x0e, 0x4b, 0xe9, 0xb7, 0x5a, 0x87, 0x10, 0x0d, 0x85, 0xc0, 0x83, 0xdd, 0xd4, 0xca, 0x9f, 0xc7, 0x72, 0x4e, 0x8f, 0x2e, 0xf1, 0x47, 0x9b, 0xb1, 0x85, 0x8c, 0xbb, 0x87, 0x1a, 0x5f, + /* (2^ 27)P */ 0xb8, 0x51, 0x7f, 0x43, 0xb6, 0xd0, 0xe9, 0x7a, 0x65, 0x90, 0x87, 0x18, 0x55, 0xce, 0xc7, 0x12, 0xee, 0x7a, 0xf7, 0x5c, 0xfe, 0x09, 0xde, 0x2a, 0x27, 0x56, 0x2c, 0x7d, 0x2f, 0x5a, 0xa0, 0x23, + /* (2^ 28)P */ 0x9a, 0x16, 0x7c, 0xf1, 0x28, 0xe1, 0x08, 0x59, 0x2d, 0x85, 0xd0, 0x8a, 0xdd, 0x98, 0x74, 0xf7, 0x64, 0x2f, 0x10, 0xab, 0xce, 0xc4, 0xb4, 0x74, 0x45, 0x98, 0x13, 0x10, 0xdd, 0xba, 0x3a, 0x18, + /* (2^ 29)P */ 0xac, 0xaa, 0x92, 0xaa, 0x8d, 0xba, 0x65, 0xb1, 0x05, 0x67, 0x38, 0x99, 0x95, 0xef, 0xc5, 0xd5, 0xd1, 0x40, 0xfc, 0xf8, 0x0c, 0x8f, 0x2f, 0xbe, 0x14, 0x45, 0x20, 0xee, 0x35, 0xe6, 0x01, 0x27, + /* (2^ 30)P */ 0x14, 0x65, 0x15, 0x20, 0x00, 0xa8, 0x9f, 0x62, 0xce, 0xc1, 0xa8, 0x64, 0x87, 0x86, 0x23, 0xf2, 0x0e, 0x06, 0x3f, 0x0b, 0xff, 0x4f, 0x89, 0x5b, 0xfa, 0xa3, 0x08, 0xf7, 0x4c, 0x94, 0xd9, 0x60, + /* (2^ 31)P */ 0x1f, 0x20, 0x7a, 0x1c, 0x1a, 0x00, 0xea, 0xae, 0x63, 0xce, 0xe2, 0x3e, 0x63, 0x6a, 0xf1, 0xeb, 0xe1, 0x07, 0x7a, 0x4c, 0x59, 0x09, 0x77, 0x6f, 0xcb, 0x08, 0x02, 0x0d, 0x15, 0x58, 0xb9, 0x79, + /* (2^ 32)P */ 0xe7, 0x10, 0xd4, 0x01, 0x53, 0x5e, 0xb5, 0x24, 0x4d, 0xc8, 0xfd, 0xf3, 0xdf, 0x4e, 0xa3, 0xe3, 0xd8, 0x32, 0x40, 0x90, 0xe4, 0x68, 0x87, 0xd8, 0xec, 0xae, 0x3a, 0x7b, 0x42, 0x84, 0x13, 0x13, + /* (2^ 33)P */ 0x14, 0x4f, 0x23, 0x86, 0x12, 0xe5, 0x05, 0x84, 0x29, 0xc5, 0xb4, 0xad, 0x39, 0x47, 0xdc, 0x14, 0xfd, 0x4f, 0x63, 0x50, 0xb2, 0xb5, 0xa2, 0xb8, 0x93, 0xff, 0xa7, 0xd8, 0x4a, 0xa9, 0xe2, 0x2f, + /* (2^ 34)P */ 0xdd, 0xfa, 0x43, 0xe8, 0xef, 0x57, 0x5c, 0xec, 0x18, 0x99, 0xbb, 0xf0, 0x40, 0xce, 0x43, 0x28, 0x05, 0x63, 0x3d, 0xcf, 0xd6, 0x61, 0xb5, 0xa4, 0x7e, 0x77, 0xfb, 0xe8, 0xbd, 0x29, 0x36, 0x74, + /* (2^ 35)P */ 0x8f, 0x73, 0xaf, 0xbb, 0x46, 0xdd, 0x3e, 0x34, 0x51, 0xa6, 0x01, 0xb1, 0x28, 0x18, 0x98, 0xed, 0x7a, 0x79, 0x2c, 0x88, 0x0b, 0x76, 0x01, 0xa4, 0x30, 0x87, 0xc8, 0x8d, 0xe2, 0x23, 0xc2, 0x1f, + /* (2^ 36)P */ 0x0e, 0xba, 0x0f, 0xfc, 0x91, 0x4e, 0x60, 0x48, 0xa4, 0x6f, 0x2c, 0x05, 0x8f, 0xf7, 0x37, 0xb6, 0x9c, 0x23, 0xe9, 0x09, 0x3d, 0xac, 0xcc, 0x91, 0x7c, 0x68, 0x7a, 0x43, 0xd4, 0xee, 0xf7, 0x23, + /* (2^ 37)P */ 0x00, 0xd8, 0x9b, 0x8d, 0x11, 0xb1, 0x73, 0x51, 0xa7, 0xd4, 0x89, 0x31, 0xb6, 0x41, 0xd6, 0x29, 0x86, 0xc5, 0xbb, 0x88, 0x79, 0x17, 0xbf, 0xfd, 0xf5, 0x1d, 0xd8, 0xca, 0x4f, 0x89, 0x59, 0x29, + /* (2^ 38)P */ 0x99, 0xc8, 0xbb, 0xb4, 0xf3, 0x8e, 0xbc, 0xae, 0xb9, 0x92, 0x69, 0xb2, 0x5a, 0x99, 0x48, 0x41, 0xfb, 0x2c, 0xf9, 0x34, 0x01, 0x0b, 0xe2, 0x24, 0xe8, 0xde, 0x05, 0x4a, 0x89, 0x58, 0xd1, 0x40, + /* (2^ 39)P */ 0xf6, 0x76, 0xaf, 0x85, 0x11, 0x0b, 0xb0, 0x46, 0x79, 0x7a, 0x18, 0x73, 0x78, 0xc7, 0xba, 0x26, 0x5f, 0xff, 0x8f, 0xab, 0x95, 0xbf, 0xc0, 0x3d, 0xd7, 0x24, 0x55, 0x94, 0xd8, 0x8b, 0x60, 0x2a, + /* (2^ 40)P */ 0x02, 0x63, 0x44, 0xbd, 0x88, 0x95, 0x44, 0x26, 0x9c, 0x43, 0x88, 0x03, 0x1c, 0xc2, 0x4b, 0x7c, 0xb2, 0x11, 0xbd, 0x83, 0xf3, 0xa4, 0x98, 0x8e, 0xb9, 0x76, 0xd8, 0xc9, 0x7b, 0x8d, 0x21, 0x26, + /* (2^ 41)P */ 0x8a, 0x17, 0x7c, 0x99, 0x42, 0x15, 0x08, 0xe3, 0x6f, 0x60, 0xb6, 0x6f, 0xa8, 0x29, 0x2d, 0x3c, 0x74, 0x93, 0x27, 0xfa, 0x36, 0x77, 0x21, 0x5c, 0xfa, 0xb1, 0xfe, 0x4a, 0x73, 0x05, 0xde, 0x7d, + /* (2^ 42)P */ 0xab, 0x2b, 0xd4, 0x06, 0x39, 0x0e, 0xf1, 0x3b, 0x9c, 0x64, 0x80, 0x19, 0x3e, 0x80, 0xf7, 0xe4, 0x7a, 0xbf, 0x95, 0x95, 0xf8, 0x3b, 0x05, 0xe6, 0x30, 0x55, 0x24, 0xda, 0x38, 0xaf, 0x4f, 0x39, + /* (2^ 43)P */ 0xf4, 0x28, 0x69, 0x89, 0x58, 0xfb, 0x8e, 0x7a, 0x3c, 0x11, 0x6a, 0xcc, 0xe9, 0x78, 0xc7, 0xfb, 0x6f, 0x59, 0xaf, 0x30, 0xe3, 0x0c, 0x67, 0x72, 0xf7, 0x6c, 0x3d, 0x1d, 0xa8, 0x22, 0xf2, 0x48, + /* (2^ 44)P */ 0xa7, 0xca, 0x72, 0x0d, 0x41, 0xce, 0x1f, 0xf0, 0x95, 0x55, 0x3b, 0x21, 0xc7, 0xec, 0x20, 0x5a, 0x83, 0x14, 0xfa, 0xc1, 0x65, 0x11, 0xc2, 0x7b, 0x41, 0xa7, 0xa8, 0x1d, 0xe3, 0x9a, 0xf8, 0x07, + /* (2^ 45)P */ 0xf9, 0x0f, 0x83, 0xc6, 0xb4, 0xc2, 0xd2, 0x05, 0x93, 0x62, 0x31, 0xc6, 0x0f, 0x33, 0x3e, 0xd4, 0x04, 0xa9, 0xd3, 0x96, 0x0a, 0x59, 0xa5, 0xa5, 0xb6, 0x33, 0x53, 0xa6, 0x91, 0xdb, 0x5e, 0x70, + /* (2^ 46)P */ 0xf7, 0xa5, 0xb9, 0x0b, 0x5e, 0xe1, 0x8e, 0x04, 0x5d, 0xaf, 0x0a, 0x9e, 0xca, 0xcf, 0x40, 0x32, 0x0b, 0xa4, 0xc4, 0xed, 0xce, 0x71, 0x4b, 0x8f, 0x6d, 0x4a, 0x54, 0xde, 0xa3, 0x0d, 0x1c, 0x62, + /* (2^ 47)P */ 0x91, 0x40, 0x8c, 0xa0, 0x36, 0x28, 0x87, 0x92, 0x45, 0x14, 0xc9, 0x10, 0xb0, 0x75, 0x83, 0xce, 0x94, 0x63, 0x27, 0x4f, 0x52, 0xeb, 0x72, 0x8a, 0x35, 0x36, 0xc8, 0x7e, 0xfa, 0xfc, 0x67, 0x26, + /* (2^ 48)P */ 0x2a, 0x75, 0xe8, 0x45, 0x33, 0x17, 0x4c, 0x7f, 0xa5, 0x79, 0x70, 0xee, 0xfe, 0x47, 0x1b, 0x06, 0x34, 0xff, 0x86, 0x9f, 0xfa, 0x9a, 0xdd, 0x25, 0x9c, 0xc8, 0x5d, 0x42, 0xf5, 0xce, 0x80, 0x37, + /* (2^ 49)P */ 0xe9, 0xb4, 0x3b, 0x51, 0x5a, 0x03, 0x46, 0x1a, 0xda, 0x5a, 0x57, 0xac, 0x79, 0xf3, 0x1e, 0x3e, 0x50, 0x4b, 0xa2, 0x5f, 0x1c, 0x5f, 0x8c, 0xc7, 0x22, 0x9f, 0xfd, 0x34, 0x76, 0x96, 0x1a, 0x32, + /* (2^ 50)P */ 0xfa, 0x27, 0x6e, 0x82, 0xb8, 0x07, 0x67, 0x94, 0xd0, 0x6f, 0x50, 0x4c, 0xd6, 0x84, 0xca, 0x3d, 0x36, 0x14, 0xe9, 0x75, 0x80, 0x21, 0x89, 0xc1, 0x84, 0x84, 0x3b, 0x9b, 0x16, 0x84, 0x92, 0x6d, + /* (2^ 51)P */ 0xdf, 0x2d, 0x3f, 0x38, 0x40, 0xe8, 0x67, 0x3a, 0x75, 0x9b, 0x4f, 0x0c, 0xa3, 0xc9, 0xee, 0x33, 0x47, 0xef, 0x83, 0xa7, 0x6f, 0xc8, 0xc7, 0x3e, 0xc4, 0xfb, 0xc9, 0xba, 0x9f, 0x44, 0xec, 0x26, + /* (2^ 52)P */ 0x7d, 0x9e, 0x9b, 0xa0, 0xcb, 0x38, 0x0f, 0x5c, 0x8c, 0x47, 0xa3, 0x62, 0xc7, 0x8c, 0x16, 0x81, 0x1c, 0x12, 0xfc, 0x06, 0xd3, 0xb0, 0x23, 0x3e, 0xdd, 0xdc, 0xef, 0xa5, 0xa0, 0x8a, 0x23, 0x5a, + /* (2^ 53)P */ 0xff, 0x43, 0xea, 0xc4, 0x21, 0x61, 0xa2, 0x1b, 0xb5, 0x32, 0x88, 0x7c, 0x7f, 0xc7, 0xf8, 0x36, 0x9a, 0xf9, 0xdc, 0x0a, 0x0b, 0xea, 0xfb, 0x88, 0xf9, 0xeb, 0x5b, 0xc2, 0x8e, 0x93, 0xa9, 0x5c, + /* (2^ 54)P */ 0xa0, 0xcd, 0xfc, 0x51, 0x5e, 0x6a, 0x43, 0xd5, 0x3b, 0x89, 0xcd, 0xc2, 0x97, 0x47, 0xbc, 0x1d, 0x08, 0x4a, 0x22, 0xd3, 0x65, 0x6a, 0x34, 0x19, 0x66, 0xf4, 0x9a, 0x9b, 0xe4, 0x34, 0x50, 0x0f, + /* (2^ 55)P */ 0x6e, 0xb9, 0xe0, 0xa1, 0x67, 0x39, 0x3c, 0xf2, 0x88, 0x4d, 0x7a, 0x86, 0xfa, 0x08, 0x8b, 0xe5, 0x79, 0x16, 0x34, 0xa7, 0xc6, 0xab, 0x2f, 0xfb, 0x46, 0x69, 0x02, 0xb6, 0x1e, 0x38, 0x75, 0x2a, + /* (2^ 56)P */ 0xac, 0x20, 0x94, 0xc1, 0xe4, 0x3b, 0x0a, 0xc8, 0xdc, 0xb6, 0xf2, 0x81, 0xc6, 0xf6, 0xb1, 0x66, 0x88, 0x33, 0xe9, 0x61, 0x67, 0x03, 0xf7, 0x7c, 0xc4, 0xa4, 0x60, 0xa6, 0xd8, 0xbb, 0xab, 0x25, + /* (2^ 57)P */ 0x98, 0x51, 0xfd, 0x14, 0xba, 0x12, 0xea, 0x91, 0xa9, 0xff, 0x3c, 0x4a, 0xfc, 0x50, 0x49, 0x68, 0x28, 0xad, 0xf5, 0x30, 0x21, 0x84, 0x26, 0xf8, 0x41, 0xa4, 0x01, 0x53, 0xf7, 0x88, 0xa9, 0x3e, + /* (2^ 58)P */ 0x6f, 0x8c, 0x5f, 0x69, 0x9a, 0x10, 0x78, 0xc9, 0xf3, 0xc3, 0x30, 0x05, 0x4a, 0xeb, 0x46, 0x17, 0x95, 0x99, 0x45, 0xb4, 0x77, 0x6d, 0x4d, 0x44, 0xc7, 0x5c, 0x4e, 0x05, 0x8c, 0x2b, 0x95, 0x75, + /* (2^ 59)P */ 0xaa, 0xd6, 0xf4, 0x15, 0x79, 0x3f, 0x70, 0xa3, 0xd8, 0x47, 0x26, 0x2f, 0x20, 0x46, 0xc3, 0x66, 0x4b, 0x64, 0x1d, 0x81, 0xdf, 0x69, 0x14, 0xd0, 0x1f, 0xd7, 0xa5, 0x81, 0x7d, 0xa4, 0xfe, 0x77, + /* (2^ 60)P */ 0x81, 0xa3, 0x7c, 0xf5, 0x9e, 0x52, 0xe9, 0xc5, 0x1a, 0x88, 0x2f, 0xce, 0xb9, 0xb4, 0xee, 0x6e, 0xd6, 0x9b, 0x00, 0xe8, 0x28, 0x1a, 0xe9, 0xb6, 0xec, 0x3f, 0xfc, 0x9a, 0x3e, 0xbe, 0x80, 0x4b, + /* (2^ 61)P */ 0xc5, 0xd2, 0xae, 0x26, 0xc5, 0x73, 0x37, 0x7e, 0x9d, 0xa4, 0xc9, 0x53, 0xb4, 0xfc, 0x4a, 0x1b, 0x4d, 0xb2, 0xff, 0xba, 0xd7, 0xbd, 0x20, 0xa9, 0x0e, 0x40, 0x2d, 0x12, 0x9f, 0x69, 0x54, 0x7c, + /* (2^ 62)P */ 0xc8, 0x4b, 0xa9, 0x4f, 0xe1, 0xc8, 0x46, 0xef, 0x5e, 0xed, 0x52, 0x29, 0xce, 0x74, 0xb0, 0xe0, 0xd5, 0x85, 0xd8, 0xdb, 0xe1, 0x50, 0xa4, 0xbe, 0x2c, 0x71, 0x0f, 0x32, 0x49, 0x86, 0xb6, 0x61, + /* (2^ 63)P */ 0xd1, 0xbd, 0xcc, 0x09, 0x73, 0x5f, 0x48, 0x8a, 0x2d, 0x1a, 0x4d, 0x7d, 0x0d, 0x32, 0x06, 0xbd, 0xf4, 0xbe, 0x2d, 0x32, 0x73, 0x29, 0x23, 0x25, 0x70, 0xf7, 0x17, 0x8c, 0x75, 0xc4, 0x5d, 0x44, + /* (2^ 64)P */ 0x3c, 0x93, 0xc8, 0x7c, 0x17, 0x34, 0x04, 0xdb, 0x9f, 0x05, 0xea, 0x75, 0x21, 0xe8, 0x6f, 0xed, 0x34, 0xdb, 0x53, 0xc0, 0xfd, 0xbe, 0xfe, 0x1e, 0x99, 0xaf, 0x5d, 0xc6, 0x67, 0xe8, 0xdb, 0x4a, + /* (2^ 65)P */ 0xdf, 0x09, 0x06, 0xa9, 0xa2, 0x71, 0xcd, 0x3a, 0x50, 0x40, 0xd0, 0x6d, 0x85, 0x91, 0xe9, 0xe5, 0x3c, 0xc2, 0x57, 0x81, 0x68, 0x9b, 0xc6, 0x1e, 0x4d, 0xfe, 0x5c, 0x88, 0xf6, 0x27, 0x74, 0x69, + /* (2^ 66)P */ 0x51, 0xa8, 0xe1, 0x65, 0x9b, 0x7b, 0xbe, 0xd7, 0xdd, 0x36, 0xc5, 0x22, 0xd5, 0x28, 0x3d, 0xa0, 0x45, 0xb6, 0xd2, 0x8f, 0x65, 0x9d, 0x39, 0x28, 0xe1, 0x41, 0x26, 0x7c, 0xe1, 0xb7, 0xe5, 0x49, + /* (2^ 67)P */ 0xa4, 0x57, 0x04, 0x70, 0x98, 0x3a, 