am 56ede7fa: Merge "support e=65537 for libmincrypt, DumpPublicKey" (316f10df) · Commits · e / os / android_system_core

include/mincrypt/rsa.h

+6 −5

Original line number	Diff line number	Diff line
		@@ -42,6 +42,7 @@ typedef struct RSAPublicKey {
		uint32_t n0inv; /* -1 / n[0] mod 2^32 */
		uint32_t n[RSANUMWORDS]; /* modulus as little endian array */
		uint32_t rr[RSANUMWORDS]; /* R^2 as little endian array */
		int exponent; /* 3 or 65537 */
		} RSAPublicKey;

		int RSA_verify(const RSAPublicKey *key,

libmincrypt/Android.mk

+2 −2

Original line number	Diff line number	Diff line
		@@ -4,13 +4,13 @@ LOCAL_PATH := $(call my-dir)
		include $(CLEAR_VARS)

		LOCAL_MODULE := libmincrypt
		LOCAL_SRC_FILES := rsa.c sha.c
		LOCAL_SRC_FILES := rsa.c rsa_e_3.c rsa_e_f4.c sha.c
		include $(BUILD_STATIC_LIBRARY)

		include $(CLEAR_VARS)

		LOCAL_MODULE := libmincrypt
		LOCAL_SRC_FILES := rsa.c sha.c
		LOCAL_SRC_FILES := rsa.c rsa_e_3.c rsa_e_f4.c sha.c
		include $(BUILD_HOST_STATIC_LIBRARY)

libmincrypt/rsa.c

+22 −166

Original line number	Diff line number	Diff line
		/* rsa.c
		**
		** Copyright 2008, The Android Open Source Project
		** Copyright 2012, The Android Open Source Project
		**
		** Redistribution and use in source and binary forms, with or without
		** modification, are permitted provided that the following conditions are met:
		@@ -26,173 +26,29 @@
		*/

		#include "mincrypt/rsa.h"
		#include "mincrypt/sha.h"

		/* a[] -= mod */
		static void subM(const RSAPublicKey key, uint32_t a) {
		int64_t A = 0;
		int i;
		for (i = 0; i < key->len; ++i) {
		A += (uint64_t)a[i] - key->n[i];
		a[i] = (uint32_t)A;
		A >>= 32;
		}
		}

		/* return a[] >= mod */
		static int geM(const RSAPublicKey key, const uint32_t a) {
		int i;
		for (i = key->len; i;) {
		--i;
		if (a[i] < key->n[i]) return 0;
		if (a[i] > key->n[i]) return 1;
		}
		return 1; /* equal */
		}

		/* montgomery c[] += a * b[] / R % mod */
		static void montMulAdd(const RSAPublicKey *key,
		uint32_t* c,
		const uint32_t a,
		const uint32_t* b) {
		uint64_t A = (uint64_t)a * b[0] + c[0];
		uint32_t d0 = (uint32_t)A * key->n0inv;
		uint64_t B = (uint64_t)d0 * key->n[0] + (uint32_t)A;
		int i;

		for (i = 1; i < key->len; ++i) {
		A = (A >> 32) + (uint64_t)a * b[i] + c[i];
		B = (B >> 32) + (uint64_t)d0 * key->n[i] + (uint32_t)A;
		c[i - 1] = (uint32_t)B;
		}

		A = (A >> 32) + (B >> 32);

		c[i - 1] = (uint32_t)A;

		if (A >> 32) {
		subM(key, c);
		}
		}

		/* montgomery c[] = a[] * b[] / R % mod */
		static void montMul(const RSAPublicKey *key,
		uint32_t* c,
		const uint32_t* a,
		const uint32_t* b) {
		int i;
		for (i = 0; i < key->len; ++i) {
		c[i] = 0;
		}
		for (i = 0; i < key->len; ++i) {
		montMulAdd(key, c, a[i], b);
		}
		}

		/* In-place public exponentiation.
		** Input and output big-endian byte array in inout.
		*/
		static void modpow3(const RSAPublicKey *key,
		uint8_t* inout) {
		uint32_t a[RSANUMWORDS];
		uint32_t aR[RSANUMWORDS];
		uint32_t aaR[RSANUMWORDS];
		uint32_t aaa = aR; / Re-use location. */
		int i;

