crypto/rsa: check CRT result.

This change adds a check after computing an RSA signature that the
signature is correct. This prevents an error in the CRT computation from
leaking the private key. See references in the linked bug.

benchmark                  old ns/op     new ns/op     delta
BenchmarkRSA2048Sign-3     5713305       6225215       +8.96%

Fixes #12453

Change-Id: I1f24e0b542f7c9a3f7e7ad4e971db3dc440ed3c1
Reviewed-on: https://go-review.googlesource.com/17862Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>
Reviewed-by: Russ Cox <rsc@golang.org>

src/crypto/rsa/pkcs1v15.go

@@ -223,7 +223,7 @@ func SignPKCS1v15(rand io.Reader, priv *PrivateKey, hash crypto.Hash, hashed []b
 	copy(em[k-hashLen:k], hashed)
 
 	m := new(big.Int).SetBytes(em)
-	c, err := decrypt(rand, priv, m)
+	c, err := decryptAndCheck(rand, priv, m)
 	if err != nil {
 		return
 	}

src/crypto/rsa/pss.go

@@ -198,7 +198,7 @@ func signPSSWithSalt(rand io.Reader, priv *PrivateKey, hash crypto.Hash, hashed,
 		return
 	}
 	m := new(big.Int).SetBytes(em)
-	c, err := decrypt(rand, priv, m)
+	c, err := decryptAndCheck(rand, priv, m)
 	if err != nil {
 		return
 	}

src/crypto/rsa/rsa.go

@@ -506,6 +506,21 @@ func decrypt(random io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err er
 	return
 }
 
+func decryptAndCheck(random io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err error) {
+	m, err = decrypt(random, priv, c)
+	if err != nil {
+		return nil, err
+	}
+
+	// In order to defend against errors in the CRT computation, m^e is
+	// calculated, which should match the original ciphertext.
+	check := encrypt(new(big.Int), &priv.PublicKey, m)
+	if c.Cmp(check) != 0 {
+		return nil, errors.New("rsa: internal error")
+	}
+	return m, nil
+}
+
 // DecryptOAEP decrypts ciphertext using RSA-OAEP.
 // If random != nil, DecryptOAEP uses RSA blinding to avoid timing side-channel attacks.
 func DecryptOAEP(hash hash.Hash, random io.Reader, priv *PrivateKey, ciphertext []byte, label []byte) (msg []byte, err error) {

src/crypto/rsa/rsa_test.go

@@ -6,8 +6,10 @@ package rsa
 
 import (
 	"bytes"
+	"crypto"
 	"crypto/rand"
 	"crypto/sha1"
+	"crypto/sha256"
 	"math/big"
 	"testing"
 )
@@ -127,9 +129,10 @@ func fromBase10(base10 string) *big.Int {
 	return i
 }
 
-func BenchmarkRSA2048Decrypt(b *testing.B) {
-	b.StopTimer()
-	priv := &PrivateKey{
+var test2048Key *PrivateKey
+
+func init() {
+	test2048Key = &PrivateKey{
 		PublicKey: PublicKey{
 			N: fromBase10("14314132931241006650998084889274020608918049032671858325988396851334124245188214251956198731333464217832226406088020736932173064754214329009979944037640912127943488972644697423190955557435910767690712778463524983667852819010259499695177313115447116110358524558307947613422897787329221478860907963827160223559690523660574329011927531289655711860504630573766609239332569210831325633840174683944553667352219670930408593321661375473885147973879086994006440025257225431977751512374815915392249179976902953721486040787792801849818254465486633791826766873076617116727073077821584676715609985777563958286637185868165868520557"),
 			E: 3,
@@ -140,14 +143,28 @@ func BenchmarkRSA2048Decrypt(b *testing.B) {
 			fromBase10("109348945610485453577574767652527472924289229538286649661240938988020367005475727988253438647560958573506159449538793540472829815903949343191091817779240101054552748665267574271163617694640513549693841337820602726596756351006149518830932261246698766355347898158548465400674856021497190430791824869615170301029"),
 		},
 	}
-	priv.Precompute()
+	test2048Key.Precompute()
+}
+
+func BenchmarkRSA2048Decrypt(b *testing.B) {
+	b.StopTimer()
 
 	c := fromBase10("8472002792838218989464636159316973636630013835787202418124758118372358261975764365740026024610403138425986214991379012696600761514742817632790916315594342398720903716529235119816755589383377471752116975374952783629225022962092351886861518911824745188989071172097120352727368980275252089141512321893536744324822590480751098257559766328893767334861211872318961900897793874075248286439689249972315699410830094164386544311554704755110361048571142336148077772023880664786019636334369759624917224888206329520528064315309519262325023881707530002540634660750469137117568199824615333883758410040459705787022909848740188613313")
 
 	b.StartTimer()
 
 	for i := 0; i < b.N; i++ {
-		decrypt(nil, priv, c)
+		decrypt(nil, test2048Key, c)
+	}
+}
+
+func BenchmarkRSA2048Sign(b *testing.B) {
+	b.StopTimer()
+	hashed := sha256.Sum256([]byte("testing"))
+	b.StartTimer()
+
+	for i := 0; i < b.N; i++ {
+		SignPKCS1v15(rand.Reader, test2048Key, crypto.SHA256, hashed[:])
 	}
 }