0x8c, 0x6f, 0x78, 0x67, 0xbb, 0x5e, 0xa2, 0xf0, 0x78, 0x50, 0x0f, 0x96, 0x82, 0xc3, 0xcb, 0x3c, 0x3c, 0xd1, 0xb1, 0x84, 0xdf, 0xa7, 0x58, 0x32, 0x00, 0x2e, + /* (2^ 68)P */ 0x1c, 0x6a, 0x29, 0xe6, 0x9b, 0xf3, 0xd1, 0x8a, 0xb2, 0xbf, 0x5f, 0x2a, 0x65, 0xaa, 0xee, 0xc1, 0xcb, 0xf3, 0x26, 0xfd, 0x73, 0x06, 0xee, 0x33, 0xcc, 0x2c, 0x9d, 0xa6, 0x73, 0x61, 0x25, 0x59, + /* (2^ 69)P */ 0x41, 0xfc, 0x18, 0x4e, 0xaa, 0x07, 0xea, 0x41, 0x1e, 0xa5, 0x87, 0x7c, 0x52, 0x19, 0xfc, 0xd9, 0x6f, 0xca, 0x31, 0x58, 0x80, 0xcb, 0xaa, 0xbd, 0x4f, 0x69, 0x16, 0xc9, 0x2d, 0x65, 0x5b, 0x44, + /* (2^ 70)P */ 0x15, 0x23, 0x17, 0xf2, 0xa7, 0xa3, 0x92, 0xce, 0x64, 0x99, 0x1b, 0xe1, 0x2d, 0x28, 0xdc, 0x1e, 0x4a, 0x31, 0x4c, 0xe0, 0xaf, 0x3a, 0x82, 0xa1, 0x86, 0xf5, 0x7c, 0x43, 0x94, 0x2d, 0x0a, 0x79, + /* (2^ 71)P */ 0x09, 0xe0, 0xf6, 0x93, 0xfb, 0x47, 0xc4, 0x71, 0x76, 0x52, 0x84, 0x22, 0x67, 0xa5, 0x22, 0x89, 0x69, 0x51, 0x4f, 0x20, 0x3b, 0x90, 0x70, 0xbf, 0xfe, 0x19, 0xa3, 0x1b, 0x89, 0x89, 0x7a, 0x2f, + /* (2^ 72)P */ 0x0c, 0x14, 0xe2, 0x77, 0xb5, 0x8e, 0xa0, 0x02, 0xf4, 0xdc, 0x7b, 0x42, 0xd4, 0x4e, 0x9a, 0xed, 0xd1, 0x3c, 0x32, 0xe4, 0x44, 0xec, 0x53, 0x52, 0x5b, 0x35, 0xe9, 0x14, 0x3c, 0x36, 0x88, 0x3e, + /* (2^ 73)P */ 0x8c, 0x0b, 0x11, 0x77, 0x42, 0xc1, 0x66, 0xaa, 0x90, 0x33, 0xa2, 0x10, 0x16, 0x39, 0xe0, 0x1a, 0xa2, 0xc2, 0x3f, 0xc9, 0x12, 0xbd, 0x30, 0x20, 0xab, 0xc7, 0x55, 0x95, 0x57, 0x41, 0xe1, 0x3e, + /* (2^ 74)P */ 0x41, 0x7d, 0x6e, 0x6d, 0x3a, 0xde, 0x14, 0x92, 0xfe, 0x7e, 0xf1, 0x07, 0x86, 0xd8, 0xcd, 0x3c, 0x17, 0x12, 0xe1, 0xf8, 0x88, 0x12, 0x4f, 0x67, 0xd0, 0x93, 0x9f, 0x32, 0x0f, 0x25, 0x82, 0x56, + /* (2^ 75)P */ 0x6e, 0x39, 0x2e, 0x6d, 0x13, 0x0b, 0xf0, 0x6c, 0xbf, 0xde, 0x14, 0x10, 0x6f, 0xf8, 0x4c, 0x6e, 0x83, 0x4e, 0xcc, 0xbf, 0xb5, 0xb1, 0x30, 0x59, 0xb6, 0x16, 0xba, 0x8a, 0xb4, 0x69, 0x70, 0x04, + /* (2^ 76)P */ 0x93, 0x07, 0xb2, 0x69, 0xab, 0xe4, 0x4c, 0x0d, 0x9e, 0xfb, 0xd0, 0x97, 0x1a, 0xb9, 0x4d, 0xb2, 0x1d, 0xd0, 0x00, 0x4e, 0xf5, 0x50, 0xfa, 0xcd, 0xb5, 0xdd, 0x8b, 0x36, 0x85, 0x10, 0x1b, 0x22, + /* (2^ 77)P */ 0xd2, 0xd8, 0xe3, 0xb1, 0x68, 0x94, 0xe5, 0xe7, 0x93, 0x2f, 0x12, 0xbd, 0x63, 0x65, 0xc5, 0x53, 0x09, 0x3f, 0x66, 0xe0, 0x03, 0xa9, 0xe8, 0xee, 0x42, 0x3d, 0xbe, 0xcb, 0x62, 0xa6, 0xef, 0x61, + /* (2^ 78)P */ 0x2a, 0xab, 0x6e, 0xde, 0xdd, 0xdd, 0xf8, 0x2c, 0x31, 0xf2, 0x35, 0x14, 0xd5, 0x0a, 0xf8, 0x9b, 0x73, 0x49, 0xf0, 0xc9, 0xce, 0xda, 0xea, 0x5d, 0x27, 0x9b, 0xd2, 0x41, 0x5d, 0x5b, 0x27, 0x29, + /* (2^ 79)P */ 0x4f, 0xf1, 0xeb, 0x95, 0x08, 0x0f, 0xde, 0xcf, 0xa7, 0x05, 0x49, 0x05, 0x6b, 0xb9, 0xaa, 0xb9, 0xfd, 0x20, 0xc4, 0xa1, 0xd9, 0x0d, 0xe8, 0xca, 0xc7, 0xbb, 0x73, 0x16, 0x2f, 0xbf, 0x63, 0x0a, + /* (2^ 80)P */ 0x8c, 0xbc, 0x8f, 0x95, 0x11, 0x6e, 0x2f, 0x09, 0xad, 0x2f, 0x82, 0x04, 0xe8, 0x81, 0x2a, 0x67, 0x17, 0x25, 0xd5, 0x60, 0x15, 0x35, 0xc8, 0xca, 0xf8, 0x92, 0xf1, 0xc8, 0x22, 0x77, 0x3f, 0x6f, + /* (2^ 81)P */ 0xb7, 0x94, 0xe8, 0xc2, 0xcc, 0x90, 0xba, 0xf8, 0x0d, 0x9f, 0xff, 0x38, 0xa4, 0x57, 0x75, 0x2c, 0x59, 0x23, 0xe5, 0x5a, 0x85, 0x1d, 0x4d, 0x89, 0x69, 0x3d, 0x74, 0x7b, 0x15, 0x22, 0xe1, 0x68, + /* (2^ 82)P */ 0xf3, 0x19, 0xb9, 0xcf, 0x70, 0x55, 0x7e, 0xd8, 0xb9, 0x8d, 0x79, 0x95, 0xcd, 0xde, 0x2c, 0x3f, 0xce, 0xa2, 0xc0, 0x10, 0x47, 0x15, 0x21, 0x21, 0xb2, 0xc5, 0x6d, 0x24, 0x15, 0xa1, 0x66, 0x3c, + /* (2^ 83)P */ 0x72, 0xcb, 0x4e, 0x29, 0x62, 0xc5, 0xed, 0xcb, 0x16, 0x0b, 0x28, 0x6a, 0xc3, 0x43, 0x71, 0xba, 0x67, 0x8b, 0x07, 0xd4, 0xef, 0xc2, 0x10, 0x96, 0x1e, 0x4b, 0x6a, 0x94, 0x5d, 0x73, 0x44, 0x61, + /* (2^ 84)P */ 0x50, 0x33, 0x5b, 0xd7, 0x1e, 0x11, 0x6f, 0x53, 0x1b, 0xd8, 0x41, 0x20, 0x8c, 0xdb, 0x11, 0x02, 0x3c, 0x41, 0x10, 0x0e, 0x00, 0xb1, 0x3c, 0xf9, 0x76, 0x88, 0x9e, 0x03, 0x3c, 0xfd, 0x9d, 0x14, + /* (2^ 85)P */ 0x5b, 0x15, 0x63, 0x6b, 0xe4, 0xdd, 0x79, 0xd4, 0x76, 0x79, 0x83, 0x3c, 0xe9, 0x15, 0x6e, 0xb6, 0x38, 0xe0, 0x13, 0x1f, 0x3b, 0xe4, 0xfd, 0xda, 0x35, 0x0b, 0x4b, 0x2e, 0x1a, 0xda, 0xaf, 0x5f, + /* (2^ 86)P */ 0x81, 0x75, 0x19, 0x17, 0xdf, 0xbb, 0x00, 0x36, 0xc2, 0xd2, 0x3c, 0xbe, 0x0b, 0x05, 0x72, 0x39, 0x86, 0xbe, 0xd5, 0xbd, 0x6d, 0x90, 0x38, 0x59, 0x0f, 0x86, 0x9b, 0x3f, 0xe4, 0xe5, 0xfc, 0x34, + /* (2^ 87)P */ 0x02, 0x4d, 0xd1, 0x42, 0xcd, 0xa4, 0xa8, 0x75, 0x65, 0xdf, 0x41, 0x34, 0xc5, 0xab, 0x8d, 0x82, 0xd3, 0x31, 0xe1, 0xd2, 0xed, 0xab, 0xdc, 0x33, 0x5f, 0xd2, 0x14, 0xb8, 0x6f, 0xd7, 0xba, 0x3e, + /* (2^ 88)P */ 0x0f, 0xe1, 0x70, 0x6f, 0x56, 0x6f, 0x90, 0xd4, 0x5a, 0x0f, 0x69, 0x51, 0xaa, 0xf7, 0x12, 0x5d, 0xf2, 0xfc, 0xce, 0x76, 0x6e, 0xb1, 0xad, 0x45, 0x99, 0x29, 0x23, 0xad, 0xae, 0x68, 0xf7, 0x01, + /* (2^ 89)P */ 0xbd, 0xfe, 0x48, 0x62, 0x7b, 0xc7, 0x6c, 0x2b, 0xfd, 0xaf, 0x3a, 0xec, 0x28, 0x06, 0xd3, 0x3c, 0x6a, 0x48, 0xef, 0xd4, 0x80, 0x0b, 0x1c, 0xce, 0x23, 0x6c, 0xf6, 0xa6, 0x2e, 0xff, 0x3b, 0x4c, + /* (2^ 90)P */ 0x5f, 0xeb, 0xea, 0x4a, 0x09, 0xc4, 0x2e, 0x3f, 0xa7, 0x2c, 0x37, 0x6e, 0x28, 0x9b, 0xb1, 0x61, 0x1d, 0x70, 0x2a, 0xde, 0x66, 0xa9, 0xef, 0x5e, 0xef, 0xe3, 0x55, 0xde, 0x65, 0x05, 0xb2, 0x23, + /* (2^ 91)P */ 0x57, 0x85, 0xd5, 0x79, 0x52, 0xca, 0x01, 0xe3, 0x4f, 0x87, 0xc2, 0x27, 0xce, 0xd4, 0xb2, 0x07, 0x67, 0x1d, 0xcf, 0x9d, 0x8a, 0xcd, 0x32, 0xa5, 0x56, 0xff, 0x2b, 0x3f, 0xe2, 0xfe, 0x52, 0x2a, + /* (2^ 92)P */ 0x3d, 0x66, 0xd8, 0x7c, 0xb3, 0xef, 0x24, 0x86, 0x94, 0x75, 0xbd, 0xff, 0x20, 0xac, 0xc7, 0xbb, 0x45, 0x74, 0xd3, 0x82, 0x9c, 0x5e, 0xb8, 0x57, 0x66, 0xec, 0xa6, 0x86, 0xcb, 0x52, 0x30, 0x7b, + /* (2^ 93)P */ 0x1e, 0xe9, 0x25, 0x25, 0xad, 0xf0, 0x82, 0x34, 0xa0, 0xdc, 0x8e, 0xd2, 0x43, 0x80, 0xb6, 0x2c, 0x3a, 0x00, 0x1b, 0x2e, 0x05, 0x6d, 0x4f, 0xaf, 0x0a, 0x1b, 0x78, 0x29, 0x25, 0x8c, 0x5f, 0x18, + /* (2^ 94)P */ 0xd6, 0xe0, 0x0c, 0xd8, 0x5b, 0xde, 0x41, 0xaa, 0xd6, 0xe9, 0x53, 0x68, 0x41, 0xb2, 0x07, 0x94, 0x3a, 0x4c, 0x7f, 0x35, 0x6e, 0xc3, 0x3e, 0x56, 0xce, 0x7b, 0x29, 0x0e, 0xdd, 0xb8, 0xc4, 0x4c, + /* (2^ 95)P */ 0x0e, 0x73, 0xb8, 0xff, 0x52, 0x1a, 0xfc, 0xa2, 0x37, 0x8e, 0x05, 0x67, 0x6e, 0xf1, 0x11, 0x18, 0xe1, 0x4e, 0xdf, 0xcd, 0x66, 0xa3, 0xf9, 0x10, 0x99, 0xf0, 0xb9, 0xa0, 0xc4, 0xa0, 0xf4, 0x72, + /* (2^ 96)P */ 0xa7, 0x4e, 0x3f, 0x66, 0x6f, 0xc0, 0x16, 0x8c, 0xba, 0x0f, 0x97, 0x4e, 0xf7, 0x3a, 0x3b, 0x69, 0x45, 0xc3, 0x9e, 0xd6, 0xf1, 0xe7, 0x02, 0x21, 0x89, 0x80, 0x8a, 0x96, 0xbc, 0x3c, 0xa5, 0x0b, + /* (2^ 97)P */ 0x37, 0x55, 0xa1, 0xfe, 0xc7, 0x9d, 0x3d, 0xca, 0x93, 0x64, 0x53, 0x51, 0xbb, 0x24, 0x68, 0x4c, 0xb1, 0x06, 0x40, 0x84, 0x14, 0x63, 0x88, 0xb9, 0x60, 0xcc, 0x54, 0xb4, 0x2a, 0xa7, 0xd2, 0x40, + /* (2^ 98)P */ 0x75, 0x09, 0x57, 0x12, 0xb7, 0xa1, 0x36, 0x59, 0x57, 0xa6, 0xbd, 0xde, 0x48, 0xd6, 0xb9, 0x91, 0xea, 0x30, 0x43, 0xb6, 0x4b, 0x09, 0x44, 0x33, 0xd0, 0x51, 0xee, 0x12, 0x0d, 0xa1, 0x6b, 0x00, + /* (2^ 99)P */ 0x58, 0x5d, 0xde, 0xf5, 0x68, 0x84, 0x22, 0x19, 0xb0, 0x05, 0xcc, 0x38, 0x4c, 0x2f, 0xb1, 0x0e, 0x90, 0x19, 0x60, 0xd5, 0x9d, 0x9f, 0x03, 0xa1, 0x0b, 0x0e, 0xff, 0x4f, 0xce, 0xd4, 0x02, 0x45, + /* (2^100)P */ 0x89, 0xc1, 0x37, 0x68, 0x10, 0x54, 0x20, 0xeb, 0x3c, 0xb9, 0xd3, 0x6d, 0x4c, 0x54, 0xf6, 0xd0, 0x4f, 0xd7, 0x16, 0xc4, 0x64, 0x70, 0x72, 0x40, 0xf0, 0x2e, 0x50, 0x4b, 0x11, 0xc6, 0x15, 0x6e, + /* (2^101)P */ 0x6b, 0xa7, 0xb1, 0xcf, 0x98, 0xa3, 0xf2, 0x4d, 0xb1, 0xf6, 0xf2, 0x19, 0x74, 0x6c, 0x25, 0x11, 0x43, 0x60, 0x6e, 0x06, 0x62, 0x79, 0x49, 0x4a, 0x44, 0x5b, 0x35, 0x41, 0xab, 0x3a, 0x5b, 0x70, + /* (2^102)P */ 0xd8, 0xb1, 0x97, 0xd7, 0x36, 0xf5, 0x5e, 0x36, 0xdb, 0xf0, 0xdd, 0x22, 0xd6, 0x6b, 0x07, 0x00, 0x88, 0x5a, 0x57, 0xe0, 0xb0, 0x33, 0xbf, 0x3b, 0x4d, 0xca, 0xe4, 0xc8, 0x05, 0xaa, 0x77, 0x37, + /* (2^103)P */ 0x5f, 0xdb, 0x78, 0x55, 0xc8, 0x45, 0x27, 0x39, 0xe2, 0x5a, 0xae, 0xdb, 0x49, 0x41, 0xda, 0x6f, 0x67, 0x98, 0xdc, 0x8a, 0x0b, 0xb0, 0xf0, 0xb1, 0xa3, 0x1d, 0x6f, 0xd3, 0x37, 0x34, 0x96, 0x09, + /* (2^104)P */ 0x53, 0x38, 0xdc, 0xa5, 0x90, 0x4e, 0x82, 0x7e, 0xbd, 0x5c, 0x13, 0x1f, 0x64, 0xf6, 0xb5, 0xcc, 0xcc, 0x8f, 0xce, 0x87, 0x6c, 0xd8, 0x36, 0x67, 0x9f, 0x24, 0x04, 0x66, 0xe2, 0x3c, 0x5f, 0x62, + /* (2^105)P */ 0x3f, 0xf6, 0x02, 0x95, 0x05, 0xc8, 0x8a, 0xaf, 0x69, 0x14, 0x35, 0x2e, 0x0a, 0xe7, 0x05, 0x0c, 0x05, 0x63, 0x4b, 0x76, 0x9c, 0x2e, 0x29, 0x35, 0xc3, 0x3a, 0xe2, 0xc7, 0x60, 0x43, 0x39, 0x1a, + /* (2^106)P */ 0x64, 0x32, 0x18, 0x51, 0x32, 0xd5, 0xc6, 0xd5, 0x4f, 0xb7, 0xc2, 0x43, 0xbd, 0x5a, 0x06, 0x62, 0x9b, 0x3f, 0x97, 0x3b, 0xd0, 0xf5, 0xfb, 0xb5, 0x5e, 0x6e, 0x20, 0x61, 0x36, 0xda, 0xa3, 0x13, + /* (2^107)P */ 0xe5, 0x94, 0x5d, 0x72, 0x37, 0x58, 0xbd, 0xc6, 0xc5, 0x16, 0x50, 0x20, 0x12, 0x09, 0xe3, 0x18, 0x68, 0x3c, 0x03, 0x70, 0x15, 0xce, 0x88, 0x20, 0x87, 0x79, 0x83, 0x5c, 0x49, 0x1f, 0xba, 0x7f, + /* (2^108)P */ 0x9d, 0x07, 0xf9, 0xf2, 0x23, 0x74, 0x8c, 0x5a, 0xc5, 0x3f, 0x02, 