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Diffstat (limited to 'vendor/golang.org/x/crypto/internal/poly1305/sum_generic.go')
| -rw-r--r-- | vendor/golang.org/x/crypto/internal/poly1305/sum_generic.go | 310 |
1 files changed, 310 insertions, 0 deletions
diff --git a/vendor/golang.org/x/crypto/internal/poly1305/sum_generic.go b/vendor/golang.org/x/crypto/internal/poly1305/sum_generic.go new file mode 100644 index 0000000..c942a65 --- /dev/null +++ b/vendor/golang.org/x/crypto/internal/poly1305/sum_generic.go @@ -0,0 +1,310 @@ +// Copyright 2018 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// This file provides the generic implementation of Sum and MAC. Other files +// might provide optimized assembly implementations of some of this code. + +package poly1305 + +import "encoding/binary" + +// Poly1305 [RFC 7539] is a relatively simple algorithm: the authentication tag +// for a 64 bytes message is approximately +// +// s + m[0:16] * r⁴ + m[16:32] * r³ + m[32:48] * r² + m[48:64] * r mod 2¹³⁰ - 5 +// +// for some secret r and s. It can be computed sequentially like +// +// for len(msg) > 0: +// h += read(msg, 16) +// h *= r +// h %= 2¹³⁰ - 5 +// return h + s +// +// All the complexity is about doing performant constant-time math on numbers +// larger than any available numeric type. + +func sumGeneric(out *[TagSize]byte, msg []byte, key *[32]byte) { + h := newMACGeneric(key) + h.Write(msg) + h.Sum(out) +} + +func newMACGeneric(key *[32]byte) macGeneric { + m := macGeneric{} + initialize(key, &m.macState) + return m +} + +// macState holds numbers in saturated 64-bit little-endian limbs. That is, +// the value of [x0, x1, x2] is x[0] + x[1] * 2⁶⁴ + x[2] * 2¹²⁸. +type macState struct { + // h is the main accumulator. It is to be interpreted modulo 2¹³⁰ - 5, but + // can grow larger during and after rounds. It must, however, remain below + // 2 * (2¹³⁰ - 5). + h [3]uint64 + // r and s are the private key components. + r [2]uint64 + s [2]uint64 +} + +type macGeneric struct { + macState + + buffer [TagSize]byte + offset int +} + +// Write splits the incoming message into TagSize chunks, and passes them to +// update. It buffers incomplete chunks. +func (h *macGeneric) Write(p []byte) (int, error) { + nn := len(p) + if h.offset > 0 { + n := copy(h.buffer[h.offset:], p) + if h.offset+n < TagSize { + h.offset += n + return nn, nil + } + p = p[n:] + h.offset = 0 + updateGeneric(&h.macState, h.buffer[:]) + } + if n := len(p) - (len(p) % TagSize); n > 0 { + updateGeneric(&h.macState, p[:n]) + p = p[n:] + } + if len(p) > 0 { + h.offset += copy(h.buffer[h.offset:], p) + } + return nn, nil +} + +// Sum flushes the last incomplete chunk from the buffer, if any, and generates +// the MAC output. It does not modify its state, in order to allow for multiple +// calls to Sum, even if no Write is allowed after Sum. +func (h *macGeneric) Sum(out *[TagSize]byte) { + state := h.macState + if h.offset > 0 { + updateGeneric(&state, h.buffer[:h.offset]) + } + finalize(out, &state.h, &state.s) +} + +// [rMask0, rMask1] is the specified Poly1305 clamping mask in little-endian. It +// clears some bits of the secret coefficient to make it possible to implement +// multiplication more efficiently. +const ( + rMask0 = 0x0FFFFFFC0FFFFFFF + rMask1 = 0x0FFFFFFC0FFFFFFC +) + +// initialize