mixing: introduce module

This introduces a new package and module containing code for supporting
peer-to-peer transaction mixing derived from CoinShuffle++.  The mixing
package contains the function and type primitives that will be used by mixing
clients to perform the slot reservation and XOR DC-nets.

mixing/dcnet.go

@@ -0,0 +1,174 @@
+package mixing
+
+import (
+	"encoding/binary"
+	"math/big"
+
+	"github.com/decred/dcrd/crypto/blake256"
+	"github.com/decred/dcrd/wire"
+)
+
+// SRMixPads creates a vector of exponential DC-net pads from a vector of
+// shared secrets with each participating peer in the DC-net.
+func SRMixPads(kp [][]byte, my uint32) []*big.Int {
+	h := blake256.New()
+	scratch := make([]byte, 8)
+
+	pads := make([]*big.Int, len(kp))
+	partialPad := new(big.Int)
+	for j := uint32(0); int(j) < len(kp); j++ {
+		pads[j] = new(big.Int)
+		for i := uint32(0); int(i) < len(kp); i++ {
+			if my == i {
+				continue
+			}
+			binary.LittleEndian.PutUint64(scratch, uint64(j)+1)
+			h.Reset()
+			h.Write(kp[i])
+			h.Write(scratch)
+			digest := h.Sum(nil)
+			partialPad.SetBytes(digest)
+			if my > i {
+				pads[j].Add(pads[j], partialPad)
+			} else {
+				pads[j].Sub(pads[j], partialPad)
+			}
+		}
+		pads[j].Mod(pads[j], F)
+	}
+	return pads
+}
+
+// SRMix creates the padded {m**1, m**2, ..., m**n} message exponentials
+// vector.  Message must be bounded by the field prime and must be unique to
+// every exponential SR run in a mix session to ensure anonymity.
+func SRMix(m *big.Int, pads []*big.Int) []*big.Int {
+	mix := make([]*big.Int, len(pads))
+	exp := new(big.Int)
+	for i := int64(0); i < int64(len(mix)); i++ {
+		mexp := new(big.Int).Exp(m, exp.SetInt64(i+1), nil)
+		mix[i] = mexp.Add(mexp, pads[i])
+		mix[i].Mod(mix[i], F)
+	}
+	return mix
+}
+
+// IntVectorsFromBytes creates a 2-dimensional *big.Int slice from their absolute
+// values as bytes.
+func IntVectorsFromBytes(vs [][][]byte) [][]*big.Int {
+	ints := make([][]*big.Int, len(vs))
+	for i := range vs {
+		ints[i] = make([]*big.Int, len(vs[i]))
+		for j := range vs[i] {
+			ints[i][j] = new(big.Int).SetBytes(vs[i][j])
+		}
+	}
+	return ints
+}
+
+// IntVectorsToBytes creates a 2-dimensional slice of big.Int absolute values as
+// bytes.
+func IntVectorsToBytes(ints [][]*big.Int) [][][]byte {
+	bytes := make([][][]byte, len(ints))
+	for i := range ints {
+		bytes[i] = make([][]byte, len(ints[i]))
+		for j := range ints[i] {
+			bytes[i][j] = ints[i][j].Bytes()
+		}
+	}
+	return bytes
+}
+
+// AddVectors sums each vector element over F, returning a new vector.  When
