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// Copyright 2012 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 implements the Socialist Millionaires Protocol as described in
// http://www.cypherpunks.ca/otr/Protocol-v2-3.1.0.html. The protocol
// specification is required in order to understand this code and, where
// possible, the variable names in the code match up with the spec.
package otr
import (
"bytes"
"crypto/sha256"
"errors"
"hash"
"math/big"
)
type smpFailure string
func (s smpFailure) Error() string {
return string(s)
}
var smpFailureError = smpFailure("otr: SMP protocol failed")
var smpSecretMissingError = smpFailure("otr: mutual secret needed")
const smpVersion = 1
const (
smpState1 = iota
smpState2
smpState3
smpState4
)
type smpState struct {
state int
a2, a3, b2, b3, pb, qb *big.Int
g2a, g3a *big.Int
g2, g3 *big.Int
g3b, papb, qaqb, ra *big.Int
saved *tlv
secret *big.Int
question string
}
func (c *Conversation) startSMP(question string) (tlvs []tlv) {
if c.smp.state != smpState1 {
tlvs = append(tlvs, c.generateSMPAbort())
}
tlvs = append(tlvs, c.generateSMP1(question))
c.smp.question = ""
c.smp.state = smpState2
return
}
func (c *Conversation) resetSMP() {
c.smp.state = smpState1
c.smp.secret = nil
c.smp.question = ""
}
func (c *Conversation) processSMP(in tlv) (out tlv, complete bool, err error) {
data := in.data
switch in.typ {
case tlvTypeSMPAbort:
if c.smp.state != smpState1 {
err = smpFailureError
}
c.resetSMP()
return
case tlvTypeSMP1WithQuestion:
// We preprocess this into a SMP1 message.
nulPos := bytes.IndexByte(data, 0)
if nulPos == -1 {
err = errors.New("otr: SMP message with question didn't contain a NUL byte")
return
}
c.smp.question = string(data[:nulPos])
data = data[nulPos+1:]
}
numMPIs, data, ok := getU32(data)
if !ok || numMPIs > 20 {
err = errors.New("otr: corrupt SMP message")
return
}
mpis := make([]*big.Int, numMPIs)
for i := range mpis {
var ok bool
mpis[i], data, ok = getMPI(data)
if !ok {
err = errors.New("otr: corrupt SMP message")
return
}
}
switch in.typ {
case tlvTypeSMP1, tlvTypeSMP1WithQuestion:
if c.smp.state != smpState1 {
c.resetSMP()
out = c.generateSMPAbort()
return
}
if c.smp.secret == nil {
err = smpSecretMissingError
return
}
if err = c.processSMP1(mpis); err != nil {
return
}
c.smp.state = smpState3
out = c.generateSMP2()
case tlvTypeSMP2:
if c.smp.state != smpState2 {
c.resetSMP()
out = c.generateSMPAbort()
return
}
if out, err = c.processSMP2(mpis); err != nil {
out = c.generateSMPAbort()
return
}
c.smp.state = smpState4
case tlvTypeSMP3:
if c.smp.state != smpState3 {
c.resetSMP()
out = c.generateSMPAbort()
return
}
if out, err = c.processSMP3(mpis); err != nil {
return
}
c.smp.state = smpState1
c.smp.secret = nil
complete = true
case tlvTypeSMP4:
if c.smp.state != smpState4 {
c.resetSMP()
out = c.generateSMPAbort()
return
}
if err = c.processSMP4(mpis); err != nil {
out = c.generateSMPAbort()
return
}
c.smp.state = smpState1
c.smp.secret = nil
complete = true
default:
panic("unknown SMP message")
}
return
}
func (c *Conversation) calcSMPSecret(mutualSecret []byte, weStarted bool) {
h := sha256.New()
h.Write([]byte{smpVersion})
if weStarted {
h.Write(c.PrivateKey.PublicKey.Fingerprint())
h.Write(c.TheirPublicKey.Fingerprint())
} else {
h.Write(c.TheirPublicKey.Fingerprint())
h.Write(c.PrivateKey.PublicKey.Fingerprint())
}
h.Write(c.SSID[:])
h.Write(mutualSecret)
c.smp.secret = new(big.Int).SetBytes(h.Sum(nil))
}
func (c *Conversation) generateSMP1(question string) tlv {
var randBuf [16]byte
c.smp.a2 = c.randMPI(randBuf[:])
c.smp.a3 = c.randMPI(randBuf[:])
g2a := new(big.Int).Exp(g, c.smp.a2, p)
g3a := new(big.Int).Exp(g, c.smp.a3, p)
h := sha256.New()
r2 := c.randMPI(randBuf[:])
r := new(big.Int).Exp(g, r2, p)
c2 := new(big.Int).SetBytes(hashMPIs(h, 1, r))
d2 := new(big.Int).Mul(c.smp.a2, c2)
d2.Sub(r2, d2)
d2.Mod(d2, q)
if d2.Sign() < 0 {
d2.Add(d2, q)
}
r3 := c.randMPI(randBuf[:])
r.Exp(g, r3, p)
c3 := new(big.Int).SetBytes(hashMPIs(h, 2, r))
d3 := new(big.Int).Mul(c.smp.a3, c3)
d3.Sub(r3, d3)
d3.Mod(d3, q)
if d3.Sign() < 0 {
d3.Add(d3, q)
}
var ret tlv
if len(question) > 0 {
ret.typ = tlvTypeSMP1WithQuestion
ret.data = append(ret.data, question...)