0x34, 0x7b, 0x15, 0x35, 0x17, 0x51, 0xb3, 0xfa, 0xd2, 0x9a, 0xb4, 0xf9, 0xe4, 0x3c, 0xe3, 0x78, 0xc8, 0x72, 0xff, 0x91, 0x66, + /* (2^109)P */ 0x3e, 0xff, 0x5e, 0xdc, 0xde, 0x2a, 0x2c, 0x12, 0xf4, 0x6c, 0x95, 0xd8, 0xf1, 0x4b, 0xdd, 0xf8, 0xda, 0x5b, 0x9e, 0x9e, 0x5d, 0x20, 0x86, 0xeb, 0x43, 0xc7, 0x75, 0xd9, 0xb9, 0x92, 0x9b, 0x04, + /* (2^110)P */ 0x5a, 0xc0, 0xf6, 0xb0, 0x30, 0x97, 0x37, 0xa5, 0x53, 0xa5, 0xf3, 0xc6, 0xac, 0xff, 0xa0, 0x72, 0x6d, 0xcd, 0x0d, 0xb2, 0x34, 0x2c, 0x03, 0xb0, 0x4a, 0x16, 0xd5, 0x88, 0xbc, 0x9d, 0x0e, 0x47, + /* (2^111)P */ 0x47, 0xc0, 0x37, 0xa2, 0x0c, 0xf1, 0x9c, 0xb1, 0xa2, 0x81, 0x6c, 0x1f, 0x71, 0x66, 0x54, 0xb6, 0x43, 0x0b, 0xd8, 0x6d, 0xd1, 0x1b, 0x32, 0xb3, 0x8e, 0xbe, 0x5f, 0x0c, 0x60, 0x4f, 0xc1, 0x48, + /* (2^112)P */ 0x03, 0xc8, 0xa6, 0x4a, 0x26, 0x1c, 0x45, 0x66, 0xa6, 0x7d, 0xfa, 0xa4, 0x04, 0x39, 0x6e, 0xb6, 0x95, 0x83, 0x12, 0xb3, 0xb0, 0x19, 0x5f, 0xd4, 0x10, 0xbc, 0xc9, 0xc3, 0x27, 0x26, 0x60, 0x31, + /* (2^113)P */ 0x0d, 0xe1, 0xe4, 0x32, 0x48, 0xdc, 0x20, 0x31, 0xf7, 0x17, 0xc7, 0x56, 0x67, 0xc4, 0x20, 0xeb, 0x94, 0x02, 0x28, 0x67, 0x3f, 0x2e, 0xf5, 0x00, 0x09, 0xc5, 0x30, 0x47, 0xc1, 0x4f, 0x6d, 0x56, + /* (2^114)P */ 0x06, 0x72, 0x83, 0xfd, 0x40, 0x5d, 0x3a, 0x7e, 0x7a, 0x54, 0x59, 0x71, 0xdc, 0x26, 0xe9, 0xc1, 0x95, 0x60, 0x8d, 0xa6, 0xfb, 0x30, 0x67, 0x21, 0xa7, 0xce, 0x69, 0x3f, 0x84, 0xc3, 0xe8, 0x22, + /* (2^115)P */ 0x2b, 0x4b, 0x0e, 0x93, 0xe8, 0x74, 0xd0, 0x33, 0x16, 0x58, 0xd1, 0x84, 0x0e, 0x35, 0xe4, 0xb6, 0x65, 0x23, 0xba, 0xd6, 0x6a, 0xc2, 0x34, 0x55, 0xf3, 0xf3, 0xf1, 0x89, 0x2f, 0xc1, 0x73, 0x77, + /* (2^116)P */ 0xaa, 0x62, 0x79, 0xa5, 0x4d, 0x40, 0xba, 0x8c, 0x56, 0xce, 0x99, 0x19, 0xa8, 0x97, 0x98, 0x5b, 0xfc, 0x92, 0x16, 0x12, 0x2f, 0x86, 0x8e, 0x50, 0x91, 0xc2, 0x93, 0xa0, 0x7f, 0x90, 0x81, 0x3a, + /* (2^117)P */ 0x10, 0xa5, 0x25, 0x47, 0xff, 0xd0, 0xde, 0x0d, 0x03, 0xc5, 0x3f, 0x67, 0x10, 0xcc, 0xd8, 0x10, 0x89, 0x4e, 0x1f, 0x9f, 0x1c, 0x15, 0x9d, 0x5b, 0x4c, 0xa4, 0x09, 0xcb, 0xd5, 0xc1, 0xa5, 0x32, + /* (2^118)P */ 0xfb, 0x41, 0x05, 0xb9, 0x42, 0xa4, 0x0a, 0x1e, 0xdb, 0x85, 0xb4, 0xc1, 0x7c, 0xeb, 0x85, 0x5f, 0xe5, 0xf2, 0x9d, 0x8a, 0xce, 0x95, 0xe5, 0xbe, 0x36, 0x22, 0x42, 0x22, 0xc7, 0x96, 0xe4, 0x25, + /* (2^119)P */ 0xb9, 0xe5, 0x0f, 0xcd, 0x46, 0x3c, 0xdf, 0x5e, 0x88, 0x33, 0xa4, 0xd2, 0x7e, 0x5a, 0xe7, 0x34, 0x52, 0xe3, 0x61, 0xd7, 0x11, 0xde, 0x88, 0xe4, 0x5c, 0x54, 0x85, 0xa0, 0x01, 0x8a, 0x87, 0x0e, + /* (2^120)P */ 0x04, 0xbb, 0x21, 0xe0, 0x77, 0x3c, 0x49, 0xba, 0x9a, 0x89, 0xdf, 0xc7, 0x43, 0x18, 0x4d, 0x2b, 0x67, 0x0d, 0xe8, 0x7a, 0x48, 0x7a, 0xa3, 0x9e, 0x94, 0x17, 0xe4, 0x11, 0x80, 0x95, 0xa9, 0x67, + /* (2^121)P */ 0x65, 0xb0, 0x97, 0x66, 0x1a, 0x05, 0x58, 0x4b, 0xd4, 0xa6, 0x6b, 0x8d, 0x7d, 0x3f, 0xe3, 0x47, 0xc1, 0x46, 0xca, 0x83, 0xd4, 0xa8, 0x4d, 0xbb, 0x0d, 0xdb, 0xc2, 0x81, 0xa1, 0xca, 0xbe, 0x68, + /* (2^122)P */ 0xa5, 0x9a, 0x98, 0x0b, 0xe9, 0x80, 0x89, 0x8d, 0x9b, 0xc9, 0x93, 0x2c, 0x4a, 0xb1, 0x5e, 0xf9, 0xa2, 0x73, 0x6e, 0x79, 0xc4, 0xc7, 0xc6, 0x51, 0x69, 0xb5, 0xef, 0xb5, 0x63, 0x83, 0x22, 0x6e, + /* (2^123)P */ 0xc8, 0x24, 0xd6, 0x2d, 0xb0, 0xc0, 0xbb, 0xc6, 0xee, 0x70, 0x81, 0xec, 0x7d, 0xb4, 0x7e, 0x77, 0xa9, 0xaf, 0xcf, 0x04, 0xa0, 0x15, 0xde, 0x3c, 0x9b, 0xbf, 0x60, 0x71, 0x08, 0xbc, 0xc6, 0x1d, + /* (2^124)P */ 0x02, 0x40, 0xc3, 0xee, 0x43, 0xe0, 0x07, 0x2e, 0x7f, 0xdc, 0x68, 0x7a, 0x67, 0xfc, 0xe9, 0x18, 0x9a, 0x5b, 0xd1, 0x8b, 0x18, 0x03, 0xda, 0xd8, 0x53, 0x82, 0x56, 0x00, 0xbb, 0xc3, 0xfb, 0x48, + /* (2^125)P */ 0xe1, 0x4c, 0x65, 0xfb, 0x4c, 0x7d, 0x54, 0x57, 0xad, 0xe2, 0x58, 0xa0, 0x82, 0x5b, 0x56, 0xd3, 0x78, 0x44, 0x15, 0xbf, 0x0b, 0xaf, 0x3e, 0xf6, 0x18, 0xbb, 0xdf, 0x14, 0xf1, 0x1e, 0x53, 0x47, + /* (2^126)P */ 0x87, 0xc5, 0x78, 0x42, 0x0a, 0x63, 0xec, 0xe1, 0xf3, 0x83, 0x8e, 0xca, 0x46, 0xd5, 0x07, 0x55, 0x2b, 0x0c, 0xdc, 0x3a, 0xc6, 0x35, 0xe1, 0x85, 0x4e, 0x84, 0x82, 0x56, 0xa8, 0xef, 0xa7, 0x0a, + /* (2^127)P */ 0x15, 0xf6, 0xe1, 0xb3, 0xa8, 0x1b, 0x69, 0x72, 0xfa, 0x3f, 0xbe, 0x1f, 0x70, 0xe9, 0xb4, 0x32, 0x68, 0x78, 0xbb, 0x39, 0x2e, 0xd9, 0xb6, 0x97, 0xe8, 0x39, 0x2e, 0xa0, 0xde, 0x53, 0xfe, 0x2c, + /* (2^128)P */ 0xb0, 0x52, 0xcd, 0x85, 0xcd, 0x92, 0x73, 0x68, 0x31, 0x98, 0xe2, 0x10, 0xc9, 0x66, 0xff, 0x27, 0x06, 0x2d, 0x83, 0xa9, 0x56, 0x45, 0x13, 0x97, 0xa0, 0xf8, 0x84, 0x0a, 0x36, 0xb0, 0x9b, 0x26, + /* (2^129)P */ 0x5c, 0xf8, 0x43, 0x76, 0x45, 0x55, 0x6e, 0x70, 0x1b, 0x7d, 0x59, 0x9b, 0x8c, 0xa4, 0x34, 0x37, 0x72, 0xa4, 0xef, 0xc6, 0xe8, 0x91, 0xee, 0x7a, 0xe0, 0xd9, 0xa9, 0x98, 0xc1, 0xab, 0xd6, 0x5c, + /* (2^130)P */ 0x1a, 0xe4, 0x3c, 0xcb, 0x06, 0xde, 0x04, 0x0e, 0x38, 0xe1, 0x02, 0x34, 0x89, 0xeb, 0xc6, 0xd8, 0x72, 0x37, 0x6e, 0x68, 0xbb, 0x59, 0x46, 0x90, 0xc8, 0xa8, 0x6b, 0x74, 0x71, 0xc3, 0x15, 0x72, + /* (2^131)P */ 0xd9, 0xa2, 0xe4, 0xea, 0x7e, 0xa9, 0x12, 0xfd, 0xc5, 0xf2, 0x94, 0x63, 0x51, 0xb7, 0x14, 0x95, 0x94, 0xf2, 0x08, 0x92, 0x80, 0xd5, 0x6f, 0x26, 0xb9, 0x26, 0x9a, 0x61, 0x85, 0x70, 0x84, 0x5c, + /* (2^132)P */ 0xea, 0x94, 0xd6, 0xfe, 0x10, 0x54, 0x98, 0x52, 0x54, 0xd2, 0x2e, 0x4a, 0x93, 0x5b, 0x90, 0x3c, 0x67, 0xe4, 0x3b, 0x2d, 0x69, 0x47, 0xbb, 0x10, 0xe1, 0xe9, 0xe5, 0x69, 0x2d, 0x3d, 0x3b, 0x06, + /* (2^133)P */ 0xeb, 0x7d, 0xa5, 0xdd, 0xee, 0x26, 0x27, 0x47, 0x91, 0x18, 0xf4, 0x10, 0xae, 0xc4, 0xb6, 0xef, 0x14, 0x76, 0x30, 0x7b, 0x91, 0x41, 0x16, 0x2b, 0x7c, 0x5b, 0xf4, 0xc4, 0x4f, 0x55, 0x7c, 0x11, + /* (2^134)P */ 0x12, 0x88, 0x9d, 0x8f, 0x11, 0xf3, 0x7c, 0xc0, 0x39, 0x79, 0x01, 0x50, 0x20, 0xd8, 0xdb, 0x01, 0x27, 0x28, 0x1b, 0x17, 0xf4, 0x03, 0xe8, 0xd7, 0xea, 0x25, 0xd2, 0x87, 0x74, 0xe8, 0x15, 0x10, + /* (2^135)P */ 0x4d, 0xcc, 0x3a, 0xd2, 0xfe, 0xe3, 0x8d, 0xc5, 0x2d, 0xbe, 0xa7, 0x94, 0xc2, 0x91, 0xdb, 0x50, 0x57, 0xf4, 0x9c, 0x1c, 0x3d, 0xd4, 0x94, 0x0b, 0x4a, 0x52, 0x37, 0x6e, 0xfa, 0x40, 0x16, 0x6b, + /* (2^136)P */ 0x09, 0x0d, 0xda, 0x5f, 0x6c, 0x34, 0x2f, 0x69, 0x51, 0x31, 0x4d, 0xfa, 0x59, 0x1c, 0x0b, 0x20, 0x96, 0xa2, 0x77, 0x07, 0x76, 0x6f, 0xc4, 0xb8, 0xcf, 0xfb, 0xfd, 0x3f, 0x5f, 0x39, 0x38, 0x4b, + /* (2^137)P */ 0x71, 0xd6, 0x54, 0xbe, 0x00, 0x5e, 0xd2, 0x18, 0xa6, 0xab, 0xc8, 0xbe, 0x82, 0x05, 0xd5, 0x60, 0x82, 0xb9, 0x78, 0x3b, 0x26, 0x8f, 0xad, 0x87, 0x32, 0x04, 0xda, 0x9c, 0x4e, 0xf6, 0xfd, 0x50, + /* (2^138)P */ 0xf0, 0xdc, 0x78, 0xc5, 0xaa, 0x67, 0xf5, 0x90, 0x3b, 0x13, 0xa3, 0xf2, 0x0e, 0x9b, 0x1e, 0xef, 0x71, 0xde, 0xd9, 0x42, 0x92, 0xba, 0xeb, 0x0e, 0xc7, 0x01, 0x31, 0xf0, 0x9b, 0x3c, 0x47, 0x15, + /* (2^139)P */ 0x95, 0x80, 0xb7, 0x56, 0xae, 0xe8, 0x77, 0x7c, 0x8e, 0x07, 0x6f, 0x6e, 0x66, 0xe7, 0x78, 0xb6, 0x1f, 0xba, 0x48, 0x53, 0x61, 0xb9, 0xa0, 0x2d, 0x0b, 0x3f, 0x73, 0xff, 0xc1, 0x31, 0xf9, 0x7c, + /* (2^140)P */ 0x6c, 0x36, 0x0a, 0x0a, 0xf5, 0x57, 0xb3, 0x26, 0x32, 0xd7, 0x87, 0x2b, 0xf4, 0x8c, 0x70, 0xe9, 0xc0, 0xb2, 0x1c, 0xf9, 0xa5, 0xee, 0x3a, 0xc1, 0x4c, 0xbb, 0x43, 0x11, 0x99, 0x0c, 0xd9, 0x35, + /* (2^141)P */ 0xdc, 0xd9, 0xa0, 0xa9, 0x04, 0xc4, 0xc1, 0x47, 0x51, 0xd2, 0x72, 0x19, 0x45, 0x58, 0x9e, 0x65, 0x31, 0x8c, 0xb3, 0x73, 0xc4, 0xa8, 0x75, 0x38, 0x24, 0x1f, 0x56, 0x79, 0xd3, 0x9e, 0xbd, 0x1f, + /* (2^142)P */ 0x8d, 0xc2, 0x1e, 0xd4, 0x6f, 0xbc, 0xfa, 0x11, 0xca, 0x2d, 0x2a, 0xcd, 0xe3, 0xdf, 0xf8, 0x7e, 0x95, 0x45, 0x40, 0x8c, 0x5d, 0x3b, 0xe7, 0x72, 0x27, 0x2f, 0xb7, 0x54, 0x49, 0xfa, 0x35, 0x61, + /* (2^143)P */ 0x9c, 0xb6, 0x24, 0xde, 0xa2, 0x32, 0xfc, 0xcc, 0x88, 0x5d, 0x09, 0x1f, 0x8c, 0x69, 0x55, 0x3f, 0x29, 0xf9, 0xc3, 0x5a, 0xed, 0x50, 0x33, 0xbe, 0xeb, 0x7e, 0x47, 0xca, 0x06, 0xf8, 0x9b, 0x5e, + /* (2^144)P */ 0x68, 0x9f, 0x30, 0x3c, 0xb6, 0x8f, 0xce, 0xe9, 0xf4, 0xf9, 0xe1, 0x65, 0x35, 0xf6, 0x76, 0x53, 0xf1, 0x93, 0x63, 0x5a, 0xb3, 0xcf, 0xaf, 0xd1, 0x06, 0x35, 0x62, 0xe5, 0xed, 0xa1, 0x32, 0x66, + /* (2^145)P */ 0x4c, 0xed, 0x2d, 0x0c, 0x39, 0x6c, 0x7d, 0x0b, 0x1f, 0xcb, 0x04, 0xdf, 0x81, 0x32, 0xcb, 0x56, 0xc7, 0xc3, 0xec, 0x49, 0x12, 0x5a, 0x30, 0x66, 0x2a, 0xa7, 0x8c, 0xa3, 0x60, 0x8b, 0x58, 0x5d, + /* (2^146)P */ 0x2d, 0xf4, 0xe5, 0xe8, 0x78, 0xbf, 0xec, 0xa6, 0xec, 0x3e, 0x8a, 0x3c, 0x4b, 0xb4, 0xee, 0x86, 0x04, 0x16, 0xd2, 0xfb, 0x48, 0x9c, 0x21, 0xec, 0x31, 0x67, 0xc3, 0x17, 0xf5, 0x1a, 0xaf, 0x1a, + /* (2^147)P */ 0xe7, 0xbd, 0x69, 0x67, 0x83, 0xa2, 0x06, 0xc3, 0xdb, 0x2a, 0x1e, 0x2b, 0x62, 0x80, 0x82, 0x20, 0xa6, 0x94, 0xff, 0xfb, 0x1f, 0xf5, 0x27, 0x80, 0x6b, 0xf2, 0x24, 0x11, 0xce, 0xa1, 0xcf, 0x76, + /* (2^148)P */ 0xb6, 0xab, 0x22, 0x24, 0x56, 0x00, 0xeb, 0x18, 0xc3, 0x29, 0x8c, 0x8f, 0xd5, 0xc4, 0x77, 0xf3, 0x1a, 0x56, 0x31, 0xf5, 0x07, 0xc2, 0xbb, 0x4d, 0x27, 0x8a, 0x12, 0x82, 0xf0, 0xb7, 0x53, 0x02, + /* (2^149)P */ 0xe0, 0x17, 0x2c, 0xb6, 0x1c, 0x09, 0x1f, 0x3d, 0xa9, 0x28, 0x46, 0xd6, 0xab, 0xe1, 0x60, 