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240 lines
5.1 KiB
240 lines
5.1 KiB
// Copyright 2012 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// +build amd64,!gccgo,!appengine
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package curve25519
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// These functions are implemented in the .s files. The names of the functions
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// in the rest of the file are also taken from the SUPERCOP sources to help
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// people following along.
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//go:noescape
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func cswap(inout *[5]uint64, v uint64)
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//go:noescape
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func ladderstep(inout *[5][5]uint64)
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//go:noescape
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func freeze(inout *[5]uint64)
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//go:noescape
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func mul(dest, a, b *[5]uint64)
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//go:noescape
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func square(out, in *[5]uint64)
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// mladder uses a Montgomery ladder to calculate (xr/zr) *= s.
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func mladder(xr, zr *[5]uint64, s *[32]byte) {
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var work [5][5]uint64
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work[0] = *xr
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setint(&work[1], 1)
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setint(&work[2], 0)
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work[3] = *xr
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setint(&work[4], 1)
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j := uint(6)
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var prevbit byte
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for i := 31; i >= 0; i-- {
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for j < 8 {
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bit := ((*s)[i] >> j) & 1
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swap := bit ^ prevbit
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prevbit = bit
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cswap(&work[1], uint64(swap))
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ladderstep(&work)
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j--
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}
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j = 7
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}
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*xr = work[1]
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*zr = work[2]
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}
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func scalarMult(out, in, base *[32]byte) {
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var e [32]byte
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copy(e[:], (*in)[:])
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e[0] &= 248
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e[31] &= 127
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e[31] |= 64
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var t, z [5]uint64
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unpack(&t, base)
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mladder(&t, &z, &e)
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invert(&z, &z)
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mul(&t, &t, &z)
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pack(out, &t)
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}
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func setint(r *[5]uint64, v uint64) {
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r[0] = v
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r[1] = 0
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r[2] = 0
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r[3] = 0
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r[4] = 0
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}
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// unpack sets r = x where r consists of 5, 51-bit limbs in little-endian
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// order.
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func unpack(r *[5]uint64, x *[32]byte) {
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r[0] = uint64(x[0]) |
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uint64(x[1])<<8 |
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uint64(x[2])<<16 |
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uint64(x[3])<<24 |
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uint64(x[4])<<32 |
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uint64(x[5])<<40 |
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uint64(x[6]&7)<<48
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r[1] = uint64(x[6])>>3 |
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uint64(x[7])<<5 |
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uint64(x[8])<<13 |
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uint64(x[9])<<21 |
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uint64(x[10])<<29 |
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uint64(x[11])<<37 |
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uint64(x[12]&63)<<45
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r[2] = uint64(x[12])>>6 |
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uint64(x[13])<<2 |
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uint64(x[14])<<10 |
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uint64(x[15])<<18 |
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uint64(x[16])<<26 |
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uint64(x[17])<<34 |
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uint64(x[18])<<42 |
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uint64(x[19]&1)<<50
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r[3] = uint64(x[19])>>1 |
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uint64(x[20])<<7 |
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uint64(x[21])<<15 |
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uint64(x[22])<<23 |
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uint64(x[23])<<31 |
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uint64(x[24])<<39 |
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uint64(x[25]&15)<<47
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r[4] = uint64(x[25])>>4 |
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uint64(x[26])<<4 |
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uint64(x[27])<<12 |
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uint64(x[28])<<20 |
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uint64(x[29])<<28 |
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uint64(x[30])<<36 |
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uint64(x[31]&127)<<44
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}
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// pack sets out = x where out is the usual, little-endian form of the 5,
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// 51-bit limbs in x.