ret.data = append(ret.data, 0)
} else {
ret.typ = tlvTypeSMP1
}
ret.data = appendU32(ret.data, 6)
ret.data = appendMPIs(ret.data, g2a, c2, d2, g3a, c3, d3)
return ret
}
func (c *Conversation) processSMP1(mpis []*big.Int) error {
if len(mpis) != 6 {
return errors.New("otr: incorrect number of arguments in SMP1 message")
}
g2a := mpis[0]
c2 := mpis[1]
d2 := mpis[2]
g3a := mpis[3]
c3 := mpis[4]
d3 := mpis[5]
h := sha256.New()
r := new(big.Int).Exp(g, d2, p)
s := new(big.Int).Exp(g2a, c2, p)
r.Mul(r, s)
r.Mod(r, p)
t := new(big.Int).SetBytes(hashMPIs(h, 1, r))
if c2.Cmp(t) != 0 {
return errors.New("otr: ZKP c2 incorrect in SMP1 message")
}
r.Exp(g, d3, p)
s.Exp(g3a, c3, p)
r.Mul(r, s)
r.Mod(r, p)
t.SetBytes(hashMPIs(h, 2, r))
if c3.Cmp(t) != 0 {
return errors.New("otr: ZKP c3 incorrect in SMP1 message")
}
c.smp.g2a = g2a
c.smp.g3a = g3a
return nil
}
func (c *Conversation) generateSMP2() tlv {
var randBuf [16]byte
b2 := c.randMPI(randBuf[:])
c.smp.b3 = c.randMPI(randBuf[:])
r2 := c.randMPI(randBuf[:])
r3 := c.randMPI(randBuf[:])
r4 := c.randMPI(randBuf[:])
r5 := c.randMPI(randBuf[:])
r6 := c.randMPI(randBuf[:])
g2b := new(big.Int).Exp(g, b2, p)
g3b := new(big.Int).Exp(g, c.smp.b3, p)
r := new(big.Int).Exp(g, r2, p)
h := sha256.New()
c2 := new(big.Int).SetBytes(hashMPIs(h, 3, r))
d2 := new(big.Int).Mul(b2, c2)
d2.Sub(r2, d2)
d2.Mod(d2, q)
if d2.Sign() < 0 {
d2.Add(d2, q)
}
r.Exp(g, r3, p)
c3 := new(big.Int).SetBytes(hashMPIs(h, 4, r))
d3 := new(big.Int).Mul(c.smp.b3, c3)
d3.Sub(r3, d3)
d3.Mod(d3, q)
if d3.Sign() < 0 {
d3.Add(d3, q)
}
c.smp.g2 = new(big.Int).Exp(c.smp.g2a, b2, p)
c.smp.g3 = new(big.Int).Exp(c.smp.g3a, c.smp.b3, p)
c.smp.pb = new(big.Int).Exp(c.smp.g3, r4, p)
c.smp.qb = new(big.Int).Exp(g, r4, p)
r.Exp(c.smp.g2, c.smp.secret, p)
c.smp.qb.Mul(c.smp.qb, r)
c.smp.qb.Mod(c.smp.qb, p)
s := new(big.Int)
s.Exp(c.smp.g2, r6, p)
r.Exp(g, r5, p)
s.Mul(r, s)
s.Mod(s, p)
r.Exp(c.smp.g3, r5, p)
cp := new(big.Int).SetBytes(hashMPIs(h, 5, r, s))
// D5 = r5 - r4 cP mod q and D6 = r6 - y cP mod q
s.Mul(r4, cp)
r.Sub(r5, s)
d5 := new(big.Int).Mod(r, q)
if d5.Sign() < 0 {
d5.Add(d5, q)
}
s.Mul(c.smp.secret, cp)
r.Sub(r6, s)
d6 := new(big.Int).Mod(r, q)
if d6.Sign() < 0 {
d6.Add(d6, q)
}
var ret tlv
ret.typ = tlvTypeSMP2
ret.data = appendU32(ret.data, 11)
