image: Add RSA support for image signing

RSA provides a public key encryption facility which is ideal for image
signing and verification.

Images are signed using a private key by mkimage. Then at run-time, the
images are verified using a private key.

This implementation uses openssl for the host part (mkimage). To avoid
bringing large libraries into the U-Boot binary, the RSA public key
is encoded using a simple numeric representation in the device tree.

Signed-off-by: Simon Glass <sjg@chromium.org>

Makefile

@@ -247,6 +247,7 @@ OBJS := $(addprefix $(obj),$(OBJS))
 HAVE_VENDOR_COMMON_LIB = $(if $(wildcard board/$(VENDOR)/common/Makefile),y,n)
 
 LIBS-y += lib/libgeneric.o
+LIBS-y += lib/rsa/librsa.o
 LIBS-y += lib/lzma/liblzma.o
 LIBS-y += lib/lzo/liblzo.o
 LIBS-y += lib/zlib/libz.o

README

@@ -2581,6 +2581,16 @@ CBFS (Coreboot Filesystem) support
 		Note: There is also a sha1sum command, which should perhaps
 		be deprecated in favour of 'hash sha1'.
 
+- Signing support:
+		CONFIG_RSA
+
+		This enables the RSA algorithm used for FIT image verification
+		in U-Boot. See doc/uImage/signature for more information.
+
+		The signing part is build into mkimage regardless of this
+		option.
+
+
 - Show boot progress:
 		CONFIG_SHOW_BOOT_PROGRESS
 

common/image-sig.c

@@ -27,8 +27,15 @@ DECLARE_GLOBAL_DATA_PTR;
 #endif /* !USE_HOSTCC*/
 #include <errno.h>
 #include <image.h>
+#include <rsa.h>
 
 struct image_sig_algo image_sig_algos[] = {
+	{
+		"sha1,rsa2048",
+		rsa_sign,
+		rsa_add_verify_data,
+		rsa_verify,
+	}
 };
 
 struct image_sig_algo *image_get_sig_algo(const char *name)

config.mk

@@ -96,6 +96,7 @@ HOSTCFLAGS	+= $(call os_x_before, 10, 4, "-traditional-cpp")
 HOSTLDFLAGS	+= $(call os_x_before, 10, 5, "-multiply_defined suppress")
 else
 HOSTCC		= gcc
+HOSTLIBS	+= -lssl -lcrypto
 endif
 
 ifeq ($(HOSTOS),cygwin)

include/rsa.h

@@ -0,0 +1,108 @@
+/*
+ * Copyright (c) 2013, Google Inc.
+ *
+ * (C) Copyright 2008 Semihalf
+ *
+ * (C) Copyright 2000-2006
+ * Wolfgang Denk, DENX Software Engineering, wd@denx.de.
+ *
+ * See file CREDITS for list of people who contributed to this
+ * project.
+ *
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License as
+ * published by the Free Software Foundation; either version 2 of
+ * the License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston,
+ * MA 02111-1307 USA
+ */
+
+#ifndef _RSA_H
+#define _RSA_H
+
+#include <errno.h>
+#include <image.h>
+
+#if IMAGE_ENABLE_SIGN
+/**
+ * sign() - calculate and return signature for given input data
+ *
+ * @info:	Specifies key and FIT information
+ * @data:	Pointer to the input data
+ * @data_len:	Data length
+ * @sigp:	Set to an allocated buffer holding the signature
+ * @sig_len:	Set to length of the calculated hash
+ *
+ * This computes input data signature according to selected algorithm.
+ * Resulting signature value is placed in an allocated buffer, the
+ * pointer is returned as *sigp. The length of the calculated
+ * signature is returned via the sig_len pointer argument. The caller
+ * should free *sigp.
+ *
+ * @return: 0, on success, -ve on error
+ */
+int rsa_sign(struct image_sign_info *info,
+	     const struct image_region region[],
+	     int region_count, uint8_t **sigp, uint *sig_len);
+
+/**
+ * add_verify_data() - Add verification information to FDT
+ *
+ * Add public key information to the FDT node, suitable for
+ * verification at run-time. The information added depends on the
+ * algorithm being used.
+ *
+ * @info:	Specifies key and FIT information
+ * @keydest:	Destination FDT blob for public key data
+ * @return: 0, on success, -ve on error
+*/
+int rsa_add_verify_data(struct image_sign_info *info, void *keydest);
+#else
+static inline int rsa_sign(struct image_sign_info *info,
+		const struct image_region region[], int region_count,
+		uint8_t **sigp, uint *sig_len)
+{
+	return -ENXIO;
+}
+
+static inline int rsa_add_verify_data(struct image_sign_info *info,
+				      void *keydest)
+{
+	return -ENXIO;
+}
+#endif
+
+#if IMAGE_ENABLE_VERIFY
+/**
+ * rsa_verify() - Verify a signature against some data
+ *
+ * Verify a RSA PKCS1.5 signature against an expected hash.
+ *
+ * @info:	Specifies key and FIT information
+ * @data:	Pointer to the input data
+ * @data_len:	Data length
+ * @sig:	Signature
+ * @sig_len:	Number of bytes in signature
+ * @return 0 if verified, -ve on error
+ */
+int rsa_verify(struct image_sign_info *info,
+	       const struct image_region region[], int region_count,
+	       uint8_t *sig, uint sig_len);
+#else
+static inline int rsa_verify(struct image_sign_info *info,
+		const struct image_region region[], int region_count,
+		uint8_t *sig, uint sig_len)
+{
+	return -ENXIO;
+}
+#endif
+
+#endif

