crypto/rsa: add support for precomputing CRT values.

This speeds up private key operations by 3.5x (for a 2048-bit
modulus).

R=golang-dev, r, rsc1
CC=golang-dev
https://golang.org/cl/4348053

src/pkg/crypto/rsa/rsa.go

@@ -13,6 +13,7 @@ import (
 	"hash"
 	"io"
 	"os"
+	"sync"
 )
 
 var bigZero = big.NewInt(0)
@@ -92,12 +93,16 @@ type PrivateKey struct {
 	PublicKey          // public part.
 	D         *big.Int // private exponent
 	P, Q      *big.Int // prime factors of N
+
+	rwMutex sync.RWMutex // protects the following
+	dP, dQ  *big.Int     // D mod (P-1) (or mod Q-1) 
+	pInv    *big.Int     // p^-1 mod q
 }
 
 // Validate performs basic sanity checks on the key.
 // It returns nil if the key is valid, or else an os.Error describing a problem.
 
-func (priv PrivateKey) Validate() os.Error {
+func (priv *PrivateKey) Validate() os.Error {
 	// Check that p and q are prime. Note that this is just a sanity
 	// check. Since the random witnesses chosen by ProbablyPrime are
 	// deterministic, given the candidate number, it's easy for an attack
@@ -321,6 +326,18 @@ func modInverse(a, n *big.Int) (ia *big.Int, ok bool) {
 	return x, true
 }
 
+// precompute performs some calculations that speed up private key operations
+// in the future.
+func (priv *PrivateKey) precompute() {
+	priv.dP = new(big.Int).Sub(priv.P, bigOne)
+	priv.dP.Mod(priv.D, priv.dP)
+
+	priv.dQ = new(big.Int).Sub(priv.Q, bigOne)
+	priv.dQ.Mod(priv.D, priv.dQ)
+
+	priv.pInv = new(big.Int).ModInverse(priv.P, priv.Q)
+}
+
 // decrypt performs an RSA decryption, resulting in a plaintext integer. If a
 // random source is given, RSA blinding is used.
 func decrypt(rand io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err os.Error) {
@@ -359,7 +376,35 @@ func decrypt(rand io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err os.E
 		c.Mod(c, priv.N)
 	}
 
+	priv.rwMutex.RLock()
+
+	if priv.dP == nil && priv.P != nil {
+		priv.rwMutex.RUnlock()
+		priv.rwMutex.Lock()
+		if priv.dP == nil && priv.P != nil {
+			priv.precompute()
+		}
+		priv.rwMutex.Unlock()
+		priv.rwMutex.RLock()
+	}
+
+	if priv.dP == nil {
 		m = new(big.Int).Exp(c, priv.D, priv.N)
+	} else {
+		// We have the precalculated values needed for the CRT.
+		m = new(big.Int).Exp(c, priv.dP, priv.P)
+		m2 := new(big.Int).Exp(c, priv.dQ, priv.Q)
+		m2.Sub(m2, m)
+		if m2.Sign() < 0 {
+			m2.Add(m2, priv.Q)
+		}
+		m2.Mul(m2, priv.pInv)
+		m2.Mod(m2, priv.Q)
+		m2.Mul(m2, priv.P)
+		m.Add(m, m2)
+	}
+
+	priv.rwMutex.RUnlock()
 
 	if ir != nil {
 		// Unblind.

src/pkg/crypto/rsa/rsa_test.go

@@ -13,13 +13,11 @@ import (
 )
 
 func TestKeyGeneration(t *testing.T) {
-	random := rand.Reader
-
 	size := 1024
 	if testing.Short() {
 		size = 128
 	}
-	priv, err := GenerateKey(random, size)
+	priv, err := GenerateKey(rand.Reader, size)
 	if err != nil {
 		t.Errorf("failed to generate key")
 	}
@@ -34,7 +32,7 @@ func TestKeyGeneration(t *testing.T) {
 		t.Errorf("got:%v, want:%v (%s)", m2, m, priv)
 	}
 
-	m3, err := decrypt(random, priv, c)
+	m3, err := decrypt(rand.Reader, priv, c)
 	if err != nil {
 		t.Errorf("error while decrypting (blind): %s", err)
 	}
@@ -43,6 +41,36 @@ func TestKeyGeneration(t *testing.T) {
 	}
 }
 