ret.data = appendMPIs(ret.data, g2b, c2, d2, g3b, c3, d3, c.smp.pb, c.smp.qb, cp, d5, d6)
return ret
}
func (c *Conversation) processSMP2(mpis []*big.Int) (out tlv, err error) {
if len(mpis) != 11 {
err = errors.New("otr: incorrect number of arguments in SMP2 message")
return
}
g2b := mpis[0]
c2 := mpis[1]
d2 := mpis[2]
g3b := mpis[3]
c3 := mpis[4]
d3 := mpis[5]
pb := mpis[6]
qb := mpis[7]
cp := mpis[8]
d5 := mpis[9]
d6 := mpis[10]
h := sha256.New()
r := new(big.Int).Exp(g, d2, p)
s := new(big.Int).Exp(g2b, c2, p)
r.Mul(r, s)
r.Mod(r, p)
s.SetBytes(hashMPIs(h, 3, r))
if c2.Cmp(s) != 0 {
err = errors.New("otr: ZKP c2 failed in SMP2 message")
return
}
r.Exp(g, d3, p)
s.Exp(g3b, c3, p)
r.Mul(r, s)
r.Mod(r, p)
s.SetBytes(hashMPIs(h, 4, r))
if c3.Cmp(s) != 0 {
err = errors.New("otr: ZKP c3 failed in SMP2 message")
return
}
c.smp.g2 = new(big.Int).Exp(g2b, c.smp.a2, p)
c.smp.g3 = new(big.Int).Exp(g3b, c.smp.a3, p)
r.Exp(g, d5, p)
s.Exp(c.smp.g2, d6, p)
r.Mul(r, s)
s.Exp(qb, cp, p)
r.Mul(r, s)
r.Mod(r, p)
s.Exp(c.smp.g3, d5, p)
t := new(big.Int).Exp(pb, cp, p)
s.Mul(s, t)
s.Mod(s, p)
t.SetBytes(hashMPIs(h, 5, s, r))
if cp.Cmp(t) != 0 {
err = errors.New("otr: ZKP cP failed in SMP2 message")
return
}
var randBuf [16]byte
r4 := c.randMPI(randBuf[:])
r5 := c.randMPI(randBuf[:])
r6 := c.randMPI(randBuf[:])
r7 := c.randMPI(randBuf[:])
pa := new(big.Int).Exp(c.smp.g3, r4, p)
r.Exp(c.smp.g2, c.smp.secret, p)
qa := new(big.Int).Exp(g, r4, p)
qa.Mul(qa, r)
qa.Mod(qa, p)
r.Exp(g, r5, p)
s.Exp(c.smp.g2, r6, p)
r.Mul(r, s)
r.Mod(r, p)
s.Exp(c.smp.g3, r5, p)
cp.SetBytes(hashMPIs(h, 6, s, r))
r.Mul(r4, cp)
d5 = new(big.Int).Sub(r5, r)
d5.Mod(d5, q)
if d5.Sign() < 0 {
d5.Add(d5, q)
}
r.Mul(c.smp.secret, cp)
d6 = new(big.Int).Sub(r6, r)
d6.Mod(d6, q)
if d6.Sign() < 0 {
d6.Add(d6, q)
}
r.ModInverse(qb, p)
qaqb := new(big.Int).Mul(qa, r)
qaqb.Mod(qaqb, p)
ra := new(big.Int).Exp(qaqb, c.smp.a3, p)
r.Exp(qaqb, r7, p)
s.Exp(g, r7, p)
cr := new(big.Int).SetBytes(hashMPIs(h, 7, s, r))
r.Mul(c.smp.a3, cr)
d7 := new(big.Int).Sub(r7, r)
d7.Mod(d7, q)
if d7.Sign() < 0 {
d7.Add(d7, q)
}
c.smp.g3b = g3b
c.smp.qaqb = qaqb
r.ModInverse(pb, p)
c.smp.papb = new(big.Int).Mul(pa, r)
c.smp.papb.Mod(c.smp.papb, p)
c.smp.ra = ra
out.typ = tlvTypeSMP3
out.data = appendU32(out.data, 8)
out.data = appendMPIs(out.data, pa, qa, cp, d5, d6, ra, cr, d7)
return
}