+// peers are honest (DC-mix pads sum to zero) this creates the unpadded vector
+// of message power sums.
+func AddVectors(vs ...[]*big.Int) []*big.Int {
+	sums := make([]*big.Int, len(vs))
+	for i := range sums {
+		sums[i] = new(big.Int)
+		for j := range vs {
+			sums[i].Add(sums[i], vs[j][i])
+		}
+		sums[i].Mod(sums[i], F)
+	}
+	return sums
+}
+
+// Coefficients calculates a{0}..a{n} for the polynomial:
+//
+//	g(x) = a{0} + a{1}x + a{2}x**2 + ... + a{n-1}x**(n-1) + a{n}x**n  (mod F)
+//
+// where
+//
+//	a{n}   = -1
+//	a{n-1} = -(1/1) *    a{n}*S{0}
+//	a{n-2} = -(1/2) * (a{n-1}*S{0} +   a{n}*S{1})
+//	a{n-3} = -(1/3) * (a{n-2}*S{0} + a{n-1}*S{1} + a{n}*S{2})
+//	...
+//
+// The roots of this polynomial are the set of recovered messages.
+//
+// Note that the returned slice of coefficients is one element larger than the
+// slice of partial sums.
+func Coefficients(S []*big.Int) []*big.Int {
+	n := len(S) + 1
+	a := make([]*big.Int, n)
+	a[len(a)-1] = big.NewInt(-1)
+	a[len(a)-1].Add(a[len(a)-1], F) // a{n} = -1 (mod F) = F - 1
+	scratch := new(big.Int)
+	for i := 0; i < len(a)-1; i++ {
+		a[n-2-i] = new(big.Int)
+		for j := 0; j <= i; j++ {
+			a[n-2-i].Add(a[n-2-i], scratch.Mul(a[n-1-i+j], S[j]))
+		}
+		xinv := scratch.ModInverse(scratch.SetInt64(int64(i)+1), F)
+		xinv.Neg(xinv)
+		a[n-2-i].Mul(a[n-2-i], xinv)
+		a[n-2-i].Mod(a[n-2-i], F)
+	}
+	return a
+}
+
+// IsRoot checks that the message m is a root of the polynomial with
+// coefficients a (mod F) without solving for every root.
+func IsRoot(m *big.Int, a []*big.Int) bool {
+	sum := new(big.Int)
+	scratch := new(big.Int)
+	for i := range a {
+		scratch.Exp(m, scratch.SetInt64(int64(i)), F)
+		scratch.Mul(scratch, a[i])
+		sum.Add(sum, scratch)
+	}
+	sum.Mod(sum, F)
+	return sum.Sign() == 0
+}
+
+// DCMixPads creates the vector of DC-net pads from shared secrets with each mix
+// participant.
+func DCMixPads(kp []wire.MixVect, my uint32) Vec {
+	pads := make(Vec, len(kp))
+	for i := range kp {
+		if i == int(my) {
+			continue
+		}
+		pads.Xor(pads, (Vec)(kp[i]))
+	}
+	return pads
+}
+
+// DCMix creates the DC-net vector of message m xor'd into m's reserved
+// anonymous slot position of the pads DC-net pads.  Panics if len(m) is not the
+// vector's message size.
+func DCMix(pads Vec, m []byte, slot uint32) Vec {
+	if len(m) != Msize {
+		panic("m is not len Msize")
+	}
+
+	dcmix := make(Vec, len(pads))
+	copy(dcmix, pads)
+	slotm := dcmix[slot][:]
+	for i := range m {
+		slotm[i] ^= m[i]
+	}
+	return dcmix
+}