+func fromBase10(base10 string) *big.Int {
+	i := new(big.Int)
+	i.SetString(base10, 10)
+	return i
+}
+
+func BenchmarkRSA2048Decrypt(b *testing.B) {
+	b.StopTimer()
+	priv := &PrivateKey{
+		PublicKey: PublicKey{
+			N: fromBase10("14314132931241006650998084889274020608918049032671858325988396851334124245188214251956198731333464217832226406088020736932173064754214329009979944037640912127943488972644697423190955557435910767690712778463524983667852819010259499695177313115447116110358524558307947613422897787329221478860907963827160223559690523660574329011927531289655711860504630573766609239332569210831325633840174683944553667352219670930408593321661375473885147973879086994006440025257225431977751512374815915392249179976902953721486040787792801849818254465486633791826766873076617116727073077821584676715609985777563958286637185868165868520557"),
+			E: 3,
+		},
+		D:    fromBase10("9542755287494004433998723259516013739278699355114572217325597900889416163458809501304132487555642811888150937392013824621448709836142886006653296025093941418628992648429798282127303704957273845127141852309016655778568546006839666463451542076964744073572349705538631742281931858219480985907271975884773482372966847639853897890615456605598071088189838676728836833012254065983259638538107719766738032720239892094196108713378822882383694456030043492571063441943847195939549773271694647657549658603365629458610273821292232646334717612674519997533901052790334279661754176490593041941863932308687197618671528035670452762731"),
+		P:    fromBase10("130903255182996722426771613606077755295583329135067340152947172868415809027537376306193179624298874215608270802054347609836776473930072411958753044562214537013874103802006369634761074377213995983876788718033850153719421695468704276694983032644416930879093914927146648402139231293035971427838068945045019075433"),
+		Q:    fromBase10("109348945610485453577574767652527472924289229538286649661240938988020367005475727988253438647560958573506159449538793540472829815903949343191091817779240101054552748665267574271163617694640513549693841337820602726596756351006149518830932261246698766355347898158548465400674856021497190430791824869615170301029"),
+		dP:   fromBase10("87268836788664481617847742404051836863722219423378226768631448578943872685024917537462119749532582810405513868036231739891184315953381607972502029708143024675916069201337579756507382918142663989251192478689233435812947796979136184463322021762944620586062609951431098934759487528690647618558712630030012716955"),
+		dQ:   fromBase10("72899297073656969051716511768351648616192819692191099774160625992013578003650485325502292431707305715670772966359195693648553210602632895460727878519493400703035165776845049514109078463093675699795894225213735151064504234004099679220621507497799177570231932105698976933783237347664793620527883246410113534019"),
+		pInv: fromBase10("74869409553139788560900845468611147033712996668881056834763135832685363742570238895177002569942885113085732953539155658733820506625547963252830054212438299203610450637505048191657603373418647673681301519272938658040214027296599301464801590350649336869828810772124696732917293401353635425510209977859621865087"),
+	}
+
+	c := fromBase10("1000")
+
+	b.StartTimer()
+
+	for i := 0; i < b.N; i++ {
+		decrypt(nil, priv, c)
+	}
+}
+
 type testEncryptOAEPMessage struct {
 	in   []byte
 	seed []byte
@@ -85,10 +113,12 @@ func TestDecryptOAEP(t *testing.T) {
 	for i, test := range testEncryptOAEPData {
 		n.SetString(test.modulus, 16)
 		d.SetString(test.d, 16)
-		private := PrivateKey{PublicKey{n, test.e}, d, nil, nil}
+		private := new(PrivateKey)
+		private.PublicKey = PublicKey{n, test.e}
+		private.D = d
 
 		for j, message := range test.msgs {
-			out, err := DecryptOAEP(sha1, nil, &private, message.out, nil)
+			out, err := DecryptOAEP(sha1, nil, private, message.out, nil)
 			if err != nil {
 				t.Errorf("#%d,%d error: %s", i, j, err)
 			} else if bytes.Compare(out, message.in) != 0 {
@@ -96,7 +126,7 @@ func TestDecryptOAEP(t *testing.T) {
 			}
 
 			// Decrypt with blinding.
-			out, err = DecryptOAEP(sha1, random, &private, message.out, nil)
+			out, err = DecryptOAEP(sha1, random, private, message.out, nil)
 			if err != nil {
 				t.Errorf("#%d,%d (blind) error: %s", i, j, err)
 			} else if bytes.Compare(out, message.in) != 0 {

src/pkg/crypto/x509/x509.go

@@ -54,20 +54,21 @@ func ParsePKCS1PrivateKey(der []byte) (key *rsa.PrivateKey, err os.Error) {
 		return
 	}
 
-	key = &rsa.PrivateKey{
-		PublicKey: rsa.PublicKey{
+	key = new(rsa.PrivateKey)
+	key.PublicKey = rsa.PublicKey{
 		E: priv.E,
 		N: new(big.Int).SetBytes(priv.N.Bytes),
-		},
-		D: new(big.Int).SetBytes(priv.D.Bytes),
-		P: new(big.Int).SetBytes(priv.P.Bytes),
-		Q: new(big.Int).SetBytes(priv.Q.Bytes),
 	}
 
+	key.D = new(big.Int).SetBytes(priv.D.Bytes)
+	key.P = new(big.Int).SetBytes(priv.P.Bytes)
+	key.Q = new(big.Int).SetBytes(priv.Q.Bytes)
+
 	err = key.Validate()
 	if err != nil {
 		return nil, err
 	}
+
 	return
 }
 

src/pkg/crypto/x509/x509_test.go

@@ -11,7 +11,6 @@ import (
 	"crypto/rsa"
 	"encoding/hex"
 	"encoding/pem"
-	"reflect"
 	"testing"
 	"time"
 )
@@ -22,7 +21,11 @@ func TestParsePKCS1PrivateKey(t *testing.T) {
 	if err != nil {
 		t.Errorf("Failed to parse private key: %s", err)
 	}
-	if !reflect.DeepEqual(priv, rsaPrivateKey) {
+	if priv.PublicKey.N.Cmp(rsaPrivateKey.PublicKey.N) != 0 ||
+		priv.PublicKey.E != rsaPrivateKey.PublicKey.E ||
+		priv.D.Cmp(rsaPrivateKey.D) != 0 ||
+		priv.P.Cmp(rsaPrivateKey.P) != 0 ||
+		priv.Q.Cmp(rsaPrivateKey.Q) != 0 {
 		t.Errorf("got:%+v want:%+v", priv, rsaPrivateKey)
 	}
 }