mirror of
https://github.com/go-gitea/gitea
synced 2024-11-05 09:44:26 +00:00
308 lines
9.4 KiB
Go
308 lines
9.4 KiB
Go
// 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) (h macGeneric) {
|
|
initialize(key, &h.r, &h.s)
|
|
return
|
|
}
|
|
|
|
// 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.
|
|
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
|
|
)
|
|
|
|
func initialize(key *[32]byte, r, s *[2]uint64) {
|
|
r[0] = binary.LittleEndian.Uint64(key[0:8]) & rMask0
|
|
r[1] = binary.LittleEndian.Uint64(key[8:16]) & rMask1
|
|
s[0] = binary.LittleEndian.Uint64(key[16:24])
|
|
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)
|
|
}
|