		/* Convert from big endian byte array to little endian word array. */
		for (i = 0; i < key->len; ++i) {
		uint32_t tmp =
		(inout[((key->len - 1 - i) * 4) + 0] << 24) \|
		(inout[((key->len - 1 - i) * 4) + 1] << 16) \|
		(inout[((key->len - 1 - i) * 4) + 2] << 8) \|
		(inout[((key->len - 1 - i) * 4) + 3] << 0);
		a[i] = tmp;
		}

		montMul(key, aR, a, key->rr); /* aR = a * RR / R mod M */
		montMul(key, aaR, aR, aR); /* aaR = aR * aR / R mod M */
		montMul(key, aaa, aaR, a); /* aaa = aaR * a / R mod M */

		/* Make sure aaa < mod; aaa is at most 1x mod too large. */
		if (geM(key, aaa)) {
		subM(key, aaa);
		}

		/* Convert to bigendian byte array */
		for (i = key->len - 1; i >= 0; --i) {
		uint32_t tmp = aaa[i];
		*inout++ = tmp >> 24;
		*inout++ = tmp >> 16;
		*inout++ = tmp >> 8;
		*inout++ = tmp >> 0;
		}
		}
		int RSA_e_f4_verify(const RSAPublicKey* key,
		const uint8_t* signature,
		const int len,
		const uint8_t* sha);

		/* Expected PKCS1.5 signature padding bytes, for a keytool RSA signature.
		** Has the 0-length optional parameter encoded in the ASN1 (as opposed to the
		** other flavor which omits the optional parameter entirely). This code does not
		** accept signatures without the optional parameter.
		*/
		static const uint8_t padding[RSANUMBYTES - SHA_DIGEST_SIZE] = {
		0x00,0x01,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x00,
		0x30,0x21,0x30,0x09,0x06,0x05,0x2b,0x0e,0x03,0x02,0x1a,0x05,0x00,
		0x04,0x14
		};
		int RSA_e_3_verify(const RSAPublicKey *key,
		const uint8_t *signature,
		const int len,
		const uint8_t *sha);

		/* Verify a 2048 bit RSA PKCS1.5 signature against an expected SHA-1 hash.
		** Returns 0 on failure, 1 on success.
		*/
		int RSA_verify(const RSAPublicKey *key,
		const uint8_t *signature,
		const int len,
		const uint8_t *sha) {
		uint8_t buf[RSANUMBYTES];
		int i;

		if (key->len != RSANUMWORDS) {
		return 0; /* Wrong key passed in. */
		}

		if (len != sizeof(buf)) {
		return 0; /* Wrong input length. */
		}

		for (i = 0; i < len; ++i) {
		buf[i] = signature[i];
		}

		modpow3(key, buf);

		/* Check pkcs1.5 padding bytes. */
		for (i = 0; i < (int) sizeof(padding); ++i) {
		if (buf[i] != padding[i]) {
		switch (key->exponent) {
		case 3:
		return RSA_e_3_verify(key, signature, len, sha);
		break;
		case 65537:
		return RSA_e_f4_verify(key, signature, len, sha);
		break;
		default:
		return 0;
		}
		}

		/* Check sha digest matches. */
		for (; i < len; ++i) {
		if (buf[i] != *sha++) {
		return 0;
		}
		}

		return 1;
		}

libmincrypt/rsa_e_3.c

0 → 100644

+202 −0

Original line number	Diff line number	Diff line
		/* rsa_e_3.c
		**
		** Copyright 2008, The Android Open Source Project
		**
		** Redistribution and use in source and binary forms, with or without
		** modification, are permitted provided that the following conditions are met:
		** * Redistributions of source code must retain the above copyright
		** notice, this list of conditions and the following disclaimer.
		** * Redistributions in binary form must reproduce the above copyright
		** notice, this list of conditions and the following disclaimer in the
		** documentation and/or other materials provided with the distribution.
		** * Neither the name of Google Inc. nor the names of its contributors may
		** be used to endorse or promote products derived from this software
		** without specific prior written permission.
		**
		** THIS SOFTWARE IS PROVIDED BY Google Inc. ``AS IS'' AND ANY EXPRESS OR
		** IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
		** MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
		** EVENT SHALL Google Inc. BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
		** SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
		** PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
		** OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
		** WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
		** OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
		** ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
		*/