lib/rsa/Makefile

@@ -0,0 +1,48 @@
+#
+# Copyright (c) 2013, Google Inc.
+#
+# (C) Copyright 2000-2007
+# Wolfgang Denk, DENX Software Engineering, wd@denx.de.
+#
+# See file CREDITS for list of people who contributed to this
+# project.
+#
+# This program is free software; you can redistribute it and/or
+# modify it under the terms of the GNU General Public License as
+# published by the Free Software Foundation; either version 2 of
+# the License, or (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program; if not, write to the Free Software
+# Foundation, Inc., 59 Temple Place, Suite 330, Boston,
+# MA 02111-1307 USA
+#
+
+include $(TOPDIR)/config.mk
+
+LIB	= $(obj)librsa.o
+
+ifdef CONFIG_FIT_SIGNATURE
+COBJS-$(CONFIG_RSA) += rsa-verify.o
+endif
+
+COBJS	:= $(sort $(COBJS-y))
+SRCS	:= $(COBJS:.o=.c)
+OBJS	:= $(addprefix $(obj),$(COBJS))
+
+$(LIB):	$(obj).depend $(OBJS)
+	$(call cmd_link_o_target, $(OBJS))
+
+#########################################################################
+
+# defines $(obj).depend target
+include $(SRCTREE)/rules.mk
+
+sinclude $(obj).depend
+
+#########################################################################