func (c *Conversation) processSMP3(mpis []*big.Int) (out tlv, err error) {
if len(mpis) != 8 {
err = errors.New("otr: incorrect number of arguments in SMP3 message")
return
}
pa := mpis[0]
qa := mpis[1]
cp := mpis[2]
d5 := mpis[3]
d6 := mpis[4]
ra := mpis[5]
cr := mpis[6]
d7 := mpis[7]
h := sha256.New()
r := new(big.Int).Exp(g, d5, p)
s := new(big.Int).Exp(c.smp.g2, d6, p)
r.Mul(r, s)
s.Exp(qa, cp, p)
r.Mul(r, s)
r.Mod(r, p)
s.Exp(c.smp.g3, d5, p)
t := new(big.Int).Exp(pa, cp, p)
s.Mul(s, t)
s.Mod(s, p)
t.SetBytes(hashMPIs(h, 6, s, r))
if t.Cmp(cp) != 0 {
err = errors.New("otr: ZKP cP failed in SMP3 message")
return
}
r.ModInverse(c.smp.qb, p)
qaqb := new(big.Int).Mul(qa, r)
qaqb.Mod(qaqb, p)
r.Exp(qaqb, d7, p)
s.Exp(ra, cr, p)
r.Mul(r, s)
r.Mod(r, p)
s.Exp(g, d7, p)
t.Exp(c.smp.g3a, cr, p)
s.Mul(s, t)
s.Mod(s, p)
t.SetBytes(hashMPIs(h, 7, s, r))
if t.Cmp(cr) != 0 {
err = errors.New("otr: ZKP cR failed in SMP3 message")
return
}
var randBuf [16]byte
r7 := c.randMPI(randBuf[:])
rb := new(big.Int).Exp(qaqb, c.smp.b3, p)
r.Exp(qaqb, r7, p)
s.Exp(g, r7, p)
cr = new(big.Int).SetBytes(hashMPIs(h, 8, s, r))
r.Mul(c.smp.b3, cr)
d7 = new(big.Int).Sub(r7, r)
d7.Mod(d7, q)
if d7.Sign() < 0 {
d7.Add(d7, q)
}
out.typ = tlvTypeSMP4
out.data = appendU32(out.data, 3)
out.data = appendMPIs(out.data, rb, cr, d7)
r.ModInverse(c.smp.pb, p)
r.Mul(pa, r)
r.Mod(r, p)
s.Exp(ra, c.smp.b3, p)
if r.Cmp(s) != 0 {
err = smpFailureError
}
return
}
func (c *Conversation) processSMP4(mpis []*big.Int) error {
if len(mpis) != 3 {
return errors.New("otr: incorrect number of arguments in SMP4 message")
}
rb := mpis[0]
cr := mpis[1]
d7 := mpis[2]
h := sha256.New()
r := new(big.Int).Exp(c.smp.qaqb, d7, p)
s := new(big.Int).Exp(rb, cr, p)
r.Mul(r, s)
r.Mod(r, p)
s.Exp(g, d7, p)
t := new(big.Int).Exp(c.smp.g3b, cr, p)
s.Mul(s, t)
s.Mod(s, p)
t.SetBytes(hashMPIs(h, 8, s, r))
if t.Cmp(cr) != 0 {
return errors.New("otr: ZKP cR failed in SMP4 message")
}
r.Exp(rb, c.smp.a3, p)
if r.Cmp(c.smp.papb) != 0 {
return smpFailureError
}
return nil
}
func (c *Conversation) generateSMPAbort() tlv {
return tlv{typ: tlvTypeSMPAbort}
}
func hashMPIs(h hash.Hash, magic byte, mpis ...*big.Int) []byte {
if h != nil {
h.Reset()
} else {
h = sha256.New()
}
h.Write([]byte{magic})
for _, mpi := range mpis {
h.Write(appendMPI(nil, mpi))
}
return h.Sum(nil)
}