		#include "mincrypt/rsa.h"
		#include "mincrypt/sha.h"

		/* a[] -= mod */
		static void subM(const RSAPublicKey key, uint32_t a) {
		int64_t A = 0;
		int i;
		for (i = 0; i < key->len; ++i) {
		A += (uint64_t)a[i] - key->n[i];
		a[i] = (uint32_t)A;
		A >>= 32;
		}
		}

		/* return a[] >= mod */
		static int geM(const RSAPublicKey key, const uint32_t a) {
		int i;
		for (i = key->len; i;) {
		--i;
		if (a[i] < key->n[i]) return 0;
		if (a[i] > key->n[i]) return 1;
		}
		return 1; /* equal */
		}

		/* montgomery c[] += a * b[] / R % mod */
		static void montMulAdd(const RSAPublicKey *key,
		uint32_t* c,
		const uint32_t a,
		const uint32_t* b) {
		uint64_t A = (uint64_t)a * b[0] + c[0];
		uint32_t d0 = (uint32_t)A * key->n0inv;
		uint64_t B = (uint64_t)d0 * key->n[0] + (uint32_t)A;
		int i;

		for (i = 1; i < key->len; ++i) {
		A = (A >> 32) + (uint64_t)a * b[i] + c[i];
		B = (B >> 32) + (uint64_t)d0 * key->n[i] + (uint32_t)A;
		c[i - 1] = (uint32_t)B;
		}

		A = (A >> 32) + (B >> 32);

		c[i - 1] = (uint32_t)A;

		if (A >> 32) {
		subM(key, c);
		}
		}

		/* montgomery c[] = a[] * b[] / R % mod */
		static void montMul(const RSAPublicKey *key,
		uint32_t* c,
		const uint32_t* a,
		const uint32_t* b) {
		int i;
		for (i = 0; i < key->len; ++i) {
		c[i] = 0;
		}
		for (i = 0; i < key->len; ++i) {
		montMulAdd(key, c, a[i], b);
		}
		}

		/* In-place public exponentiation.
		** Input and output big-endian byte array in inout.
		*/
		static void modpow3(const RSAPublicKey *key,
		uint8_t* inout) {
		uint32_t a[RSANUMWORDS];
		uint32_t aR[RSANUMWORDS];
		uint32_t aaR[RSANUMWORDS];
		uint32_t aaa = aR; / Re-use location. */
		int i;

		/* Convert from big endian byte array to little endian word array. */
		for (i = 0; i < key->len; ++i) {
		uint32_t tmp =
		(inout[((key->len - 1 - i) * 4) + 0] << 24) \|
		(inout[((key->len - 1 - i) * 4) + 1] << 16) \|
		(inout[((key->len - 1 - i) * 4) + 2] << 8) \|
		(inout[((key->len - 1 - i) * 4) + 3] << 0);
		a[i] = tmp;
		}

		montMul(key, aR, a, key->rr); /* aR = a * RR / R mod M */
		montMul(key, aaR, aR, aR); /* aaR = aR * aR / R mod M */
		montMul(key, aaa, aaR, a); /* aaa = aaR * a / R mod M */

		/* Make sure aaa < mod; aaa is at most 1x mod too large. */
		if (geM(key, aaa)) {
		subM(key, aaa);
		}

		/* Convert to bigendian byte array */
		for (i = key->len - 1; i >= 0; --i) {
		uint32_t tmp = aaa[i];
		*inout++ = tmp >> 24;
		*inout++ = tmp >> 16;
		*inout++ = tmp >> 8;
		*inout++ = tmp >> 0;
		}
		}

		/* Expected PKCS1.5 signature padding bytes, for a keytool RSA signature.
		** Has the 0-length optional parameter encoded in the ASN1 (as opposed to the
		** other flavor which omits the optional parameter entirely). This code does not
		** accept signatures without the optional parameter.
		*/
		static const uint8_t padding[RSANUMBYTES - SHA_DIGEST_SIZE] = {
		0x00,0x01,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,
		0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x00,
		0x30,0x21,0x30,0x09,0x06,0x05,0x2b,0x0e,0x03,0x02,0x1a,0x05,0x00,
		0x04,0x14
		};