0x48, 0x53, 0x42, 0x9d, 0x30, 0x36, 0x74, 0xd1, 0x52, 0x76, 0xe5, 0xfa, 0x3e, 0xe1, 0x97, 0x6f, 0x35, + /* (2^150)P */ 0x5b, 0x53, 0x50, 0xa1, 0x1a, 0xe1, 0x51, 0xd3, 0xcc, 0x78, 0xd8, 0x1d, 0xbb, 0x45, 0x6b, 0x3e, 0x98, 0x2c, 0xd9, 0xbe, 0x28, 0x61, 0x77, 0x0c, 0xb8, 0x85, 0x28, 0x03, 0x93, 0xae, 0x34, 0x1d, + /* (2^151)P */ 0xc3, 0xa4, 0x5b, 0xa8, 0x8c, 0x48, 0xa0, 0x4b, 0xce, 0xe6, 0x9c, 0x3c, 0xc3, 0x48, 0x53, 0x98, 0x70, 0xa7, 0xbd, 0x97, 0x6f, 0x4c, 0x12, 0x66, 0x4a, 0x12, 0x54, 0x06, 0x29, 0xa0, 0x81, 0x0f, + /* (2^152)P */ 0xfd, 0x86, 0x9b, 0x56, 0xa6, 0x9c, 0xd0, 0x9e, 0x2d, 0x9a, 0xaf, 0x18, 0xfd, 0x09, 0x10, 0x81, 0x0a, 0xc2, 0xd8, 0x93, 0x3f, 0xd0, 0x08, 0xff, 0x6b, 0xf2, 0xae, 0x9f, 0x19, 0x48, 0xa1, 0x52, + /* (2^153)P */ 0x73, 0x1b, 0x8d, 0x2d, 0xdc, 0xf9, 0x03, 0x3e, 0x70, 0x1a, 0x96, 0x73, 0x18, 0x80, 0x05, 0x42, 0x70, 0x59, 0xa3, 0x41, 0xf0, 0x87, 0xd9, 0xc0, 0x49, 0xd5, 0xc0, 0xa1, 0x15, 0x1f, 0xaa, 0x07, + /* (2^154)P */ 0x24, 0x72, 0xd2, 0x8c, 0xe0, 0x6c, 0xd4, 0xdf, 0x39, 0x42, 0x4e, 0x93, 0x4f, 0x02, 0x0a, 0x6d, 0x59, 0x7b, 0x89, 0x99, 0x63, 0x7a, 0x8a, 0x80, 0xa2, 0x95, 0x3d, 0xe1, 0xe9, 0x56, 0x45, 0x0a, + /* (2^155)P */ 0x45, 0x30, 0xc1, 0xe9, 0x1f, 0x99, 0x1a, 0xd2, 0xb8, 0x51, 0x77, 0xfe, 0x48, 0x85, 0x0e, 0x9b, 0x35, 0x00, 0xf3, 0x4b, 0xcb, 0x43, 0xa6, 0x5d, 0x21, 0xf7, 0x40, 0x39, 0xd6, 0x28, 0xdb, 0x77, + /* (2^156)P */ 0x11, 0x90, 0xdc, 0x4a, 0x61, 0xeb, 0x5e, 0xfc, 0xeb, 0x11, 0xc4, 0xe8, 0x9a, 0x41, 0x29, 0x52, 0x74, 0xcf, 0x1d, 0x7d, 0x78, 0xe7, 0xc3, 0x9e, 0xb5, 0x4c, 0x6e, 0x21, 0x3e, 0x05, 0x0d, 0x34, + /* (2^157)P */ 0xb4, 0xf2, 0x8d, 0xb4, 0x39, 0xaf, 0xc7, 0xca, 0x94, 0x0a, 0xa1, 0x71, 0x28, 0xec, 0xfa, 0xc0, 0xed, 0x75, 0xa5, 0x5c, 0x24, 0x69, 0x0a, 0x14, 0x4c, 0x3a, 0x27, 0x34, 0x71, 0xc3, 0xf1, 0x0c, + /* (2^158)P */ 0xa5, 0xb8, 0x24, 0xc2, 0x6a, 0x30, 0xee, 0xc8, 0xb0, 0x30, 0x49, 0xcb, 0x7c, 0xee, 0xea, 0x57, 0x4f, 0xe7, 0xcb, 0xaa, 0xbd, 0x06, 0xe8, 0xa1, 0x7d, 0x65, 0xeb, 0x2e, 0x74, 0x62, 0x9a, 0x7d, + /* (2^159)P */ 0x30, 0x48, 0x6c, 0x54, 0xef, 0xb6, 0xb6, 0x9e, 0x2e, 0x6e, 0xb3, 0xdd, 0x1f, 0xca, 0x5c, 0x88, 0x05, 0x71, 0x0d, 0xef, 0x83, 0xf3, 0xb9, 0xe6, 0x12, 0x04, 0x2e, 0x9d, 0xef, 0x4f, 0x65, 0x58, + /* (2^160)P */ 0x26, 0x8e, 0x0e, 0xbe, 0xff, 0xc4, 0x05, 0xa9, 0x6e, 0x81, 0x31, 0x9b, 0xdf, 0xe5, 0x2d, 0x94, 0xe1, 0x88, 0x2e, 0x80, 0x3f, 0x72, 0x7d, 0x49, 0x8d, 0x40, 0x2f, 0x60, 0xea, 0x4d, 0x68, 0x30, + /* (2^161)P */ 0x34, 0xcb, 0xe6, 0xa3, 0x78, 0xa2, 0xe5, 0x21, 0xc4, 0x1d, 0x15, 0x5b, 0x6f, 0x6e, 0xfb, 0xae, 0x15, 0xca, 0x77, 0x9d, 0x04, 0x8e, 0x0b, 0xb3, 0x81, 0x89, 0xb9, 0x53, 0xcf, 0xc9, 0xc3, 0x28, + /* (2^162)P */ 0x2a, 0xdd, 0x6c, 0x55, 0x21, 0xb7, 0x7f, 0x28, 0x74, 0x22, 0x02, 0x97, 0xa8, 0x7c, 0x31, 0x0d, 0x58, 0x32, 0x54, 0x3a, 0x42, 0xc7, 0x68, 0x74, 0x2f, 0x64, 0xb5, 0x4e, 0x46, 0x11, 0x7f, 0x4a, + /* (2^163)P */ 0xa6, 0x3a, 0x19, 0x4d, 0x77, 0xa4, 0x37, 0xa2, 0xa1, 0x29, 0x21, 0xa9, 0x6e, 0x98, 0x65, 0xd8, 0x88, 0x1a, 0x7c, 0xf8, 0xec, 0x15, 0xc5, 0x24, 0xeb, 0xf5, 0x39, 0x5f, 0x57, 0x03, 0x40, 0x60, + /* (2^164)P */ 0x27, 0x9b, 0x0a, 0x57, 0x89, 0xf1, 0xb9, 0x47, 0x78, 0x4b, 0x5e, 0x46, 0xde, 0xce, 0x98, 0x2b, 0x20, 0x5c, 0xb8, 0xdb, 0x51, 0xf5, 0x6d, 0x02, 0x01, 0x19, 0xe2, 0x47, 0x10, 0xd9, 0xfc, 0x74, + /* (2^165)P */ 0xa3, 0xbf, 0xc1, 0x23, 0x0a, 0xa9, 0xe2, 0x13, 0xf6, 0x19, 0x85, 0x47, 0x4e, 0x07, 0xb0, 0x0c, 0x44, 0xcf, 0xf6, 0x3a, 0xbe, 0xcb, 0xf1, 0x5f, 0xbe, 0x2d, 0x81, 0xbe, 0x38, 0x54, 0xfe, 0x67, + /* (2^166)P */ 0xb0, 0x05, 0x0f, 0xa4, 0x4f, 0xf6, 0x3c, 0xd1, 0x87, 0x37, 0x28, 0x32, 0x2f, 0xfb, 0x4d, 0x05, 0xea, 0x2a, 0x0d, 0x7f, 0x5b, 0x91, 0x73, 0x41, 0x4e, 0x0d, 0x61, 0x1f, 0x4f, 0x14, 0x2f, 0x48, + /* (2^167)P */ 0x34, 0x82, 0x7f, 0xb4, 0x01, 0x02, 0x21, 0xf6, 0x90, 0xb9, 0x70, 0x9e, 0x92, 0xe1, 0x0a, 0x5d, 0x7c, 0x56, 0x49, 0xb0, 0x55, 0xf4, 0xd7, 0xdc, 0x01, 0x6f, 0x91, 0xf0, 0xf1, 0xd0, 0x93, 0x7e, + /* (2^168)P */ 0xfa, 0xb4, 0x7d, 0x8a, 0xf1, 0xcb, 0x79, 0xdd, 0x2f, 0xc6, 0x74, 0x6f, 0xbf, 0x91, 0x83, 0xbe, 0xbd, 0x91, 0x82, 0x4b, 0xd1, 0x45, 0x71, 0x02, 0x05, 0x17, 0xbf, 0x2c, 0xea, 0x73, 0x5a, 0x58, + /* (2^169)P */ 0xb2, 0x0d, 0x8a, 0x92, 0x3e, 0xa0, 0x5c, 0x48, 0xe7, 0x57, 0x28, 0x74, 0xa5, 0x01, 0xfc, 0x10, 0xa7, 0x51, 0xd5, 0xd6, 0xdb, 0x2e, 0x48, 0x2f, 0x8a, 0xdb, 0x8f, 0x04, 0xb5, 0x33, 0x04, 0x0f, + /* (2^170)P */ 0x47, 0x62, 0xdc, 0xd7, 0x8d, 0x2e, 0xda, 0x60, 0x9a, 0x81, 0xd4, 0x8c, 0xd3, 0xc9, 0xb4, 0x88, 0x97, 0x66, 0xf6, 0x01, 0xc0, 0x3a, 0x03, 0x13, 0x75, 0x7d, 0x36, 0x3b, 0xfe, 0x24, 0x3b, 0x27, + /* (2^171)P */ 0xd4, 0xb9, 0xb3, 0x31, 0x6a, 0xf6, 0xe8, 0xc6, 0xd5, 0x49, 0xdf, 0x94, 0xa4, 0x14, 0x15, 0x28, 0xa7, 0x3d, 0xb2, 0xc8, 0xdf, 0x6f, 0x72, 0xd1, 0x48, 0xe5, 0xde, 0x03, 0xd1, 0xe7, 0x3a, 0x4b, + /* (2^172)P */ 0x7e, 0x9d, 0x4b, 0xce, 0x19, 0x6e, 0x25, 0xc6, 0x1c, 0xc6, 0xe3, 0x86, 0xf1, 0x5c, 0x5c, 0xff, 0x45, 0xc1, 0x8e, 0x4b, 0xa3, 0x3c, 0xc6, 0xac, 0x74, 0x65, 0xe6, 0xfe, 0x88, 0x18, 0x62, 0x74, + /* (2^173)P */ 0x1e, 0x0a, 0x29, 0x45, 0x96, 0x40, 0x6f, 0x95, 0x2e, 0x96, 0x3a, 0x26, 0xe3, 0xf8, 0x0b, 0xef, 0x7b, 0x64, 0xc2, 0x5e, 0xeb, 0x50, 0x6a, 0xed, 0x02, 0x75, 0xca, 0x9d, 0x3a, 0x28, 0x94, 0x06, + /* (2^174)P */ 0xd1, 0xdc, 0xa2, 0x43, 0x36, 0x96, 0x9b, 0x76, 0x53, 0x53, 0xfc, 0x09, 0xea, 0xc8, 0xb7, 0x42, 0xab, 0x7e, 0x39, 0x13, 0xee, 0x2a, 0x00, 0x4f, 0x3a, 0xd6, 0xb7, 0x19, 0x2c, 0x5e, 0x00, 0x63, + /* (2^175)P */ 0xea, 0x3b, 0x02, 0x63, 0xda, 0x36, 0x67, 0xca, 0xb7, 0x99, 0x2a, 0xb1, 0x6d, 0x7f, 0x6c, 0x96, 0xe1, 0xc5, 0x37, 0xc5, 0x90, 0x93, 0xe0, 0xac, 0xee, 0x89, 0xaa, 0xa1, 0x63, 0x60, 0x69, 0x0b, + /* (2^176)P */ 0xe5, 0x56, 0x8c, 0x28, 0x97, 0x3e, 0xb0, 0xeb, 0xe8, 0x8b, 0x8c, 0x93, 0x9f, 0x9f, 0x2a, 0x43, 0x71, 0x7f, 0x71, 0x5b, 0x3d, 0xa9, 0xa5, 0xa6, 0x97, 0x9d, 0x8f, 0xe1, 0xc3, 0xb4, 0x5f, 0x1a, + /* (2^177)P */ 0xce, 0xcd, 0x60, 0x1c, 0xad, 0xe7, 0x94, 0x1c, 0xa0, 0xc4, 0x02, 0xfc, 0x43, 0x2a, 0x20, 0xee, 0x20, 0x6a, 0xc4, 0x67, 0xd8, 0xe4, 0xaf, 0x8d, 0x58, 0x7b, 0xc2, 0x8a, 0x3c, 0x26, 0x10, 0x0a, + /* (2^178)P */ 0x4a, 0x2a, 0x43, 0xe4, 0xdf, 0xa9, 0xde, 0xd0, 0xc5, 0x77, 0x92, 0xbe, 0x7b, 0xf8, 0x6a, 0x85, 0x1a, 0xc7, 0x12, 0xc2, 0xac, 0x72, 0x84, 0xce, 0x91, 0x1e, 0xbb, 0x9b, 0x6d, 0x1b, 0x15, 0x6f, + /* (2^179)P */ 0x6a, 0xd5, 0xee, 0x7c, 0x52, 0x6c, 0x77, 0x26, 0xec, 0xfa, 0xf8, 0xfb, 0xb7, 0x1c, 0x21, 0x7d, 0xcc, 0x09, 0x46, 0xfd, 0xa6, 0x66, 0xae, 0x37, 0x42, 0x0c, 0x77, 0xd2, 0x02, 0xb7, 0x81, 0x1f, + /* (2^180)P */ 0x92, 0x83, 0xc5, 0xea, 0x57, 0xb0, 0xb0, 0x2f, 0x9d, 0x4e, 0x74, 0x29, 0xfe, 0x89, 0xdd, 0xe1, 0xf8, 0xb4, 0xbe, 0x17, 0xeb, 0xf8, 0x64, 0xc9, 0x1e, 0xd4, 0xa2, 0xc9, 0x73, 0x10, 0x57, 0x29, + /* (2^181)P */ 0x54, 0xe2, 0xc0, 0x81, 0x89, 0xa1, 0x48, 0xa9, 0x30, 0x28, 0xb2, 0x65, 0x9b, 0x36, 0xf6, 0x2d, 0xc6, 0xd3, 0xcf, 0x5f, 0xd7, 0xb2, 0x3e, 0xa3, 0x1f, 0xa0, 0x99, 0x41, 0xec, 0xd6, 0x8c, 0x07, + /* (2^182)P */ 0x2f, 0x0d, 0x90, 0xad, 0x41, 0x4a, 0x58, 0x4a, 0x52, 0x4c, 0xc7, 0xe2, 0x78, 0x2b, 0x14, 0x32, 0x78, 0xc9, 0x31, 0x84, 0x33, 0xe8, 0xc4, 0x68, 0xc2, 0x9f, 0x68, 0x08, 0x90, 0xea, 0x69, 0x7f, + /* (2^183)P */ 0x65, 0x82, 0xa3, 0x46, 0x1e, 0xc8, 0xf2, 0x52, 0xfd, 0x32, 0xa8, 0x04, 0x2d, 0x07, 0x78, 0xfd, 0x94, 0x9e, 0x35, 0x25, 0xfa, 0xd5, 0xd7, 0x8c, 0xd2, 0x29, 0xcc, 0x54, 0x74, 0x1b, 0xe7, 0x4d, + /* (2^184)P */ 0xc9, 0x6a, 0xda, 0x1e, 0xad, 0x60, 0xeb, 0x42, 0x3a, 0x9c, 0xc0, 0xdb, 0xdf, 0x37, 0xad, 0x0a, 0x91, 0xc1, 0x3c, 0xe3, 0x71, 0x4b, 0x00, 0x81, 0x3c, 0x80, 0x22, 0x51, 0x34, 0xbe, 0xe6, 0x44, + /* (2^185)P */ 0xdb, 0x20, 0x19, 0xba, 0x88, 0x83, 0xfe, 0x03, 0x08, 0xb0, 0x0d, 0x15, 0x32, 0x7c, 0xd5, 0xf5, 0x29, 0x0c, 0xf6, 0x1a, 0x28, 0xc4, 0xc8, 0x49, 0xee, 0x1a, 0x70, 0xde, 0x18, 0xb5, 0xed, 0x21, + /* (2^186)P */ 0x99, 0xdc, 0x06, 0x8f, 0x41, 0x3e, 0xb6, 0x7f, 0xb8, 0xd7, 0x66, 0xc1, 0x99, 0x0d, 0x46, 0xa4, 0x83, 0x0a, 0x52, 0xce, 0x48, 0x52, 0xdd, 0x24, 0x58, 0x83, 0x92, 0x2b, 0x71, 0xad, 0xc3, 0x5e, + /* (2^187)P */ 0x0f, 0x93, 0x17, 0xbd, 0x5f, 0x2a, 0x02, 0x15, 0xe3, 0x70, 0x25, 0xd8, 0x77, 0x4a, 0xf6, 0xa4, 0x12, 0x37, 0x78, 0x15, 0x69, 0x8d, 0xbc, 0x12, 0xbb, 0x0a, 0x62, 0xfc, 0xc0, 0x94, 0x81, 0x49, + /* (2^188)P */ 0x82, 0x6c, 0x68, 0x55, 0xd2, 0xd9, 0xa2, 0x38, 0xf0, 0x21, 0x3e, 0x19, 0xd9, 0x6b, 0x5c, 0x78, 0x84, 0x54, 0x4a, 0xb2, 0x1a, 0xc8, 0xd5, 0xe4, 0x89, 0x09, 0xe2, 0xb2, 0x60, 0x78, 0x30, 0x56, + /* (2^189)P */ 0xc4, 0x74, 0x4d, 0x8b, 0xf7, 0x55, 0x9d, 0x42, 0x31, 0x01, 0x35, 0x43, 0x46, 0x83, 0xf1, 0x22, 0xff, 0x1f, 0xc7, 0x98, 0x45, 0xc2, 0x60, 0x1e, 0xef, 0x83, 0x99, 0x97, 0x14, 0xf0, 0xf2, 0x59, + /* (2^190)P */ 0x44, 0x4a, 0x49, 0xeb, 0x56, 0x7d, 0xa4, 0x46, 0x8e, 0xa1, 0x36, 0xd6, 0x54, 0xa8, 0x22, 0x3e, 0x3b, 0x1c, 0x49, 