loads the 256-bit key into the two 128-bit secret values r and s. +func initialize(key *[32]byte, m *macState) { + m.r[0] = binary.LittleEndian.Uint64(key[0:8]) & rMask0 + m.r[1] = binary.LittleEndian.Uint64(key[8:16]) & rMask1 + m.s[0] = binary.LittleEndian.Uint64(key[16:24]) + m.s[1] = binary.LittleEndian.Uint64(key[24:32]) +} + +// uint128 holds a 128-bit number as two 64-bit limbs, for use with the +// bits.Mul64 and bits.Add64 intrinsics. +type uint128 struct { + lo, hi uint64 +} + +func mul64(a, b uint64) uint128 { + hi, lo := bitsMul64(a, b) + return uint128{lo, hi} +} + +func add128(a, b uint128) uint128 { + lo, c := bitsAdd64(a.lo, b.lo, 0) + hi, c := bitsAdd64(a.hi, b.hi, c) + if c != 0 { + panic("poly1305: unexpected overflow") + } + return uint128{lo, hi} +} + +func shiftRightBy2(a uint128) uint128 { + a.lo = a.lo>>2 | (a.hi&3)<<62 + a.hi = a.hi >> 2 + return a +} + +// updateGeneric absorbs msg into the state.h accumulator. For each chunk m of +// 128 bits of message, it computes +// +// h₊ = (h + m) * r mod 2¹³⁰ - 5 +// +// If the msg length is not a multiple of TagSize, it assumes the last +// incomplete chunk is the final one. +func updateGeneric(state *macState, msg []byte) { + h0, h1, h2 := state.h[0], state.h[1], state.h[2] + r0, r1 := state.r[0], state.r[1] + + for len(msg) > 0 { + var c uint64 + + // For the first step, h + m, we use a chain of bits.Add64 intrinsics. + // The resulting value of h might exceed 2¹³⁰ - 5, but will be partially + // reduced at the end of the multiplication below. + // + // The spec requires us to set a bit just above the message size, not to + // hide leading zeroes. For full chunks, that's 1 << 128, so we can just + // add 1 to the most significant (2¹²⁸) limb, h2. + if len(msg) >= TagSize { + h0, c = bitsAdd64(h0, binary.LittleEndian.Uint64(msg[0:8]), 0) + h1, c = bitsAdd64(h1, binary.LittleEndian.Uint64(msg[8:16]), c) + h2 += c + 1 + + msg = msg[TagSize:] + } else { + var buf [TagSize]byte + copy(buf[:], msg) + buf[len(msg)] = 1 + + h0, c = bitsAdd64(h0, binary.LittleEndian.Uint64(buf[0:8]), 0) + h1, c = bitsAdd64(h1, binary.LittleEndian.Uint64(buf[8:16]), c) + h2 += c + + msg = nil + } + + // Multiplication of big number limbs is similar to elementary school + // columnar multiplication. Instead of digits, there are 64-bit limbs. + // + // We are multiplying a 3 limbs number, h, by a 2 limbs number, r. + // + // h2 h1 h0 x + // r1 r0 = + // ---------------- + // h2r0 h1r0 h0r0 <-- individual 128-bit products + // + h2r1 h1r1 h0r1 + // ------------------------ + // m3 m2 m1 m0 <-- result in 128-bit overlapping limbs + // ------------------------ + // m3.hi m2.hi m1.hi m0.hi <-- carry propagation + // + m3.lo m2.lo m1.lo m0.lo + // ------------------------------- + // t4 t3 t2 t1 t0 <-- final result in 64-bit limbs + // + // The main difference from pen-and-paper multiplication is that we do + // carry propagation in a separate step, as if we wrote two digit sums + // at first (the 128-bit limbs), and then carried the tens all at once. + + h0r0 := mul64(h0, r0) + h1r0 := mul64(h1, r0) + h2r0 := mul64(h2, r0) + h0r1 := mul64(h0, r1) + h1r1 := mul64(h1, r1) + h2r1 := mul64(h2, r1) + + // Since h2 is known to be at most 7 (5 + 1 + 1), and r0 and r1 have their + // top 4 bits cleared by rMask{0,1}, we know that