		/* Verify a 2048 bit RSA e=3 PKCS1.5 signature against an expected SHA-1 hash.
		** Returns 0 on failure, 1 on success.
		*/
		int RSA_e_3_verify(const RSAPublicKey *key,
		const uint8_t *signature,
		const int len,
		const uint8_t *sha) {
		uint8_t buf[RSANUMBYTES];
		int i;

		if (key->len != RSANUMWORDS) {
		return 0; /* Wrong key passed in. */
		}

		if (len != sizeof(buf)) {
		return 0; /* Wrong input length. */
		}

		if (key->exponent != 3) {
		return 0; // Wrong exponent.
		}

		for (i = 0; i < len; ++i) {
		buf[i] = signature[i];
		}

		modpow3(key, buf);

		/* Check pkcs1.5 padding bytes. */
		for (i = 0; i < (int) sizeof(padding); ++i) {
		if (buf[i] != padding[i]) {
		return 0;
		}
		}

		/* Check sha digest matches. */
		for (; i < len; ++i) {
		if (buf[i] != *sha++) {
		return 0;
		}
		}

		return 1;
		}

libmincrypt/rsa_e_f4.c

0 → 100644

+196 −0

Original line number	Diff line number	Diff line
		/* rsa_e_f4.c
		**
		** Copyright 2012, The Android Open Source Project
		**
		** Redistribution and use in source and binary forms, with or without
		** modification, are permitted provided that the following conditions are met:
		** * Redistributions of source code must retain the above copyright
		** notice, this list of conditions and the following disclaimer.
		** * Redistributions in binary form must reproduce the above copyright
		** notice, this list of conditions and the following disclaimer in the
		** documentation and/or other materials provided with the distribution.
		** * Neither the name of Google Inc. nor the names of its contributors may
		** be used to endorse or promote products derived from this software
		** without specific prior written permission.
		**
		** THIS SOFTWARE IS PROVIDED BY Google Inc. ``AS IS'' AND ANY EXPRESS OR
		** IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
		** MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
		** EVENT SHALL Google Inc. BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
		** SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
		** PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
		** OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
		** WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
		** OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
		** ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
		*/

		#include "mincrypt/rsa.h"
		#include "mincrypt/sha.h"

		// a[] -= mod
		static void subM(const RSAPublicKey* key,
		uint32_t* a) {
		int64_t A = 0;
		int i;
		for (i = 0; i < key->len; ++i) {
		A += (uint64_t)a[i] - key->n[i];
		a[i] = (uint32_t)A;
		A >>= 32;
		}
		}

		// return a[] >= mod
		static int geM(const RSAPublicKey* key,
		const uint32_t* a) {
		int i;
		for (i = key->len; i;) {
		--i;
		if (a[i] < key->n[i]) return 0;
		if (a[i] > key->n[i]) return 1;
		}
		return 1; // equal
		}

		// montgomery c[] += a * b[] / R % mod
		static void montMulAdd(const RSAPublicKey* key,
		uint32_t* c,
		const uint32_t a,
		const uint32_t* b) {
		uint64_t A = (uint64_t)a * b[0] + c[0];
		uint32_t d0 = (uint32_t)A * key->n0inv;
		uint64_t B = (uint64_t)d0 * key->n[0] + (uint32_t)A;
		int i;

		for (i = 1; i < key->len; ++i) {
		A = (A >> 32) + (uint64_t)a * b[i] + c[i];
		B = (B >> 32) + (uint64_t)d0 * key->n[i] + (uint32_t)A;
		c[i - 1] = (uint32_t)B;
		}

		A = (A >> 32) + (B >> 32);

		c[i - 1] = (uint32_t)A;

		if (A >> 32) {
		subM(key, c);
		}
		}

		// montgomery c[] = a[] * b[] / R % mod
		static void montMul(const RSAPublicKey* key,
		uint32_t* c,
		const uint32_t* a,
		const uint32_t* b) {
		int i;
		for (i = 0; i < key->len; ++i) {
		c[i] = 0;
		}
		for (i = 0; i < key->len; ++i) {
		montMulAdd(key, c, a[i], b);
		}
		}