0x74, 0x52, 0xe1, 0x46, 0xb3, 0xe7, 0xcd, 0x90, 0x53, 0x4e, 0xfd, 0xea, 0x2c, + /* (2^191)P */ 0x75, 0x66, 0x0d, 0xbe, 0x38, 0x85, 0x8a, 0xba, 0x23, 0x8e, 0x81, 0x50, 0xbb, 0x74, 0x90, 0x4b, 0xc3, 0x04, 0xd3, 0x85, 0x90, 0xb8, 0xda, 0xcb, 0xc4, 0x92, 0x61, 0xe5, 0xe0, 0x4f, 0xa2, 0x61, + /* (2^192)P */ 0xcb, 0x5b, 0x52, 0xdb, 0xe6, 0x15, 0x76, 0xcb, 0xca, 0xe4, 0x67, 0xa5, 0x35, 0x8c, 0x7d, 0xdd, 0x69, 0xdd, 0xfc, 0xca, 0x3a, 0x15, 0xb4, 0xe6, 0x66, 0x97, 0x3c, 0x7f, 0x09, 0x8e, 0x66, 0x2d, + /* (2^193)P */ 0xf0, 0x5e, 0xe5, 0x5c, 0x26, 0x7e, 0x7e, 0xa5, 0x67, 0xb9, 0xd4, 0x7c, 0x52, 0x4e, 0x9f, 0x5d, 0xe5, 0xd1, 0x2f, 0x49, 0x06, 0x36, 0xc8, 0xfb, 0xae, 0xf7, 0xc3, 0xb7, 0xbe, 0x52, 0x0d, 0x09, + /* (2^194)P */ 0x7c, 0x4d, 0x7b, 0x1e, 0x5a, 0x51, 0xb9, 0x09, 0xc0, 0x44, 0xda, 0x99, 0x25, 0x6a, 0x26, 0x1f, 0x04, 0x55, 0xc5, 0xe2, 0x48, 0x95, 0xc4, 0xa1, 0xcc, 0x15, 0x6f, 0x12, 0x87, 0x42, 0xf0, 0x7e, + /* (2^195)P */ 0x15, 0xef, 0x30, 0xbd, 0x9d, 0x65, 0xd1, 0xfe, 0x7b, 0x27, 0xe0, 0xc4, 0xee, 0xb9, 0x4a, 0x8b, 0x91, 0x32, 0xdf, 0xa5, 0x36, 0x62, 0x4d, 0x88, 0x88, 0xf7, 0x5c, 0xbf, 0xa6, 0x6e, 0xd9, 0x1f, + /* (2^196)P */ 0x9a, 0x0d, 0x19, 0x1f, 0x98, 0x61, 0xa1, 0x42, 0xc1, 0x52, 0x60, 0x7e, 0x50, 0x49, 0xd8, 0x61, 0xd5, 0x2c, 0x5a, 0x28, 0xbf, 0x13, 0xe1, 0x9f, 0xd8, 0x85, 0xad, 0xdb, 0x76, 0xd6, 0x22, 0x7c, + /* (2^197)P */ 0x7d, 0xd2, 0xfb, 0x2b, 0xed, 0x70, 0xe7, 0x82, 0xa5, 0xf5, 0x96, 0xe9, 0xec, 0xb2, 0x05, 0x4c, 0x50, 0x01, 0x90, 0xb0, 0xc2, 0xa9, 0x40, 0xcd, 0x64, 0xbf, 0xd9, 0x13, 0x92, 0x31, 0x95, 0x58, + /* (2^198)P */ 0x08, 0x2e, 0xea, 0x3f, 0x70, 0x5d, 0xcc, 0xe7, 0x8c, 0x18, 0xe2, 0x58, 0x12, 0x49, 0x0c, 0xb5, 0xf0, 0x5b, 0x20, 0x48, 0xaa, 0x0b, 0xe3, 0xcc, 0x62, 0x2d, 0xa3, 0xcf, 0x9c, 0x65, 0x7c, 0x53, + /* (2^199)P */ 0x88, 0xc0, 0xcf, 0x98, 0x3a, 0x62, 0xb6, 0x37, 0xa4, 0xac, 0xd6, 0xa4, 0x1f, 0xed, 0x9b, 0xfe, 0xb0, 0xd1, 0xa8, 0x56, 0x8e, 0x9b, 0xd2, 0x04, 0x75, 0x95, 0x51, 0x0b, 0xc4, 0x71, 0x5f, 0x72, + /* (2^200)P */ 0xe6, 0x9c, 0x33, 0xd0, 0x9c, 0xf8, 0xc7, 0x28, 0x8b, 0xc1, 0xdd, 0x69, 0x44, 0xb1, 0x67, 0x83, 0x2c, 0x65, 0xa1, 0xa6, 0x83, 0xda, 0x3a, 0x88, 0x17, 0x6c, 0x4d, 0x03, 0x74, 0x19, 0x5f, 0x58, + /* (2^201)P */ 0x88, 0x91, 0xb1, 0xf1, 0x66, 0xb2, 0xcf, 0x89, 0x17, 0x52, 0xc3, 0xe7, 0x63, 0x48, 0x3b, 0xe6, 0x6a, 0x52, 0xc0, 0xb4, 0xa6, 0x9d, 0x8c, 0xd8, 0x35, 0x46, 0x95, 0xf0, 0x9d, 0x5c, 0x03, 0x3e, + /* (2^202)P */ 0x9d, 0xde, 0x45, 0xfb, 0x12, 0x54, 0x9d, 0xdd, 0x0d, 0xf4, 0xcf, 0xe4, 0x32, 0x45, 0x68, 0xdd, 0x1c, 0x67, 0x1d, 0x15, 0x9b, 0x99, 0x5c, 0x4b, 0x90, 0xf6, 0xe7, 0x11, 0xc8, 0x2c, 0x8c, 0x2d, + /* (2^203)P */ 0x40, 0x5d, 0x05, 0x90, 0x1d, 0xbe, 0x54, 0x7f, 0x40, 0xaf, 0x4a, 0x46, 0xdf, 0xc5, 0x64, 0xa4, 0xbe, 0x17, 0xe9, 0xf0, 0x24, 0x96, 0x97, 0x33, 0x30, 0x6b, 0x35, 0x27, 0xc5, 0x8d, 0x01, 0x2c, + /* (2^204)P */ 0xd4, 0xb3, 0x30, 0xe3, 0x24, 0x50, 0x41, 0xa5, 0xd3, 0x52, 0x16, 0x69, 0x96, 0x3d, 0xff, 0x73, 0xf1, 0x59, 0x9b, 0xef, 0xc4, 0x42, 0xec, 0x94, 0x5a, 0x8e, 0xd0, 0x18, 0x16, 0x20, 0x47, 0x07, + /* (2^205)P */ 0x53, 0x1c, 0x41, 0xca, 0x8a, 0xa4, 0x6c, 0x4d, 0x19, 0x61, 0xa6, 0xcf, 0x2f, 0x5f, 0x41, 0x66, 0xff, 0x27, 0xe2, 0x51, 0x00, 0xd4, 0x4d, 0x9c, 0xeb, 0xf7, 0x02, 0x9a, 0xc0, 0x0b, 0x81, 0x59, + /* (2^206)P */ 0x1d, 0x10, 0xdc, 0xb3, 0x71, 0xb1, 0x7e, 0x2a, 0x8e, 0xf6, 0xfe, 0x9f, 0xb9, 0x5a, 0x1c, 0x44, 0xea, 0x59, 0xb3, 0x93, 0x9b, 0x5c, 0x02, 0x32, 0x2f, 0x11, 0x9d, 0x1e, 0xa7, 0xe0, 0x8c, 0x5e, + /* (2^207)P */ 0xfd, 0x03, 0x95, 0x42, 0x92, 0xcb, 0xcc, 0xbf, 0x55, 0x5d, 0x09, 0x2f, 0x75, 0xba, 0x71, 0xd2, 0x1e, 0x09, 0x2d, 0x97, 0x5e, 0xad, 0x5e, 0x34, 0xba, 0x03, 0x31, 0xa8, 0x11, 0xdf, 0xc8, 0x18, + /* (2^208)P */ 0x4c, 0x0f, 0xed, 0x9a, 0x9a, 0x94, 0xcd, 0x90, 0x7e, 0xe3, 0x60, 0x66, 0xcb, 0xf4, 0xd1, 0xc5, 0x0b, 0x2e, 0xc5, 0x56, 0x2d, 0xc5, 0xca, 0xb8, 0x0d, 0x8e, 0x80, 0xc5, 0x00, 0xe4, 0x42, 0x6e, + /* (2^209)P */ 0x23, 0xfd, 0xae, 0xee, 0x66, 0x69, 0xb4, 0xa3, 0xca, 0xcd, 0x9e, 0xe3, 0x0b, 0x1f, 0x4f, 0x0c, 0x1d, 0xa5, 0x83, 0xd6, 0xc9, 0xc8, 0x9d, 0x18, 0x1b, 0x35, 0x09, 0x4c, 0x05, 0x7f, 0xf2, 0x51, + /* (2^210)P */ 0x82, 0x06, 0x32, 0x2a, 0xcd, 0x7c, 0x48, 0x4c, 0x96, 0x1c, 0xdf, 0xb3, 0x5b, 0xa9, 0x7e, 0x58, 0xe8, 0xb8, 0x5c, 0x55, 0x9e, 0xf7, 0xcc, 0xc8, 0x3d, 0xd7, 0x06, 0xa2, 0x29, 0xc8, 0x7d, 0x54, + /* (2^211)P */ 0x06, 0x9b, 0xc3, 0x80, 0xcd, 0xa6, 0x22, 0xb8, 0xc6, 0xd4, 0x00, 0x20, 0x73, 0x54, 0x6d, 0xe9, 0x4d, 0x3b, 0x46, 0x91, 0x6f, 0x5b, 0x53, 0x28, 0x1d, 0x6e, 0x48, 0xe2, 0x60, 0x46, 0x8f, 0x22, + /* (2^212)P */ 0xbf, 0x3a, 0x8d, 0xde, 0x38, 0x95, 0x79, 0x98, 0x6e, 0xca, 0xeb, 0x45, 0x00, 0x33, 0xd8, 0x8c, 0x38, 0xe7, 0x21, 0x82, 0x00, 0x2a, 0x95, 0x79, 0xbb, 0xd2, 0x5c, 0x53, 0xa7, 0xe1, 0x22, 0x43, + /* (2^213)P */ 0x1c, 0x80, 0xd1, 0x19, 0x18, 0xc1, 0x14, 0xb1, 0xc7, 0x5e, 0x3f, 0x4f, 0xd8, 0xe4, 0x16, 0x20, 0x4c, 0x0f, 0x26, 0x09, 0xf4, 0x2d, 0x0e, 0xdd, 0x66, 0x72, 0x5f, 0xae, 0xc0, 0x62, 0xc3, 0x5e, + /* (2^214)P */ 0xee, 0xb4, 0xb2, 0xb8, 0x18, 0x2b, 0x46, 0xc0, 0xfb, 0x1a, 0x4d, 0x27, 0x50, 0xd9, 0xc8, 0x7c, 0xd2, 0x02, 0x6b, 0x43, 0x05, 0x71, 0x5f, 0xf2, 0xd3, 0xcc, 0xf9, 0xbf, 0xdc, 0xf8, 0xbb, 0x43, + /* (2^215)P */ 0xdf, 0xe9, 0x39, 0xa0, 0x67, 0x17, 0xad, 0xb6, 0x83, 0x35, 0x9d, 0xf6, 0xa8, 0x4d, 0x71, 0xb0, 0xf5, 0x31, 0x29, 0xb4, 0x18, 0xfa, 0x55, 0x5e, 0x61, 0x09, 0xc6, 0x33, 0x8f, 0x55, 0xd5, 0x4e, + /* (2^216)P */ 0xdd, 0xa5, 0x47, 0xc6, 0x01, 0x79, 0xe3, 0x1f, 0x57, 0xd3, 0x81, 0x80, 0x1f, 0xdf, 0x3d, 0x59, 0xa6, 0xd7, 0x3f, 0x81, 0xfd, 0xa4, 0x49, 0x02, 0x61, 0xaf, 0x9c, 0x4e, 0x27, 0xca, 0xac, 0x69, + /* (2^217)P */ 0xc9, 0x21, 0x07, 0x33, 0xea, 0xa3, 0x7b, 0x04, 0xa0, 0x1e, 0x7e, 0x0e, 0xc2, 0x3f, 0x42, 0x83, 0x60, 0x4a, 0x31, 0x01, 0xaf, 0xc0, 0xf4, 0x1d, 0x27, 0x95, 0x28, 0x89, 0xab, 0x2d, 0xa6, 0x09, + /* (2^218)P */ 0x00, 0xcb, 0xc6, 0x9c, 0xa4, 0x25, 0xb3, 0xa5, 0xb6, 0x6c, 0xb5, 0x54, 0xc6, 0x5d, 0x4b, 0xe9, 0xa0, 0x94, 0xc9, 0xad, 0x79, 0x87, 0xe2, 0x3b, 0xad, 0x4a, 0x3a, 0xba, 0xf8, 0xe8, 0x96, 0x42, + /* (2^219)P */ 0xab, 0x1e, 0x45, 0x1e, 0x76, 0x89, 0x86, 0x32, 0x4a, 0x59, 0x59, 0xff, 0x8b, 0x59, 0x4d, 0x2e, 0x4a, 0x08, 0xa7, 0xd7, 0x53, 0x68, 0xb9, 0x49, 0xa8, 0x20, 0x14, 0x60, 0x19, 0xa3, 0x80, 0x49, + /* (2^220)P */ 0x42, 0x2c, 0x55, 0x2f, 0xe1, 0xb9, 0x65, 0x95, 0x96, 0xfe, 0x00, 0x71, 0xdb, 0x18, 0x53, 0x8a, 0xd7, 0xd0, 0xad, 0x43, 0x4d, 0x0b, 0xc9, 0x05, 0xda, 0x4e, 0x5d, 0x6a, 0xd6, 0x4c, 0x8b, 0x53, + /* (2^221)P */ 0x9f, 0x03, 0x9f, 0xe8, 0xc3, 0x4f, 0xe9, 0xf4, 0x45, 0x80, 0x61, 0x6f, 0xf2, 0x9a, 0x2c, 0x59, 0x50, 0x95, 0x4b, 0xfd, 0xb5, 0x6e, 0xa3, 0x08, 0x19, 0x14, 0xed, 0xc2, 0xf6, 0xfa, 0xff, 0x25, + /* (2^222)P */ 0x54, 0xd3, 0x79, 0xcc, 0x59, 0x44, 0x43, 0x34, 0x6b, 0x47, 0xd5, 0xb1, 0xb4, 0xbf, 0xec, 0xee, 0x99, 0x5d, 0x61, 0x61, 0xa0, 0x34, 0xeb, 0xdd, 0x73, 0xb7, 0x64, 0xeb, 0xcc, 0xce, 0x29, 0x51, + /* (2^223)P */ 0x20, 0x35, 0x99, 0x94, 0x58, 0x21, 0x43, 0xee, 0x3b, 0x0b, 0x4c, 0xf1, 0x7c, 0x9c, 0x2f, 0x77, 0xd5, 0xda, 0xbe, 0x06, 0xe3, 0xfc, 0xe2, 0xd2, 0x97, 0x6a, 0xf0, 0x46, 0xb5, 0x42, 0x5f, 0x71, + /* (2^224)P */ 0x1a, 0x5f, 0x5b, 0xda, 0xce, 0xcd, 0x4e, 0x43, 0xa9, 0x41, 0x97, 0xa4, 0x15, 0x71, 0xa1, 0x0d, 0x2e, 0xad, 0xed, 0x73, 0x7c, 0xd7, 0x0b, 0x68, 0x41, 0x90, 0xdd, 0x4e, 0x35, 0x02, 0x7c, 0x48, + /* (2^225)P */ 0xc4, 0xd9, 0x0e, 0xa7, 0xf3, 0xef, 0xef, 0xb8, 0x02, 0xe3, 0x57, 0xe8, 0xa3, 0x2a, 0xa3, 0x56, 0xa0, 0xa5, 0xa2, 0x48, 0xbd, 0x68, 0x3a, 0xdf, 0x44, 0xc4, 0x76, 0x31, 0xb7, 0x50, 0xf6, 0x07, + /* (2^226)P */ 0xb1, 0xcc, 0xe0, 0x26, 0x16, 0x9b, 0x8b, 0xe3, 0x36, 0xfb, 0x09, 0x8b, 0xc1, 0x53, 0xe0, 0x79, 0x64, 0x49, 0xf9, 0xc9, 0x19, 0x03, 0xd9, 0x56, 0xc4, 0xf5, 0x9f, 0xac, 0xe7, 0x41, 0xa9, 0x1c, + /* (2^227)P */ 0xbb, 0xa0, 0x2f, 0x16, 0x29, 0xdf, 0xc4, 0x49, 0x05, 0x33, 0xb3, 0x82, 0x32, 0xcf, 0x88, 0x84, 0x7d, 0x43, 0xbb, 0xca, 0x14, 0xda, 0xdf, 0x95, 0x86, 0xad, 0xd5, 0x64, 0x82, 0xf7, 0x91, 0x33, + /* (2^228)P */ 0x5d, 0x09, 0xb5, 0xe2, 0x6a, 0xe0, 0x9a, 0x72, 0x46, 0xa9, 0x59, 0x32, 0xd7, 0x58, 0x8a, 0xd5, 0xed, 0x21, 0x39, 0xd1, 0x62, 0x42, 0x83, 0xe9, 0x92, 0xb5, 0x4b, 0xa5, 0xfa, 0xda, 0xfe, 0x27, + /* (2^229)P */ 0xbb, 0x48, 0xad, 0x29, 0xb8, 0xc5, 0x9d, 0xa9, 0x60, 0xe2, 0x9e, 0x49, 0x42, 0x57, 0x02, 0x5f, 0xfd, 0x13, 0x75, 0x5d, 0xcd, 0x8e, 0x2c, 0x80, 0x38, 0xd9, 0x6d, 0x3f, 0xef, 0xb3, 0xce, 0x78, + /* (2^230)P */ 0x94, 0x5d, 0x13, 0x8a, 0x4f, 0xf4, 0x42, 0xc3, 0xa3, 0xdd, 0x8c, 0x82, 0x44, 0xdb, 0x9e, 0x7b, 0xe7, 0xcf, 0x37, 0x05, 0x1a, 0xd1, 0x36, 0x94, 0xc8, 0xb4, 0x1a, 0xec, 0x64, 0xb1, 0x64, 0x50, + /* (2^231)P */ 0xfc, 0xb2, 0x7e, 0xd3, 0xcf, 0xec, 0x20, 0x70, 0xfc, 0x25, 0x0d, 0xd9, 0x3e, 0xea, 0x31, 0x1f, 0x34, 0xbb, 0xa1, 0xdf, 0x7b, 0x0d, 0x93, 