lib/rsa/rsa-sign.c

@@ -0,0 +1,460 @@
+/*
+ * Copyright (c) 2013, Google Inc.
+ *
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License as
+ * published by the Free Software Foundation; either version 2 of
+ * the License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston,
+ * MA 02111-1307 USA
+ */
+
+#include "mkimage.h"
+#include <stdio.h>
+#include <string.h>
+#include <error.h>
+#include <image.h>
+#include <time.h>
+#include <openssl/rsa.h>
+#include <openssl/pem.h>
+#include <openssl/err.h>
+#include <openssl/ssl.h>
+#include <openssl/evp.h>
+
+#if OPENSSL_VERSION_NUMBER >= 0x10000000L
+#define HAVE_ERR_REMOVE_THREAD_STATE
+#endif
+
+static int rsa_err(const char *msg)
+{
+	unsigned long sslErr = ERR_get_error();
+
+	fprintf(stderr, "%s", msg);
+	fprintf(stderr, ": %s\n",
+		ERR_error_string(sslErr, 0));
+
+	return -1;
+}
+
+/**
+ * rsa_get_pub_key() - read a public key from a .crt file
+ *
+ * @keydir:	Directory containins the key
+ * @name	Name of key file (will have a .crt extension)
+ * @rsap	Returns RSA object, or NULL on failure
+ * @return 0 if ok, -ve on error (in which case *rsap will be set to NULL)
+ */
+static int rsa_get_pub_key(const char *keydir, const char *name, RSA **rsap)
+{
+	char path[1024];
+	EVP_PKEY *key;
+	X509 *cert;
+	RSA *rsa;
+	FILE *f;
+	int ret;
+
+	*rsap = NULL;
+	snprintf(path, sizeof(path), "%s/%s.crt", keydir, name);
+	f = fopen(path, "r");
+	if (!f) {
+		fprintf(stderr, "Couldn't open RSA certificate: '%s': %s\n",
+			path, strerror(errno));
+		return -EACCES;
+	}
+
+	/* Read the certificate */
+	cert = NULL;
+	if (!PEM_read_X509(f, &cert, NULL, NULL)) {
+		rsa_err("Couldn't read certificate");
+		ret = -EINVAL;
+		goto err_cert;
+	}
+
+	/* Get the public key from the certificate. */
+	key = X509_get_pubkey(cert);
+	if (!key) {
+		rsa_err("Couldn't read public key\n");
+		ret = -EINVAL;
+		goto err_pubkey;
+	}
+
+	/* Convert to a RSA_style key. */
+	rsa = EVP_PKEY_get1_RSA(key);
+	if (!rsa) {
+		rsa_err("Couldn't convert to a RSA style key");
+		goto err_rsa;
+	}
+	fclose(f);
+	EVP_PKEY_free(key);
+	X509_free(cert);
+	*rsap = rsa;
+
+	return 0;
+
+err_rsa:
+	EVP_PKEY_free(key);
+err_pubkey:
+	X509_free(cert);
+err_cert:
+	fclose(f);
+	return ret;
+}
+
+/**
+ * rsa_get_priv_key() - read a private key from a .key file
+ *
+ * @keydir:	Directory containins the key
+ * @name	Name of key file (will have a .key extension)
+ * @rsap	Returns RSA object, or NULL on failure
+ * @return 0 if ok, -ve on error (in which case *rsap will be set to NULL)
+ */
+static int rsa_get_priv_key(const char *keydir, const char *name, RSA **rsap)
+{
+	char path[1024];
+	RSA *rsa;
+	FILE *f;
+
+	*rsap = NULL;
+	snprintf(path, sizeof(path), "%s/%s.key", keydir, name);
+	f = fopen(path, "r");
+	if (!f) {
+		fprintf(stderr, "Couldn't open RSA private key: '%s': %s\n",
+			path, strerror(errno));
+		return -ENOENT;
+	}
+
+	rsa = PEM_read_RSAPrivateKey(f, 0, NULL, path);
+	if (!rsa) {
+		rsa_err("Failure reading private key");
+		fclose(f);
+		return -EPROTO;
+	}
+	fclose(f);
+	*rsap = rsa;
+
+	return 0;
+}
+
+static int rsa_init(void)
+{
+	int ret;
+
+	ret = SSL_library_init();
+	if (!ret) {
+		fprintf(stderr, "Failure to init SSL library\n");
+		return -1;
+	}
+	SSL_load_error_strings();
+
+	OpenSSL_add_all_algorithms();
+	OpenSSL_add_all_digests();
+	OpenSSL_add_all_ciphers();
+
+	return 0;
+}
+
+static void rsa_remove(void)
+{
+	CRYPTO_cleanup_all_ex_data();
+	ERR_free_strings();