		// In-place public exponentiation.
		// Input and output big-endian byte array in inout.
		static void modpowF4(const RSAPublicKey* key,
		uint8_t* inout) {
		uint32_t a[RSANUMWORDS];
		uint32_t aR[RSANUMWORDS];
		uint32_t aaR[RSANUMWORDS];
		uint32_t* aaa = aaR; // Re-use location.
		int i;

		// Convert from big endian byte array to little endian word array.
		for (i = 0; i < key->len; ++i) {
		uint32_t tmp =
		(inout[((key->len - 1 - i) * 4) + 0] << 24) \|
		(inout[((key->len - 1 - i) * 4) + 1] << 16) \|
		(inout[((key->len - 1 - i) * 4) + 2] << 8) \|
		(inout[((key->len - 1 - i) * 4) + 3] << 0);
		a[i] = tmp;
		}

		montMul(key, aR, a, key->rr); // aR = a * RR / R mod M
		for (i = 0; i < 16; i += 2) {
		montMul(key, aaR, aR, aR); // aaR = aR * aR / R mod M
		montMul(key, aR, aaR, aaR); // aR = aaR * aaR / R mod M
		}
		montMul(key, aaa, aR, a); // aaa = aR * a / R mod M

		// Make sure aaa < mod; aaa is at most 1x mod too large.
		if (geM(key, aaa)) {
		subM(key, aaa);
		}

		// Convert to bigendian byte array
		for (i = key->len - 1; i >= 0; --i) {
		uint32_t tmp = aaa[i];
		*inout++ = tmp >> 24;
		*inout++ = tmp >> 16;
		*inout++ = tmp >> 8;
		*inout++ = tmp >> 0;
		}
		}

		// Expected PKCS1.5 signature padding bytes, for a keytool RSA signature.
		// Has the 0-length optional parameter encoded in the ASN1 (as opposed to the
		// other flavor which omits the optional parameter entirely). This code does not
		// accept signatures without the optional parameter.
		/*
		static const uint8_t padding[RSANUMBYTES] = {
		0x00,0x01,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0xff,0x00,0x30,0x21,0x30,0x09,0x06,0x05,0x2b,0x0e,0x03,0x02,0x1a,0x05,0x00,0x04,0x14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
		};
		*/

		// SHA-1 of PKCS1.5 signature padding for 2048 bit, as above.
		// At the location of the bytes of the hash all 00 are hashed.
		static const uint8_t kExpectedPadShaRsa2048[SHA_DIGEST_SIZE] = {
		0xdc, 0xbd, 0xbe, 0x42, 0xd5, 0xf5, 0xa7, 0x2e, 0x6e, 0xfc,
		0xf5, 0x5d, 0xaf, 0x9d, 0xea, 0x68, 0x7c, 0xfb, 0xf1, 0x67
		};

		// Verify a 2048 bit RSA e=65537 PKCS1.5 signature against an expected
		// SHA-1 hash. Returns 0 on failure, 1 on success.
		int RSA_e_f4_verify(const RSAPublicKey* key,
		const uint8_t* signature,
		const int len,
		const uint8_t* sha) {
		uint8_t buf[RSANUMBYTES];
		int i;

		if (key->len != RSANUMWORDS) {
		return 0; // Wrong key passed in.
		}

		if (len != sizeof(buf)) {
		return 0; // Wrong input length.
		}

		if (key->exponent != 65537) {
		return 0; // Wrong exponent.
		}

		for (i = 0; i < len; ++i) { // Copy input to local workspace.
		buf[i] = signature[i];
		}

		modpowF4(key, buf); // In-place exponentiation.

		// Xor sha portion, so it all becomes 00 iff equal.
		for (i = len - SHA_DIGEST_SIZE; i < len; ++i) {
		buf[i] ^= *sha++;
		}

		// Hash resulting buf, in-place.
		SHA(buf, len, buf);

		// Compare against expected hash value.
		for (i = 0; i < SHA_DIGEST_SIZE; ++i) {
		if (buf[i] != kExpectedPadShaRsa2048[i]) {
		return 0;
		}
		}

		return 1; // All checked out OK.
		}