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func pack(out *[32]byte, x *[5]uint64) {
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t := *x
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freeze(&t)
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out[0] = byte(t[0])
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out[1] = byte(t[0] >> 8)
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out[2] = byte(t[0] >> 16)
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out[3] = byte(t[0] >> 24)
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out[4] = byte(t[0] >> 32)
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out[5] = byte(t[0] >> 40)
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out[6] = byte(t[0] >> 48)
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out[6] ^= byte(t[1]<<3) & 0xf8
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out[7] = byte(t[1] >> 5)
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out[8] = byte(t[1] >> 13)
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out[9] = byte(t[1] >> 21)
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out[10] = byte(t[1] >> 29)
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out[11] = byte(t[1] >> 37)
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out[12] = byte(t[1] >> 45)
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out[12] ^= byte(t[2]<<6) & 0xc0
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out[13] = byte(t[2] >> 2)
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out[14] = byte(t[2] >> 10)
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out[15] = byte(t[2] >> 18)
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out[16] = byte(t[2] >> 26)
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out[17] = byte(t[2] >> 34)
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out[18] = byte(t[2] >> 42)
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out[19] = byte(t[2] >> 50)
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out[19] ^= byte(t[3]<<1) & 0xfe
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out[20] = byte(t[3] >> 7)
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out[21] = byte(t[3] >> 15)
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out[22] = byte(t[3] >> 23)
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out[23] = byte(t[3] >> 31)
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out[24] = byte(t[3] >> 39)
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out[25] = byte(t[3] >> 47)
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out[25] ^= byte(t[4]<<4) & 0xf0
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out[26] = byte(t[4] >> 4)
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out[27] = byte(t[4] >> 12)
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out[28] = byte(t[4] >> 20)
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out[29] = byte(t[4] >> 28)
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out[30] = byte(t[4] >> 36)
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out[31] = byte(t[4] >> 44)
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}
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// invert calculates r = x^-1 mod p using Fermat's little theorem.
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func invert(r *[5]uint64, x *[5]uint64) {
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var z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t [5]uint64
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square(&z2, x) /* 2 */
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square(&t, &z2) /* 4 */
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square(&t, &t) /* 8 */
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mul(&z9, &t, x) /* 9 */
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mul(&z11, &z9, &z2) /* 11 */
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square(&t, &z11) /* 22 */
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mul(&z2_5_0, &t, &z9) /* 2^5 - 2^0 = 31 */
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square(&t, &z2_5_0) /* 2^6 - 2^1 */
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for i := 1; i < 5; i++ { /* 2^20 - 2^10 */
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square(&t, &t)
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}
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mul(&z2_10_0, &t, &z2_5_0) /* 2^10 - 2^0 */
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square(&t, &z2_10_0) /* 2^11 - 2^1 */
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for i := 1; i < 10; i++ { /* 2^20 - 2^10 */
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square(&t, &t)
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}
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mul(&z2_20_0, &t, &z2_10_0) /* 2^20 - 2^0 */
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square(&t, &z2_20_0) /* 2^21 - 2^1 */
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for i := 1; i < 20; i++ { /* 2^40 - 2^20 */
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square(&t, &t)
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}
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mul(&t, &t, &z2_20_0) /* 2^40 - 2^0 */
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square(&t, &t) /* 2^41 - 2^1 */
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for i := 1; i < 10; i++ { /* 2^50 - 2^10 */
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square(&t, &t)
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}
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mul(&z2_50_0, &t, &z2_10_0) /* 2^50 - 2^0 */
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square(&t, &z2_50_0) /* 2^51 - 2^1 */
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for i := 1; i < 50; i++ { /* 2^100 - 2^50 */
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square(&t, &t)
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}
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mul(&z2_100_0, &t, &z2_50_0) /* 2^100 - 2^0 */
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square(&t, &z2_100_0) /* 2^101 - 2^1 */
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for i := 1; i < 100; i++ { /* 2^200 - 2^100 */
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square(&t, &t)
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}
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mul(&t, &t, &z2_100_0) /* 2^200 - 2^0 */
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square(&t, &t) /* 2^201 - 2^1 */
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for i := 1; i < 50; i++ { /* 2^250 - 2^50 */
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square(&t, &t)
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}
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mul(&t, &t, &z2_50_0) /* 2^250 - 2^0 */
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square(&t, &t) /* 2^251 - 2^1 */
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square(&t, &t) /* 2^252 - 2^2 */
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square(&t, &t) /* 2^253 - 2^3 */
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square(&t, &t) /* 2^254 - 2^4 */
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square(&t, &t) /* 2^255 - 2^5 */
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mul(r, &t, &z11) /* 2^255 - 21 */
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}
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