+#ifdef HAVE_ERR_REMOVE_THREAD_STATE
+	ERR_remove_thread_state(NULL);
+#else
+	ERR_remove_state(0);
+#endif
+	EVP_cleanup();
+}
+
+static int rsa_sign_with_key(RSA *rsa, const struct image_region region[],
+		int region_count, uint8_t **sigp, uint *sig_size)
+{
+	EVP_PKEY *key;
+	EVP_MD_CTX *context;
+	int size, ret = 0;
+	uint8_t *sig;
+	int i;
+
+	key = EVP_PKEY_new();
+	if (!key)
+		return rsa_err("EVP_PKEY object creation failed");
+
+	if (!EVP_PKEY_set1_RSA(key, rsa)) {
+		ret = rsa_err("EVP key setup failed");
+		goto err_set;
+	}
+
+	size = EVP_PKEY_size(key);
+	sig = malloc(size);
+	if (!sig) {
+		fprintf(stderr, "Out of memory for signature (%d bytes)\n",
+			size);
+		ret = -ENOMEM;
+		goto err_alloc;
+	}
+
+	context = EVP_MD_CTX_create();
+	if (!context) {
+		ret = rsa_err("EVP context creation failed");
+		goto err_create;
+	}
+	EVP_MD_CTX_init(context);
+	if (!EVP_SignInit(context, EVP_sha1())) {
+		ret = rsa_err("Signer setup failed");
+		goto err_sign;
+	}
+
+	for (i = 0; i < region_count; i++) {
+		if (!EVP_SignUpdate(context, region[i].data, region[i].size)) {
+			ret = rsa_err("Signing data failed");
+			goto err_sign;
+		}
+	}
+
+	if (!EVP_SignFinal(context, sig, sig_size, key)) {
+		ret = rsa_err("Could not obtain signature");
+		goto err_sign;
+	}
+	EVP_MD_CTX_cleanup(context);
+	EVP_MD_CTX_destroy(context);
+	EVP_PKEY_free(key);
+
+	debug("Got signature: %d bytes, expected %d\n", *sig_size, size);
+	*sigp = sig;
+	*sig_size = size;
+
+	return 0;
+
+err_sign:
+	EVP_MD_CTX_destroy(context);
+err_create:
+	free(sig);
+err_alloc:
+err_set:
+	EVP_PKEY_free(key);
+	return ret;
+}
+
+int rsa_sign(struct image_sign_info *info,
+	     const struct image_region region[], int region_count,
+	     uint8_t **sigp, uint *sig_len)
+{
+	RSA *rsa;
+	int ret;
+
+	ret = rsa_init();
+	if (ret)
+		return ret;
+
+	ret = rsa_get_priv_key(info->keydir, info->keyname, &rsa);
+	if (ret)
+		goto err_priv;
+	ret = rsa_sign_with_key(rsa, region, region_count, sigp, sig_len);
+	if (ret)
+		goto err_sign;
+
+	RSA_free(rsa);
+	rsa_remove();
+
+	return ret;
+
+err_sign:
+	RSA_free(rsa);
+err_priv:
+	rsa_remove();
+	return ret;
+}
+
+/*
+ * rsa_get_params(): - Get the important parameters of an RSA public key
+ */
+int rsa_get_params(RSA *key, uint32_t *n0_invp, BIGNUM **modulusp,
+		   BIGNUM **r_squaredp)
+{
+	BIGNUM *big1, *big2, *big32, *big2_32;
+	BIGNUM *n, *r, *r_squared, *tmp;
+	BN_CTX *bn_ctx = BN_CTX_new();
+	int ret = 0;
+
+	/* Initialize BIGNUMs */
+	big1 = BN_new();
+	big2 = BN_new();
+	big32 = BN_new();
+	r = BN_new();
+	r_squared = BN_new();
+	tmp = BN_new();
+	big2_32 = BN_new();
+	n = BN_new();
+	if (!big1 || !big2 || !big32 || !r || !r_squared || !tmp || !big2_32 ||
+	    !n) {
+		fprintf(stderr, "Out of memory (bignum)\n");
+		return -ENOMEM;
+	}
+
+	if (!BN_copy(n, key->n) || !BN_set_word(big1, 1L) ||
+	    !BN_set_word(big2, 2L) || !BN_set_word(big32, 32L))
+		ret = -1;
+
+	/* big2_32 = 2^32 */
+	if (!BN_exp(big2_32, big2, big32, bn_ctx))
+		ret = -1;
+
+	/* Calculate n0_inv = -1 / n[0] mod 2^32 */
+	if (!BN_mod_inverse(tmp, n, big2_32, bn_ctx) ||
+	    !BN_sub(tmp, big2_32, tmp))
+		ret = -1;
+	*n0_invp = BN_get_word(tmp);
+
+	/* Calculate R = 2^(# of key bits) */
+	if (!BN_set_word(tmp, BN_num_bits(n)) ||
+	    !BN_exp(r, big2, tmp, bn_ctx))
+		ret = -1;
+
+	/* Calculate r_squared = R^2 mod n */
+	if (!BN_copy(r_squared, r) ||
+	    !BN_mul(tmp, r_squared, r, bn_ctx) ||
+	    !BN_mod(r_squared, tmp, n, bn_ctx))
+		ret = -1;
+
+	*modulusp = n;
+	*r_squaredp = r_squared;
+
+	BN_free(big1);
+	BN_free(big2);
+	BN_free(big32);
+	BN_free(r);
+	BN_free(tmp);
+	BN_free(big2_32);
+	if (ret) {
+		fprintf(stderr, "Bignum operations failed\n");
+		return -ENOMEM;
+	}
+
+	return ret;
+}
+
+static int fdt_add_bignum(void *blob, int noffset, const char *prop_name,
+			  BIGNUM *num, int num_bits)
+{
+	int nwords = num_bits / 32;
+	int size;
+	uint32_t *buf, *ptr;
+	BIGNUM *tmp, *big2, *big32, *big2_32;
+	BN_CTX *ctx;
+	int ret;
+
+	tmp = BN_new();
+	big2 = BN_new();
+	big32 = BN_new();
+	big2_32 = BN_new();
+	if (!tmp || !big2 || !big32 || !big2_32) {
+		fprintf(stderr, "Out of memory (bignum)\n");
+		return -ENOMEM;
+	}
+	ctx = BN_CTX_new();
+	if (!tmp) {
+		fprintf(stderr, "Out of memory (bignum context)\n");
+		return -ENOMEM;
+	}
+	BN_set_word(big2, 2L);
+	BN_set_word(big32, 32L);
+	BN_exp(big2_32, big2, big32, ctx); /* B = 2^32 */
+
+	size = nwords * sizeof(uint32_t);
+	buf = malloc(size);
+	if (!buf) {
+		fprintf(stderr, "Out of memory (%d bytes)\n", size);
+		return -ENOMEM;
+	}
+
+	/* Write out modulus as big endian array of integers */
+	for (ptr = buf + nwords - 1; ptr >= buf; ptr--) {
+		BN_mod(tmp, num, big2_32, ctx); /* n = N mod B */
+		*ptr = cpu_to_fdt32(BN_get_word(tmp));
+		BN_rshift(num, num, 32); /*  N = N/B */
+	}
+
+	ret = fdt_setprop(blob, noffset, prop_name, buf, size);
+	if (ret) {
+		fprintf(stderr, "Failed to write public key to FIT\n");
+		return -ENOSPC;
+	}
+	free(buf);
+	BN_free(tmp);
+	BN_free(big2);
+	BN_free(big32);
+	BN_free(big2_32);
+
+	return ret;
+}
+
+int rsa_add_verify_data(struct image_sign_info *info, void *keydest)
+{
+	BIGNUM *modulus, *r_squared;
+	uint32_t n0_inv;
+	int parent, node;
+	char name[100];
+	int ret;
+	int bits;
+	RSA *rsa;
+
+	debug("%s: Getting verification data\n", __func__);
+	ret = rsa_get_pub_key(info->keydir, info->keyname, &rsa);
+	if (ret)
+		return ret;
+	ret = rsa_get_params(rsa, &n0_inv, &modulus, &r_squared);
+	if (ret)
+		return ret;
+	bits = BN_num_bits(modulus);
+	parent = fdt_subnode_offset(keydest, 0, FIT_SIG_NODENAME);
+	if (parent == -FDT_ERR_NOTFOUND) {
+		parent = fdt_add_subnode(keydest, 0, FIT_SIG_NODENAME);
+		if (parent < 0) {
+			fprintf(stderr, "Couldn't create signature node: %s\n",
+				fdt_strerror(parent));
+			return -EINVAL;
+		}
+	}
+
+	/* Either create or overwrite the named key node */
+	snprintf(name, sizeof(name), "key-%s", info->keyname);
+	node = fdt_subnode_offset(keydest, parent, name);
+	if (node == -FDT_ERR_NOTFOUND) {
+		node = fdt_add_subnode(keydest, parent, name);
+		if (node < 0) {
+			fprintf(stderr, "Could not create key subnode: %s\n",
+				fdt_strerror(node));
+			return -EINVAL;
+		}
+	} else if (node < 0) {
+		fprintf(stderr, "Cannot select keys parent: %s\n",
+			fdt_strerror(node));
+		return -ENOSPC;
+	}
+
+	ret = fdt_setprop_string(keydest, node, "key-name-hint",
+				 info->keyname);
+	ret |= fdt_setprop_u32(keydest, node, "rsa,num-bits", bits);
+	ret |= fdt_setprop_u32(keydest, node, "rsa,n0-inverse", n0_inv);
+	ret |= fdt_add_bignum(keydest, node, "rsa,modulus", modulus, bits);
+	ret |= fdt_add_bignum(keydest, node, "rsa,r-squared", r_squared, bits);
+	ret |= fdt_setprop_string(keydest, node, FIT_ALGO_PROP,
+				  info->algo->name);
+	if (info->require_keys) {
+		fdt_setprop_string(keydest, node, "required",
+				   info->require_keys);
+	}
+	BN_free(modulus);
+	BN_free(r_squared);
+	if (ret)
+		return -EIO;
+
+	return 0;
+}