their product is not going + // to overflow 64 bits, so we can ignore the high part of the products. + // + // This also means that the product doesn't have a fifth limb (t4). + if h2r0.hi != 0 { + panic("poly1305: unexpected overflow") + } + if h2r1.hi != 0 { + panic("poly1305: unexpected overflow") + } + + m0 := h0r0 + m1 := add128(h1r0, h0r1) // These two additions don't overflow thanks again + m2 := add128(h2r0, h1r1) // to the 4 masked bits at the top of r0 and r1. + m3 := h2r1 + + t0 := m0.lo + t1, c := bitsAdd64(m1.lo, m0.hi, 0) + t2, c := bitsAdd64(m2.lo, m1.hi, c) + t3, _ := bitsAdd64(m3.lo, m2.hi, c) + + // Now we have the result as 4 64-bit limbs, and we need to reduce it + // modulo 2¹³⁰ - 5. The special shape of this Crandall prime lets us do + // a cheap partial reduction according to the reduction identity + // + // c * 2¹³⁰ + n = c * 5 + n mod 2¹³⁰ - 5 + // + // because 2¹³⁰ = 5 mod 2¹³⁰ - 5. Partial reduction since the result is + // likely to be larger than 2¹³⁰ - 5, but still small enough to fit the + // assumptions we make about h in the rest of the code. + // + // See also https://speakerdeck.com/gtank/engineering-prime-numbers?slide=23 + + // We split the final result at the 2¹³⁰ mark into h and cc, the carry. + // Note that the carry bits are effectively shifted left by 2, in other + // words, cc = c * 4 for the c in the reduction identity. + h0, h1, h2 = t0, t1, t2&maskLow2Bits + cc := uint128{t2 & maskNotLow2Bits, t3} + + // To add c * 5 to h, we first add cc = c * 4, and then add (cc >> 2) = c. + + h0, c = bitsAdd64(h0, cc.lo, 0) + h1, c = bitsAdd64(h1, cc.hi, c) + h2 += c + + cc = shiftRightBy2(cc) + + h0, c = bitsAdd64(h0, cc.lo, 0) + h1, c = bitsAdd64(h1, cc.hi, c) + h2 += c + + // h2 is at most 3 + 1 + 1 = 5, making the whole of h at most + // + // 5 * 2¹²⁸ + (2¹²⁸ - 1) = 6 * 2¹²⁸ - 1 + } + + state.h[0], state.h[1], state.h[2] = h0, h1, h2 +} + +const ( + maskLow2Bits uint64 = 0x0000000000000003 + maskNotLow2Bits uint64 = ^maskLow2Bits +) + +// select64 returns x if v == 1 and y if v == 0, in constant time. +func select64(v, x, y uint64) uint64 { return ^(v-1)&x | (v-1)&y } + +// [p0, p1, p2] is 2¹³⁰ - 5 in little endian order. +const ( + p0 = 0xFFFFFFFFFFFFFFFB + p1 = 0xFFFFFFFFFFFFFFFF + p2 = 0x0000000000000003 +) + +// finalize completes the modular reduction of h and computes +// +// out = h + s mod 2¹²⁸ +// +func finalize(out *[TagSize]byte, h *[3]uint64, s *[2]uint64) { + h0, h1, h2 := h[0], h[1], h[2] + + // After the partial reduction in updateGeneric, h might be more than + // 2¹³⁰ - 5, but will be less than 2 * (2¹³⁰ - 5). To complete the reduction + // in constant time, we compute t = h - (2¹³⁰ - 5), and select h as the + // result if the subtraction underflows, and t otherwise. + + hMinusP0, b := bitsSub64(h0, p0, 0) + hMinusP1, b := bitsSub64(h1, p1, b) + _, b = bitsSub64(h2, p2, b) + + // h = h if h < p else h - p + h0 = select64(b, h0, hMinusP0) + h1 = select64(b, h1, hMinusP1) + + // Finally, we compute the last Poly1305 step + // + // tag = h + s mod 2¹²⁸ + // + // by just doing a wide addition with the 128 low bits of h and discarding + // the overflow. + h0, c := bitsAdd64(h0, s[0], 0) + h1, _ = bitsAdd64(h1, s[1], c) + + binary.LittleEndian.PutUint64(out[0:8], h0) + binary.LittleEndian.PutUint64(out[8:16], h1) +} |