0x1b, 0x44, 0x30, 0x11, 0x48, 0x7a, 0x46, 0x44, 0x53, + /* (2^232)P */ 0xfb, 0x6d, 0x5e, 0xf2, 0x70, 0x31, 0x07, 0x70, 0xc8, 0x4c, 0x11, 0x50, 0x1a, 0xdc, 0x85, 0xe3, 0x00, 0x4f, 0xfc, 0xc8, 0x8a, 0x69, 0x48, 0x23, 0xd8, 0x40, 0xdd, 0x84, 0x52, 0xa5, 0x77, 0x2a, + /* (2^233)P */ 0xe4, 0x6c, 0x8c, 0xc9, 0xe0, 0xaf, 0x06, 0xfe, 0xe4, 0xd6, 0xdf, 0xdd, 0x96, 0xdf, 0x35, 0xc2, 0xd3, 0x1e, 0xbf, 0x33, 0x1e, 0xd0, 0x28, 0x14, 0xaf, 0xbd, 0x00, 0x93, 0xec, 0x68, 0x57, 0x78, + /* (2^234)P */ 0x3b, 0xb6, 0xde, 0x91, 0x7a, 0xe5, 0x02, 0x97, 0x80, 0x8b, 0xce, 0xe5, 0xbf, 0xb8, 0xbd, 0x61, 0xac, 0x58, 0x1d, 0x3d, 0x6f, 0x42, 0x5b, 0x64, 0xbc, 0x57, 0xa5, 0x27, 0x22, 0xa8, 0x04, 0x48, + /* (2^235)P */ 0x01, 0x26, 0x4d, 0xb4, 0x8a, 0x04, 0x57, 0x8e, 0x35, 0x69, 0x3a, 0x4b, 0x1a, 0x50, 0xd6, 0x68, 0x93, 0xc2, 0xe1, 0xf9, 0xc3, 0x9e, 0x9c, 0xc3, 0xe2, 0x63, 0xde, 0xd4, 0x57, 0xf2, 0x72, 0x41, + /* (2^236)P */ 0x01, 0x64, 0x0c, 0x33, 0x50, 0xb4, 0x68, 0xd3, 0x91, 0x23, 0x8f, 0x41, 0x17, 0x30, 0x0d, 0x04, 0x0d, 0xd9, 0xb7, 0x90, 0x60, 0xbb, 0x34, 0x2c, 0x1f, 0xd5, 0xdf, 0x8f, 0x22, 0x49, 0xf6, 0x16, + /* (2^237)P */ 0xf5, 0x8e, 0x92, 0x2b, 0x8e, 0x81, 0xa6, 0xbe, 0x72, 0x1e, 0xc1, 0xcd, 0x91, 0xcf, 0x8c, 0xe2, 0xcd, 0x36, 0x7a, 0xe7, 0x68, 0xaa, 0x4a, 0x59, 0x0f, 0xfd, 0x7f, 0x6c, 0x80, 0x34, 0x30, 0x31, + /* (2^238)P */ 0x65, 0xbd, 0x49, 0x22, 0xac, 0x27, 0x9d, 0x8a, 0x12, 0x95, 0x8e, 0x01, 0x64, 0xb4, 0xa3, 0x19, 0xc7, 0x7e, 0xb3, 0x52, 0xf3, 0xcf, 0x6c, 0xc2, 0x21, 0x7b, 0x79, 0x1d, 0x34, 0x68, 0x6f, 0x05, + /* (2^239)P */ 0x27, 0x23, 0xfd, 0x7e, 0x75, 0xd6, 0x79, 0x5e, 0x15, 0xfe, 0x3a, 0x55, 0xb6, 0xbc, 0xbd, 0xfa, 0x60, 0x5a, 0xaf, 0x6e, 0x2c, 0x22, 0xe7, 0xd3, 0x3b, 0x74, 0xae, 0x4d, 0x6d, 0xc7, 0x46, 0x70, + /* (2^240)P */ 0x55, 0x4a, 0x8d, 0xb1, 0x72, 0xe8, 0x0b, 0x66, 0x96, 0x14, 0x4e, 0x57, 0x18, 0x25, 0x99, 0x19, 0xbb, 0xdc, 0x2b, 0x30, 0x3a, 0x05, 0x03, 0xc1, 0x8e, 0x8e, 0x21, 0x0b, 0x80, 0xe9, 0xd8, 0x3e, + /* (2^241)P */ 0x3e, 0xe0, 0x75, 0xfa, 0x39, 0x92, 0x0b, 0x7b, 0x83, 0xc0, 0x33, 0x46, 0x68, 0xfb, 0xe9, 0xef, 0x93, 0x77, 0x1a, 0x39, 0xbe, 0x5f, 0xa3, 0x98, 0x34, 0xfe, 0xd0, 0xe2, 0x0f, 0x51, 0x65, 0x60, + /* (2^242)P */ 0x0c, 0xad, 0xab, 0x48, 0x85, 0x66, 0xcb, 0x55, 0x27, 0xe5, 0x87, 0xda, 0x48, 0x45, 0x58, 0xb4, 0xdd, 0xc1, 0x07, 0x01, 0xea, 0xec, 0x43, 0x2c, 0x35, 0xde, 0x72, 0x93, 0x80, 0x28, 0x60, 0x52, + /* (2^243)P */ 0x1f, 0x3b, 0x21, 0xf9, 0x6a, 0xc5, 0x15, 0x34, 0xdb, 0x98, 0x7e, 0x01, 0x4d, 0x1a, 0xee, 0x5b, 0x9b, 0x70, 0xcf, 0xb5, 0x05, 0xb1, 0xf6, 0x13, 0xb6, 0x9a, 0xb2, 0x82, 0x34, 0x0e, 0xf2, 0x5f, + /* (2^244)P */ 0x90, 0x6c, 0x2e, 0xcc, 0x75, 0x9c, 0xa2, 0x0a, 0x06, 0xe2, 0x70, 0x3a, 0xca, 0x73, 0x7d, 0xfc, 0x15, 0xc5, 0xb5, 0xc4, 0x8f, 0xc3, 0x9f, 0x89, 0x07, 0xc2, 0xff, 0x24, 0xb1, 0x86, 0x03, 0x25, + /* (2^245)P */ 0x56, 0x2b, 0x3d, 0xae, 0xd5, 0x28, 0xea, 0x54, 0xce, 0x60, 0xde, 0xd6, 0x9d, 0x14, 0x13, 0x99, 0xc1, 0xd6, 0x06, 0x8f, 0xc5, 0x4f, 0x69, 0x16, 0xc7, 0x8f, 0x01, 0xeb, 0x75, 0x39, 0xb2, 0x46, + /* (2^246)P */ 0xe2, 0xb4, 0xb7, 0xb4, 0x0f, 0x6a, 0x0a, 0x47, 0xde, 0x53, 0x72, 0x8f, 0x5a, 0x47, 0x92, 0x5d, 0xdb, 0x3a, 0xbd, 0x2f, 0xb5, 0xe5, 0xee, 0xab, 0x68, 0x69, 0x80, 0xa0, 0x01, 0x08, 0xa2, 0x7f, + /* (2^247)P */ 0xd2, 0x14, 0x77, 0x9f, 0xf1, 0xfa, 0xf3, 0x76, 0xc3, 0x60, 0x46, 0x2f, 0xc1, 0x40, 0xe8, 0xb3, 0x4e, 0x74, 0x12, 0xf2, 0x8d, 0xcd, 0xb4, 0x0f, 0xd2, 0x2d, 0x3a, 0x1d, 0x25, 0x5a, 0x06, 0x4b, + /* (2^248)P */ 0x4a, 0xcd, 0x77, 0x3d, 0x38, 0xde, 0xeb, 0x5c, 0xb1, 0x9c, 0x2c, 0x88, 0xdf, 0x39, 0xdf, 0x6a, 0x59, 0xf7, 0x9a, 0xb0, 0x2e, 0x24, 0xdd, 0xa2, 0x22, 0x64, 0x5f, 0x0e, 0xe5, 0xc0, 0x47, 0x31, + /* (2^249)P */ 0xdb, 0x50, 0x13, 0x1d, 0x10, 0xa5, 0x4c, 0x16, 0x62, 0xc9, 0x3f, 0xc3, 0x79, 0x34, 0xd1, 0xf8, 0x08, 0xda, 0xe5, 0x13, 0x4d, 0xce, 0x40, 0xe6, 0xba, 0xf8, 0x61, 0x50, 0xc4, 0xe0, 0xde, 0x4b, + /* (2^250)P */ 0xc9, 0xb1, 0xed, 0xa4, 0xc1, 0x6d, 0xc4, 0xd7, 0x8a, 0xd9, 0x7f, 0x43, 0xb6, 0xd7, 0x14, 0x55, 0x0b, 0xc0, 0xa1, 0xb2, 0x6b, 0x2f, 0x94, 0x58, 0x0e, 0x71, 0x70, 0x1d, 0xab, 0xb2, 0xff, 0x2d, + /* (2^251)P */ 0x68, 0x6d, 0x8b, 0xc1, 0x2f, 0xcf, 0xdf, 0xcc, 0x67, 0x61, 0x80, 0xb7, 0xa8, 0xcb, 0xeb, 0xa8, 0xe3, 0x37, 0x29, 0x5e, 0xf9, 0x97, 0x06, 0x98, 0x8c, 0x6e, 0x12, 0xd0, 0x1c, 0xba, 0xfb, 0x02, + /* (2^252)P */ 0x65, 0x45, 0xff, 0xad, 0x60, 0xc3, 0x98, 0xcb, 0x19, 0x15, 0xdb, 0x4b, 0xd2, 0x01, 0x71, 0x44, 0xd5, 0x15, 0xfb, 0x75, 0x74, 0xc8, 0xc4, 0x98, 0x7d, 0xa2, 0x22, 0x6e, 0x6d, 0xc7, 0xf8, 0x05, + /* (2^253)P */ 0x94, 0xf4, 0xb9, 0xfe, 0xdf, 0xe5, 0x69, 0xab, 0x75, 0x6b, 0x40, 0x18, 0x9d, 0xc7, 0x09, 0xae, 0x1d, 0x2d, 0xa4, 0x94, 0xfb, 0x45, 0x9b, 0x19, 0x84, 0xfa, 0x2a, 0xae, 0xeb, 0x0a, 0x71, 0x79, + /* (2^254)P */ 0xdf, 0xd2, 0x34, 0xf3, 0xa7, 0xed, 0xad, 0xa6, 0xb4, 0x57, 0x2a, 0xaf, 0x51, 0x9c, 0xde, 0x7b, 0xa8, 0xea, 0xdc, 0x86, 0x4f, 0xc6, 0x8f, 0xa9, 0x7b, 0xd0, 0x0e, 0xc2, 0x35, 0x03, 0xbe, 0x6b, + /* (2^255)P */ 0x44, 0x43, 0x98, 0x53, 0xbe, 0xdc, 0x7f, 0x66, 0xa8, 0x49, 0x59, 0x00, 0x1c, 0xbc, 0x72, 0x07, 0x8e, 0xd6, 0xbe, 0x4e, 0x9f, 0xa4, 0x07, 0xba, 0xbf, 0x30, 0xdf, 0xba, 0x85, 0xb0, 0xa7, 0x1f, +} diff --git a/vendor/github.com/cloudflare/circl/internal/conv/conv.go b/vendor/github.com/cloudflare/circl/internal/conv/conv.go new file mode 100644 index 00000000..b4a4f0b1 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/internal/conv/conv.go @@ -0,0 +1,89 @@ +package conv + +import ( + "fmt" + "math/big" + "strings" +) + +// BytesLe2Hex returns an hexadecimal string of a number stored in a +// little-endian order slice x. +func BytesLe2Hex(x []byte) string { + b := &strings.Builder{} + b.Grow(2*len(x) + 2) + fmt.Fprint(b, "0x") + if len(x) == 0 { + fmt.Fprint(b, "00") + } + for i := len(x) - 1; i >= 0; i-- { + fmt.Fprintf(b, "%02x", x[i]) + } + return b.String() +} + +// BytesLe2BigInt converts a little-endian slice x into a big-endian +// math/big.Int. +func BytesLe2BigInt(x []byte) *big.Int { + n := len(x) + b := new(big.Int) + if len(x) > 0 { + y := make([]byte, n) + for i := 0; i < n; i++ { + y[n-1-i] = x[i] + } + b.SetBytes(y) + } + return b +} + +// BigInt2BytesLe stores a positive big.Int number x into a little-endian slice z. +// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros). +// If x does not fit in the slice or is negative, z is not modified. +func BigInt2BytesLe(z []byte, x *big.Int) { + xLen := (x.BitLen() + 7) >> 3 + zLen := len(z) + if zLen >= xLen && x.Sign() >= 0 { + y := x.Bytes() + for i := 0; i < xLen; i++ { + z[i] = y[xLen-1-i] + } + for i := xLen; i < zLen; i++ { + z[i] = 0 + } + } +} + +// Uint64Le2BigInt converts a llitle-endian slice x into a big number. +func Uint64Le2BigInt(x []uint64) *big.Int { + n := len(x) + b := new(big.Int) + var bi big.Int + for i := n - 1; i >= 0; i-- { + bi.SetUint64(x[i]) + b.Lsh(b, 64) + b.Add(b, &bi) + } + return b +} + +// BigInt2Uint64Le stores a positive big.Int number x into a little-endian slice z. +// The slice is modified if the bitlength of x <= 8*len(z) (padding with zeros). +// If x does not fit in the slice or is negative, z is not modified. +func BigInt2Uint64Le(z []uint64, x *big.Int) { + xLen := (x.BitLen() + 63) >> 6 // number of 64-bit words + zLen := len(z) + if zLen >= xLen && x.Sign() > 0 { + var y, yi big.Int + y.Set(x) + two64 := big.NewInt(1) + two64.Lsh(two64, 64).Sub(two64, big.NewInt(1)) + for i := 0; i < xLen; i++ { + yi.And(&y, two64) + z[i] = yi.Uint64() + y.Rsh(&y, 64) + } + } + for i := xLen; i < zLen; i++ { + z[i] = 0 + } +} diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp.go b/vendor/github.com/cloudflare/circl/math/fp25519/fp.go new file mode 100644 index 00000000..704db4b7 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp.go @@ -0,0 +1,200 @@ +// Package fp25519 provides prime field arithmetic over GF(2^255-19). +package fp25519 + +import "github.com/cloudflare/circl/internal/conv" + +// Size in bytes of an element. +const Size = 32 + +// Elt is a prime field element. +type Elt [Size]byte + +func (e Elt) String() string { return conv.BytesLe2Hex(e[:]) } + +// p is the prime modulus 2^255-19. +var p = Elt{ + 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, +} + +// P returns the prime modulus 2^255-19. +func P() Elt { return p } + +// ToBytes returns the little-endian byte representation of x. +func ToBytes(b []byte, x *Elt) { + if len(b) != Size { + panic("wrong size") + } + Modp(x) + copy(b, x[:]) +} + +// IsZero returns true if x is equal to 0. +func IsZero(x *Elt) bool { Modp(x); return *x == Elt{} } + +// SetOne assigns x=1. +func SetOne(x *Elt) { *x = Elt{}; x[0] = 1 } + +// Neg calculates z = -x. +func Neg(z, x *Elt) { Sub(z, &p, x) } + +// InvSqrt calculates z = sqrt(x/y) iff x/y is a quadratic-residue, which is +// indicated by returning isQR = true. Otherwise, when x/y is a quadratic +// non-residue, z will have an undetermined value and isQR = false. +func InvSqrt(z, x, y *Elt) (isQR bool) { + sqrtMinusOne := &Elt{ + 0xb0, 0xa0, 0x0e, 0x4a, 0x27, 0x1b, 0xee, 0xc4, + 0x78, 0xe4, 0x2f, 0xad, 0x06, 0x18, 0x43, 0x2f, + 0xa7, 0xd7, 0xfb, 0x3d, 0x99, 0x00, 0x4d, 0x2b, + 0x0b, 0xdf, 0xc1, 0x4f, 0x80, 0x24, 0x83, 0x2b, + } + t0, t1, t2, t3 := &Elt{}, &Elt{}, &Elt{}, &Elt{} + + Mul(t0, x, y) // t0 = u*v + Sqr(t1, y) // t1 = v^2 + Mul(t2, t0, t1) // t2 = u*v^3 + Sqr(t0, t1) // t0 = v^4 + Mul(t1, t0, t2) // t1 = u*v^7 + + var Tab [4]*Elt + Tab[0] = &Elt{} + Tab[1] = &Elt{} + Tab[2] = t3 + Tab[3] = t1 + + *Tab[0] = *t1 + Sqr(Tab[0], Tab[0]) + Sqr(Tab[1], Tab[0]) + Sqr(Tab[1], Tab[1]) + Mul(Tab[1], Tab[1], Tab[3]) + Mul(Tab[0], Tab[0], Tab[1]) + Sqr(Tab[0], Tab[0]) + Mul(Tab[0], Tab[0], Tab[1]) + Sqr(Tab[1], Tab[0]) + for i := 0; i < 4; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[0]) + Sqr(Tab[2], Tab[1]) + for i := 0; i < 4; i++ { + Sqr(Tab[2], Tab[2]) + } + Mul(Tab[2], Tab[2], Tab[0]) + Sqr(Tab[1], Tab[2]) + for i := 0; i < 14; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[2]) + Sqr(Tab[2], Tab[1]) + for i := 0; i < 29; i++ { + Sqr(Tab[2], Tab[2]) + } + Mul(Tab[2], Tab[2], Tab[1]) + Sqr(Tab[1], Tab[2]) + for i := 0; i < 59; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[2]) + for i := 0; i < 5; i++ { + Sqr(Tab[1], Tab[1]) + } + Mul(Tab[1], Tab[1], Tab[0]) + Sqr(Tab[2], Tab[1]) + for i := 0; i < 124; i++ { + Sqr(Tab[2], Tab[2]) + } + Mul(Tab[2], Tab[2], Tab[1]) + Sqr(Tab[2], Tab[2]) + Sqr(Tab[2], Tab[2]) + Mul(Tab[2], Tab[2], Tab[3]) + + Mul(z, t3, t2) // z = xy^(p+3)/8 = xy^3*(xy^7)^(p-5)/8 + // Checking whether y z^2 == x + Sqr(t0, z) // t0 = z^2 + Mul(t0, t0, y) // t0 = yz^2 + Sub(t1, t0, x) // t1 = t0-u + Add(t2, t0, x) // t2 = t0+u + if IsZero(t1) { + return true + } else if IsZero(t2) { + Mul(z, z, sqrtMinusOne) // z = z*sqrt(-1) + return true + } else { + return false + } +} + +// Inv calculates z = 1/x mod p. +func Inv(z, x *Elt) { + x0, x1, x2 := &Elt{}, &Elt{}, &Elt{} + Sqr(x1, x) + Sqr(x0, x1) + Sqr(x0, x0) + Mul(x0, x0, x) + Mul(z, x0, x1) + Sqr(x1, z) + Mul(x0, x0, x1) + Sqr(x1, x0) + for i := 0; i < 4; i++ { + Sqr(x1, x1) + } + Mul(x0, x0, x1) + Sqr(x1, x0) + for i := 0; i < 9; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, x0) + Sqr(x2, x1) + for i := 0; i < 19; i++ { + Sqr(x2, x2) + } + Mul(x2, x2, x1) + for i := 0; i < 10; i++ { + Sqr(x2, x2) + } + Mul(x2, x2, x0) + Sqr(x0, x2) + for i := 0; i < 49; i++ { + Sqr(x0, x0) + } + Mul(x0, x0, x2) + Sqr(x1, x0) + for i := 0; i < 99; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, x0) + for i := 0; i < 50; i++ { + Sqr(x1, x1) + } + Mul(x1, x1, x2) + for i := 0; i < 5; i++ { + Sqr(x1, x1) + } + Mul(z, z, x1) +} + +// Cmov assigns y to x if n is 1. +func Cmov(x, y *Elt, n uint) { cmov(x, y, n) } + +// Cswap interchages x and y if n is 1. +func Cswap(x, y *Elt, n uint) { cswap(x, y, n) } + +// Add calculates z = x+y mod p. +func Add(z, x, y *Elt) { add(z, x, y) } + +// Sub calculates z = x-y mod p +func Sub(z, x, y *Elt) { sub(z, x, y) } + +// AddSub calculates (x,y) = (x+y mod p, x-y mod p). +func AddSub(x, y *Elt) { addsub(x, y) } + +// Mul calculates z = x*y mod p. +func Mul(z, x, y *Elt) { mul(z, x, y) } + +// Sqr calculates z = x^2 mod p. +func Sqr(z, x *Elt) { sqr(z, x) } + +// Modp ensures that z is between [0,p-1]. +func Modp(z *Elt) { modp(z) } diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.go b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.go new file mode 100644 index 00000000..1c35c007 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.go @@ -0,0 +1,44 @@ +// +build amd64,!purego + +package fp25519 + +import ( + "golang.org/x/sys/cpu" +) + +var hasBmi2Adx = cpu.X86.HasBMI2 && cpu.X86.HasADX + +var _ = hasBmi2Adx + +func cmov(x, y *Elt, n uint) { cmovAmd64(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapAmd64(x, y, n) } +func add(z, x, y *Elt) { addAmd64(z, x, y) } +func sub(z, x, y *Elt) { subAmd64(z, x, y) } +func addsub(x, y *Elt) { addsubAmd64(x, y) } +func mul(z, x, y *Elt) { mulAmd64(z, x, y) } +func sqr(z, x *Elt) { sqrAmd64(z, x) } +func modp(z *Elt) { modpAmd64(z) } + +//go:noescape +func cmovAmd64(x, y *Elt, n uint) + +//go:noescape +func cswapAmd64(x, y *Elt, n uint) + +//go:noescape +func addAmd64(z, x, y *Elt) + +//go:noescape +func subAmd64(z, x, y *Elt) + +//go:noescape +func addsubAmd64(x, y *Elt) + +//go:noescape +func mulAmd64(z, x, y *Elt) + +//go:noescape +func sqrAmd64(z, x *Elt) + +//go:noescape +func modpAmd64(z *Elt) diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.h b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.h new file mode 100644 index 00000000..7b25f16e --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_amd64.h @@ -0,0 +1,350 @@ +// This code was imported from https://github.com/armfazh/rfc7748_precomputed + +// CHECK_BMI2ADX triggers bmi2adx if supported, +// otherwise it fallbacks to legacy code. +#define CHECK_BMI2ADX(label, legacy, bmi2adx) \ + CMPB ·hasBmi2Adx(SB), $0 \ + JE label \ + bmi2adx \ + RET \ + label: \ + legacy \ + RET + +// cselect is a conditional move +// if b=1: it copies y into x; +// if b=0: x remains with the same value; +// if b<> 0,1: undefined. +// Uses: AX, DX, FLAGS +// Instr: x86_64, cmov +#define cselect(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ 0+y, DX; CMOVQNE DX, AX; MOVQ AX, 0+x; \ + MOVQ 8+x, AX; MOVQ 8+y, DX; CMOVQNE DX, AX; MOVQ AX, 8+x; \ + MOVQ 16+x, AX; MOVQ 16+y, DX; CMOVQNE DX, AX; MOVQ AX, 16+x; \ + MOVQ 24+x, AX; MOVQ 24+y, DX; CMOVQNE DX, AX; MOVQ AX, 24+x; + +// cswap is a conditional swap +// if b=1: x,y <- y,x; +// if b=0: x,y remain with the same values; +// if b<> 0,1: undefined. +// Uses: AX, DX, R8, FLAGS +// Instr: x86_64, cmov +#define cswap(x,y,b) \ + TESTQ b, b \ + MOVQ 0+x, AX; MOVQ AX, R8; MOVQ 0+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 0+x; MOVQ DX, 0+y; \ + MOVQ 8+x, AX; MOVQ AX, R8; MOVQ 8+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 8+x; MOVQ DX, 8+y; \ + MOVQ 16+x, AX; MOVQ AX, R8; MOVQ 16+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 16+x; MOVQ DX, 16+y; \ + MOVQ 24+x, AX; MOVQ AX, R8; MOVQ 24+y, DX; CMOVQNE DX, AX; CMOVQNE R8, DX; MOVQ AX, 24+x; MOVQ DX, 24+y; + +// additionLeg adds x and y and stores in z +// Uses: AX, DX, R8-R11, FLAGS +// Instr: x86_64, cmov +#define additionLeg(z,x,y) \ + MOVL $38, AX; \ + MOVL $0, DX; \ + MOVQ 0+x, R8; ADDQ 0+y, R8; \ + MOVQ 8+x, R9; ADCQ 8+y, R9; \ + MOVQ 16+x, R10; ADCQ 16+y, R10; \ + MOVQ 24+x, R11; ADCQ 24+y, R11; \ + CMOVQCS AX, DX; \ + ADDQ DX, R8; \ + ADCQ $0, R9; MOVQ R9, 8+z; \ + ADCQ $0, R10; MOVQ R10, 16+z; \ + ADCQ $0, R11; MOVQ R11, 24+z; \ + MOVL $0, DX; \ + CMOVQCS AX, DX; \ + ADDQ DX, R8; MOVQ R8, 0+z; + +// additionAdx adds x and y and stores in z +// Uses: AX, DX, R8-R11, FLAGS +// Instr: x86_64, cmov, adx +#define additionAdx(z,x,y) \ + MOVL $38, AX; \ + XORL DX, DX; \ + MOVQ 0+x, R8; ADCXQ 0+y, R8; \ + MOVQ 8+x, R9; ADCXQ 8+y, R9; \ + MOVQ 16+x, R10; ADCXQ 16+y, R10; \ + MOVQ 24+x, R11; ADCXQ 24+y, R11; \ + CMOVQCS AX, DX ; \ + XORL AX, AX; \ + ADCXQ DX, R8; \ + ADCXQ AX, R9; MOVQ R9, 8+z; \ + ADCXQ AX, R10; MOVQ R10, 16+z; \ + ADCXQ AX, R11; MOVQ R11, 24+z; \ + MOVL $38, DX; \ + CMOVQCS DX, AX; \ + ADDQ AX, R8; MOVQ R8, 0+z; + +// subtraction subtracts y from x and stores in z +// Uses: AX, DX, R8-R11, FLAGS +// Instr: x86_64, cmov +#define subtraction(z,x,y) \ + MOVL $38, AX; \ + MOVQ 0+x, R8; SUBQ 0+y, R8; \ + MOVQ 8+x, R9; SBBQ 8+y, R9; \ + MOVQ 16+x, R10; SBBQ 16+y, R10; \ + MOVQ 24+x, R11; SBBQ 24+y, R11; \ + MOVL $0, DX; \ + CMOVQCS AX, DX; \ + SUBQ DX, R8; \ + SBBQ $0, R9; MOVQ R9, 8+z; \ + SBBQ $0, R10; MOVQ R10, 16+z; \ + SBBQ $0, R11; MOVQ R11, 24+z; \ + MOVL $0, DX; \ + CMOVQCS AX, DX; \ + SUBQ DX, R8; MOVQ R8, 0+z; + +// integerMulAdx multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerMulAdx(z,x,y) \ + MOVQ 0+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R8; MOVQ AX, 0+z; \ + MULXQ 8+x, AX, R9; ADCXQ AX, R8; \ + MULXQ 16+x, AX, R10; ADCXQ AX, R9; \ + MULXQ 24+x, AX, R11; ADCXQ AX, R10; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R11; \ + MOVQ 8+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R12; ADCXQ R8, AX; MOVQ AX, 8+z; \ + MULXQ 8+x, AX, R13; ADCXQ R9, R12; ADOXQ AX, R12; \ + MULXQ 16+x, AX, R14; ADCXQ R10, R13; ADOXQ AX, R13; \ + MULXQ 24+x, AX, R15; ADCXQ R11, R14; ADOXQ AX, R14; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R15; ADOXQ AX, R15; \ + MOVQ 16+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R8; ADCXQ R12, AX; MOVQ AX, 16+z; \ + MULXQ 8+x, AX, R9; ADCXQ R13, R8; ADOXQ AX, R8; \ + MULXQ 16+x, AX, R10; ADCXQ R14, R9; ADOXQ AX, R9; \ + MULXQ 24+x, AX, R11; ADCXQ R15, R10; ADOXQ AX, R10; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R11; ADOXQ AX, R11; \ + MOVQ 24+y, DX; XORL AX, AX; \ + MULXQ 0+x, AX, R12; ADCXQ R8, AX; MOVQ AX, 24+z; \ + MULXQ 8+x, AX, R13; ADCXQ R9, R12; ADOXQ AX, R12; MOVQ R12, 32+z; \ + MULXQ 16+x, AX, R14; ADCXQ R10, R13; ADOXQ AX, R13; MOVQ R13, 40+z; \ + MULXQ 24+x, AX, R15; ADCXQ R11, R14; ADOXQ AX, R14; MOVQ R14, 48+z; \ + MOVL $0, AX;;;;;;;;; ADCXQ AX, R15; ADOXQ AX, R15; MOVQ R15, 56+z; + +// integerMulLeg multiplies x and y and stores in z +// Uses: AX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerMulLeg(z,x,y) \ + MOVQ 0+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, 0+z; MOVQ DX, R15; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R13, R15; \ + ADCQ R14, R10; MOVQ R10, 16+z; \ + ADCQ AX, R11; MOVQ R11, 24+z; \ + ADCQ $0, DX; MOVQ DX, 32+z; \ + MOVQ 8+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R12, R15; MOVQ R15, 8+z; \ + ADCQ R13, R9; \ + ADCQ R14, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + ADCQ 16+z, R9; MOVQ R9, R15; \ + ADCQ 24+z, R10; MOVQ R10, 24+z; \ + ADCQ 32+z, R11; MOVQ R11, 32+z; \ + ADCQ $0, DX; MOVQ DX, 40+z; \ + MOVQ 16+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R12, R15; MOVQ R15, 16+z; \ + ADCQ R13, R9; \ + ADCQ R14, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + ADCQ 24+z, R9; MOVQ R9, R15; \ + ADCQ 32+z, R10; MOVQ R10, 32+z; \ + ADCQ 40+z, R11; MOVQ R11, 40+z; \ + ADCQ $0, DX; MOVQ DX, 48+z; \ + MOVQ 24+y, R8; \ + MOVQ 0+x, AX; MULQ R8; MOVQ AX, R12; MOVQ DX, R9; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R13; MOVQ DX, R10; \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; \ + MOVQ 24+x, AX; MULQ R8; \ + ADDQ R12, R15; MOVQ R15, 24+z; \ + ADCQ R13, R9; \ + ADCQ R14, R10; \ + ADCQ AX, R11; \ + ADCQ $0, DX; \ + ADCQ 32+z, R9; MOVQ R9, 32+z; \ + ADCQ 40+z, R10; MOVQ R10, 40+z; \ + ADCQ 48+z, R11; MOVQ R11, 48+z; \ + ADCQ $0, DX; MOVQ DX, 56+z; + +// integerSqrLeg squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64 +#define integerSqrLeg(z,x) \ + MOVQ 0+x, R8; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, R9; MOVQ DX, R10; /* A[0]*A[1] */ \ + MOVQ 16+x, AX; MULQ R8; MOVQ AX, R14; MOVQ DX, R11; /* A[0]*A[2] */ \ + MOVQ 24+x, AX; MULQ R8; MOVQ AX, R15; MOVQ DX, R12; /* A[0]*A[3] */ \ + MOVQ 24+x, R8; \ + MOVQ 8+x, AX; MULQ R8; MOVQ AX, CX; MOVQ DX, R13; /* A[3]*A[1] */ \ + MOVQ 16+x, AX; MULQ R8; /* A[3]*A[2] */ \ + \ + ADDQ R14, R10;\ + ADCQ R15, R11; MOVL $0, R15;\ + ADCQ CX, R12;\ + ADCQ AX, R13;\ + ADCQ $0, DX; MOVQ DX, R14;\ + MOVQ 8+x, AX; MULQ 16+x;\ + \ + ADDQ AX, R11;\ + ADCQ DX, R12;\ + ADCQ $0, R13;\ + ADCQ $0, R14;\ + ADCQ $0, R15;\ + \ + SHLQ $1, R14, R15; MOVQ R15, 56+z;\ + SHLQ $1, R13, R14; MOVQ R14, 48+z;\ + SHLQ $1, R12, R13; MOVQ R13, 40+z;\ + SHLQ $1, R11, R12; MOVQ R12, 32+z;\ + SHLQ $1, R10, R11; MOVQ R11, 24+z;\ + SHLQ $1, R9, R10; MOVQ R10, 16+z;\ + SHLQ $1, R9; MOVQ R9, 8+z;\ + \ + MOVQ 0+x,AX; MULQ AX; MOVQ AX, 0+z; MOVQ DX, R9;\ + MOVQ 8+x,AX; MULQ AX; MOVQ AX, R10; MOVQ DX, R11;\ + MOVQ 16+x,AX; MULQ AX; MOVQ AX, R12; MOVQ DX, R13;\ + MOVQ 24+x,AX; MULQ AX; MOVQ AX, R14; MOVQ DX, R15;\ + \ + ADDQ 8+z, R9; MOVQ R9, 8+z;\ + ADCQ 16+z, R10; MOVQ R10, 16+z;\ + ADCQ 24+z, R11; MOVQ R11, 24+z;\ + ADCQ 32+z, R12; MOVQ R12, 32+z;\ + ADCQ 40+z, R13; MOVQ R13, 40+z;\ + ADCQ 48+z, R14; MOVQ R14, 48+z;\ + ADCQ 56+z, R15; MOVQ R15, 56+z; + +// integerSqrAdx squares x and stores in z +// Uses: AX, CX, DX, R8-R15, FLAGS +// Instr: x86_64, bmi2, adx +#define integerSqrAdx(z,x) \ + MOVQ 0+x, DX; /* A[0] */ \ + MULXQ 8+x, R8, R14; /* A[1]*A[0] */ XORL R15, R15; \ + MULXQ 16+x, R9, R10; /* A[2]*A[0] */ ADCXQ R14, R9; \ + MULXQ 24+x, AX, CX; /* A[3]*A[0] */ ADCXQ AX, R10; \ + MOVQ 24+x, DX; /* A[3] */ \ + MULXQ 8+x, R11, R12; /* A[1]*A[3] */ ADCXQ CX, R11; \ + MULXQ 16+x, AX, R13; /* A[2]*A[3] */ ADCXQ AX, R12; \ + MOVQ 8+x, DX; /* A[1] */ ADCXQ R15, R13; \ + MULXQ 16+x, AX, CX; /* A[2]*A[1] */ MOVL $0, R14; \ + ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ADCXQ R15, R14; \ + XORL R15, R15; \ + ADOXQ AX, R10; ADCXQ R8, R8; \ + ADOXQ CX, R11; ADCXQ R9, R9; \ + ADOXQ R15, R12; ADCXQ R10, R10; \ + ADOXQ R15, R13; ADCXQ R11, R11; \ + ADOXQ R15, R14; ADCXQ R12, R12; \ + ;;;;;;;;;;;;;;; ADCXQ R13, R13; \ + ;;;;;;;;;;;;;;; ADCXQ R14, R14; \ + MOVQ 0+x, DX; MULXQ DX, AX, CX; /* A[0]^2 */ \ + ;;;;;;;;;;;;;;; MOVQ AX, 0+z; \ + ADDQ CX, R8; MOVQ R8, 8+z; \ + MOVQ 8+x, DX; MULXQ DX, AX, CX; /* A[1]^2 */ \ + ADCQ AX, R9; MOVQ R9, 16+z; \ + ADCQ CX, R10; MOVQ R10, 24+z; \ + MOVQ 16+x, DX; MULXQ DX, AX, CX; /* A[2]^2 */ \ + ADCQ AX, R11; MOVQ R11, 32+z; \ + ADCQ CX, R12; MOVQ R12, 40+z; \ + MOVQ 24+x, DX; MULXQ DX, AX, CX; /* A[3]^2 */ \ + ADCQ AX, R13; MOVQ R13, 48+z; \ + ADCQ CX, R14; MOVQ R14, 56+z; + +// reduceFromDouble finds z congruent to x modulo p such that 0> 63) + // PUT BIT 255 IN CARRY FLAG AND CLEAR + x3 &^= 1 << 63 + + x0, c0 := bits.Add64(xx[0], cx, 0) + x1, c1 := bits.Add64(xx[1], 0, c0) + x2, c2 := bits.Add64(xx[2], 0, c1) + x3, _ = bits.Add64(x3, 0, c2) + + // TEST FOR BIT 255 AGAIN; ONLY TRIGGERED ON OVERFLOW MODULO 2^255-19 + // cx = C[255] ? 0 : 19 + cx = uint64(19) &^ (-(x3 >> 63)) + // CLEAR BIT 255 + x3 &^= 1 << 63 + + xx[0], c0 = bits.Sub64(x0, cx, 0) + xx[1], c1 = bits.Sub64(x1, 0, c0) + xx[2], c2 = bits.Sub64(x2, 0, c1) + xx[3], _ = bits.Sub64(x3, 0, c2) +} + +func red64(z, h *elt64) { + h0, l0 := bits.Mul64(h[0], 38) + h1, l1 := bits.Mul64(h[1], 38) + h2, l2 := bits.Mul64(h[2], 38) + h3, l3 := bits.Mul64(h[3], 38) + + l1, c0 := bits.Add64(h0, l1, 0) + l2, c1 := bits.Add64(h1, l2, c0) + l3, c2 := bits.Add64(h2, l3, c1) + l4, _ := bits.Add64(h3, 0, c2) + + l0, c0 = bits.Add64(l0, z[0], 0) + l1, c1 = bits.Add64(l1, z[1], c0) + l2, c2 = bits.Add64(l2, z[2], c1) + l3, c3 := bits.Add64(l3, z[3], c2) + l4, _ = bits.Add64(l4, 0, c3) + + _, l4 = bits.Mul64(l4, 38) + l0, c0 = bits.Add64(l0, l4, 0) + z[1], c1 = bits.Add64(l1, 0, c0) + z[2], c2 = bits.Add64(l2, 0, c1) + z[3], c3 = bits.Add64(l3, 0, c2) + z[0], _ = bits.Add64(l0, (-c3)&38, 0) +} diff --git a/vendor/github.com/cloudflare/circl/math/fp25519/fp_noasm.go b/vendor/github.com/cloudflare/circl/math/fp25519/fp_noasm.go new file mode 100644 index 00000000..08a07b66 --- /dev/null +++ b/vendor/github.com/cloudflare/circl/math/fp25519/fp_noasm.go @@ -0,0 +1,12 @@ +// +build !amd64 purego + +package fp25519 + +func cmov(x, y *Elt, n uint) { cmovGeneric(x, y, n) } +func cswap(x, y *Elt, n uint) { cswapGeneric(x, y, n) } +func add(z, x, y *Elt) { addGeneric(z, x, y) } +func sub(z, x, y *Elt) { subGeneric(z, x, y) } +func addsub(x, y *Elt) { addsubGeneric(x, y) } +func mul(z, x, y *Elt) { mulGeneric(z, x, y) } +func sqr(z, x *Elt) { sqrGeneric(z, x) } +func modp(z *Elt) { modpGeneric(z) } diff --git a/vendor/modules.txt b/vendor/modules.txt index d1b9fda8..2f4f62f2 100644 --- a/vendor/modules.txt +++ b/vendor/modules.txt @@ -9,6 +9,10 @@ github.com/aead/poly1305 # github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412 github.com/agl/ed25519 github.com/agl/ed25519/edwards25519 +# github.com/cloudflare/circl v0.0.0-20190621185434-0ba9a9382e8b +github.com/cloudflare/circl/dh/x25519 +github.com/cloudflare/circl/math/fp25519 +github.com/cloudflare/circl/internal/conv # github.com/coreos/go-systemd v0.0.0-20190321100706-95778dfbb74e github.com/coreos/go-systemd/activation github.com/coreos/go-systemd/daemon @@ -42,10 +46,10 @@ github.com/kardianos/service # github.com/miekg/dns v1.1.13 github.com/miekg/dns # golang.org/x/crypto v0.0.0-20190530122614-20be4c3c3ed5 -golang.org/x/crypto/curve25519 golang.org/x/crypto/ed25519 golang.org/x/crypto/nacl/box golang.org/x/crypto/nacl/secretbox +golang.org/x/crypto/curve25519 golang.org/x/crypto/ed25519/internal/edwards25519 golang.org/x/crypto/salsa20/salsa golang.org/x/crypto/internal/subtle @@ -64,12 +68,12 @@ golang.org/x/net/internal/iana golang.org/x/net/internal/socket # golang.org/x/sys v0.0.0-20190602015325-4c4f7f33c9ed golang.org/x/sys/windows/svc/mgr +golang.org/x/sys/cpu golang.org/x/sys/windows/svc/eventlog golang.org/x/sys/windows/registry golang.org/x/sys/windows/svc golang.org/x/sys/unix golang.org/x/sys/windows -golang.org/x/sys/cpu # golang.org/x/text v0.3.2 golang.org/x/text/secure/bidirule golang.org/x/text/unicode/bidi