lib/rsa/rsa-verify.c

@@ -0,0 +1,385 @@
+/*
+ * Copyright (c) 2013, Google Inc.
+ *
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License as
+ * published by the Free Software Foundation; either version 2 of
+ * the License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston,
+ * MA 02111-1307 USA
+ */
+
+#include <common.h>
+#include <fdtdec.h>
+#include <rsa.h>
+#include <sha1.h>
+#include <asm/byteorder.h>
+#include <asm/errno.h>
+#include <asm/unaligned.h>
+
+/**
+ * struct rsa_public_key - holder for a public key
+ *
+ * An RSA public key consists of a modulus (typically called N), the inverse
+ * and R^2, where R is 2^(# key bits).
+ */
+struct rsa_public_key {
+	uint len;		/* Length of modulus[] in number of uint32_t */
+	uint32_t n0inv;		/* -1 / modulus[0] mod 2^32 */
+	uint32_t *modulus;	/* modulus as little endian array */
+	uint32_t *rr;		/* R^2 as little endian array */
+};
+
+#define UINT64_MULT32(v, multby)  (((uint64_t)(v)) * ((uint32_t)(multby)))
+
+#define RSA2048_BYTES	(2048 / 8)
+
+/* This is the minimum/maximum key size we support, in bits */
+#define RSA_MIN_KEY_BITS	2048
+#define RSA_MAX_KEY_BITS	2048
+
+/* This is the maximum signature length that we support, in bits */
+#define RSA_MAX_SIG_BITS	2048
+
+static const uint8_t padding_sha1_rsa2048[RSA2048_BYTES - SHA1_SUM_LEN] = {
+	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
+};
+
+/**
+ * subtract_modulus() - subtract modulus from the given value
+ *
+ * @key:	Key containing modulus to subtract
+ * @num:	Number to subtract modulus from, as little endian word array
+ */
+static void subtract_modulus(const struct rsa_public_key *key, uint32_t num[])
+{
+	int64_t acc = 0;
+	uint i;
+
+	for (i = 0; i < key->len; i++) {
+		acc += (uint64_t)num[i] - key->modulus[i];
+		num[i] = (uint32_t)acc;
+		acc >>= 32;
+	}
+}
+
+/**
+ * greater_equal_modulus() - check if a value is >= modulus
+ *
+ * @key:	Key containing modulus to check
+ * @num:	Number to check against modulus, as little endian word array
+ * @return 0 if num < modulus, 1 if num >= modulus
+ */
+static int greater_equal_modulus(const struct rsa_public_key *key,
+				 uint32_t num[])
+{
+	uint32_t i;
+
+	for (i = key->len - 1; i >= 0; i--) {
+		if (num[i] < key->modulus[i])
+			return 0;
+		if (num[i] > key->modulus[i])
+			return 1;
+	}
+
+	return 1;  /* equal */
+}
+
+/**
+ * montgomery_mul_add_step() - Perform montgomery multiply-add step
+ *
+ * Operation: montgomery result[] += a * b[] / n0inv % modulus
+ *
+ * @key:	RSA key
+ * @result:	Place to put result, as little endian word array
+ * @a:		Multiplier
+ * @b:		Multiplicand, as little endian word array
+ */
+static void montgomery_mul_add_step(const struct rsa_public_key *key,
+		uint32_t result[], const uint32_t a, const uint32_t b[])
+{
+	uint64_t acc_a, acc_b;
+	uint32_t d0;
+	uint i;
+
+	acc_a = (uint64_t)a * b[0] + result[0];
+	d0 = (uint32_t)acc_a * key->n0inv;
+	acc_b = (uint64_t)d0 * key->modulus[0] + (uint32_t)acc_a;
+	for (i = 1; i < key->len; i++) {
+		acc_a = (acc_a >> 32) + (uint64_t)a * b[i] + result[i];
+		acc_b = (acc_b >> 32) + (uint64_t)d0 * key->modulus[i] +