mixing/errors.go

@@ -0,0 +1,30 @@
+// Copyright (c) 2024 The Decred developers
+// Use of this source code is governed by an ISC
+// license that can be found in the LICENSE file.
+
+package mixing
+
+import (
+	"errors"
+	"fmt"
+)
+
+var (
+	ErrInvalidPROrder = errors.New("invalid pair request order")
+
+	ErrInvalidSessionID = errors.New("invalid session ID")
+)
+
+type DecapsulateError struct {
+	SubmittingIndex uint32
+	Err             error
+}
+
+func (e *DecapsulateError) Error() string {
+	return fmt.Sprintf("decapsulate failure of ciphertext by peer %d",
+		e.SubmittingIndex)
+}
+
+func (e *DecapsulateError) Unwrap() error {
+	return e.Err
+}

mixing/expiry.go

@@ -0,0 +1,18 @@
+// Copyright (c) 2023-2024 The Decred developers
+// Use of this source code is governed by an ISC
+// license that can be found in the LICENSE file.
+
+package mixing
+
+import (
+	"time"
+
+	"github.com/decred/dcrd/chaincfg/v3"
+)
+
+// MaxExpiry returns the maximum allowed expiry for a new pair request message
+// created with a blockchain tip at tipHeight.
+func MaxExpiry(tipHeight uint32, params *chaincfg.Params) uint32 {
+	target := params.TargetTimePerBlock
+	return tipHeight + uint32(60*time.Minute/target) + 1
+}

mixing/field.go

@@ -0,0 +1,17 @@
+package mixing
+
+import (
+	"math/big"
+)
+
+// FieldPrime is the field prime 2**127 - 1.
+var F *big.Int
+
+func init() {
+	F, _ = new(big.Int).SetString("7fffffffffffffffffffffffffffffff", 16)
+}
+
+// InField returns whether x is bounded by the field F.
+func InField(x *big.Int) bool {
+	return x.Sign() != -1 && x.Cmp(F) == -1
+}

mixing/flags.go

@@ -0,0 +1,8 @@
+package mixing
+
+const (
+	// PRFlagCanSolveRoots describes a bit in the pair request flags field
+	// indicating support for solving and publishing factored slot
+	// reservation polynomials.
+	PRFlagCanSolveRoots byte = 1 << iota
+)

mixing/go.mod

@@ -0,0 +1,31 @@
+module github.com/decred/dcrd/mixing
+
+go 1.17
+
+require (
+	decred.org/cspp/v2 v2.1.1-0.20240506180342-3c816721a1d8
+	github.com/companyzero/sntrup4591761 v0.0.0-20220309191932-9e0f3af2f07a
+	github.com/davecgh/go-spew v1.1.1
+	github.com/decred/dcrd/chaincfg/chainhash v1.0.4
+	github.com/decred/dcrd/chaincfg/v3 v3.2.0
+	github.com/decred/dcrd/crypto/blake256 v1.0.1
+	github.com/decred/dcrd/dcrec/secp256k1/v4 v4.2.0
+	github.com/decred/dcrd/dcrutil/v4 v4.0.1
+	github.com/decred/dcrd/txscript/v4 v4.1.0
+	github.com/decred/dcrd/wire v1.6.0
+	github.com/decred/slog v1.2.0
+	golang.org/x/crypto v0.7.0
+)
+
+require (
+	github.com/agl/ed25519 v0.0.0-20170116200512-5312a6153412 // indirect
+	github.com/dchest/siphash v1.2.3 // indirect
+	github.com/decred/base58 v1.0.5 // indirect
+	github.com/decred/dcrd/crypto/ripemd160 v1.0.2 // indirect
+	github.com/decred/dcrd/dcrec v1.0.1 // indirect
+	github.com/decred/dcrd/dcrec/edwards/v2 v2.0.3 // indirect
+	github.com/klauspost/cpuid/v2 v2.0.9 // indirect
+	golang.org/x/sync v0.7.0 // indirect
+	golang.org/x/sys v0.6.0 // indirect
+	lukechampine.com/blake3 v1.2.1 // indirect
+)

mixing/go.sum

@@ -0,0 +1,80 @@
+decred.org/cspp/v2 v2.1.1-0.20240506180342-3c816721a1d8 h1:sMvVzvKkxl8S/kjSNV7o7HM3TO7hdVlZvkf8SZpXAYE=
+decred.org/cspp/v2 v2.1.1-0.20240506180342-3c816721a1d8/go.mod h1:9nO3bfvCheOPIFZw5f6sRQ42CjBFB5RKSaJ9Iq6G4MA=
+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/companyzero/sntrup4591761 v0.0.0-20220309191932-9e0f3af2f07a h1:clYxJ3Os0EQUKDDVU8M0oipllX0EkuFNBfhVQuIfyF0=
+github.com/companyzero/sntrup4591761 v0.0.0-20220309191932-9e0f3af2f07a/go.mod h1:z/9Ck1EDixEbBbZ2KH2qNHekEmDLTOZ+FyoIPWWSVOI=
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