+				(uint32_t)acc_a;
+		result[i - 1] = (uint32_t)acc_b;
+	}
+
+	acc_a = (acc_a >> 32) + (acc_b >> 32);
+
+	result[i - 1] = (uint32_t)acc_a;
+
+	if (acc_a >> 32)
+		subtract_modulus(key, result);
+}
+
+/**
+ * montgomery_mul() - Perform montgomery mutitply
+ *
+ * Operation: montgomery result[] = a[] * b[] / n0inv % modulus
+ *
+ * @key:	RSA key
+ * @result:	Place to put result, as little endian word array
+ * @a:		Multiplier, as little endian word array
+ * @b:		Multiplicand, as little endian word array
+ */
+static void montgomery_mul(const struct rsa_public_key *key,
+		uint32_t result[], uint32_t a[], const uint32_t b[])
+{
+	uint i;
+
+	for (i = 0; i < key->len; ++i)
+		result[i] = 0;
+	for (i = 0; i < key->len; ++i)
+		montgomery_mul_add_step(key, result, a[i], b);
+}
+
+/**
+ * pow_mod() - in-place public exponentiation
+ *
+ * @key:	RSA key
+ * @inout:	Big-endian word array containing value and result
+ */
+static int pow_mod(const struct rsa_public_key *key, uint32_t *inout)
+{
+	uint32_t *result, *ptr;
+	uint i;
+
+	/* Sanity check for stack size - key->len is in 32-bit words */
+	if (key->len > RSA_MAX_KEY_BITS / 32) {
+		debug("RSA key words %u exceeds maximum %d\n", key->len,
+		      RSA_MAX_KEY_BITS / 32);
+		return -EINVAL;
+	}
+
+	uint32_t val[key->len], acc[key->len], tmp[key->len];
+	result = tmp;  /* Re-use location. */
+
+	/* Convert from big endian byte array to little endian word array. */
+	for (i = 0, ptr = inout + key->len - 1; i < key->len; i++, ptr--)
+		val[i] = get_unaligned_be32(ptr);
+
+	montgomery_mul(key, acc, val, key->rr);  /* axx = a * RR / R mod M */
+	for (i = 0; i < 16; i += 2) {
+		montgomery_mul(key, tmp, acc, acc); /* tmp = acc^2 / R mod M */
+		montgomery_mul(key, acc, tmp, tmp); /* acc = tmp^2 / R mod M */
+	}
+	montgomery_mul(key, result, acc, val);  /* result = XX * a / R mod M */
+
+	/* Make sure result < mod; result is at most 1x mod too large. */
+	if (greater_equal_modulus(key, result))
+		subtract_modulus(key, result);
+
+	/* Convert to bigendian byte array */
+	for (i = key->len - 1, ptr = inout; (int)i >= 0; i--, ptr++)
+		put_unaligned_be32(result[i], ptr);
+
+	return 0;
+}
+
+static int rsa_verify_key(const struct rsa_public_key *key, const uint8_t *sig,
+		const uint32_t sig_len, const uint8_t *hash)
+{
+	const uint8_t *padding;
+	int pad_len;
+	int ret;
+
+	if (!key || !sig || !hash)
+		return -EIO;
+
+	if (sig_len != (key->len * sizeof(uint32_t))) {
+		debug("Signature is of incorrect length %d\n", sig_len);
+		return -EINVAL;
+	}
+
+	/* Sanity check for stack size */
+	if (sig_len > RSA_MAX_SIG_BITS / 8) {
+		debug("Signature length %u exceeds maximum %d\n", sig_len,
+		      RSA_MAX_SIG_BITS / 8);
+		return -EINVAL;
+	}
+
+	uint32_t buf[sig_len / sizeof(uint32_t)];
+
+	memcpy(buf, sig, sig_len);
+
+	ret = pow_mod(key, buf);
+	if (ret)
+		return ret;
+
+	/* Determine padding to use depending on the signature type. */
+	padding = padding_sha1_rsa2048;
+	pad_len = RSA2048_BYTES - SHA1_SUM_LEN;
+
+	/* Check pkcs1.5 padding bytes. */
+	if (memcmp(buf, padding, pad_len)) {
+		debug("In RSAVerify(): Padding check failed!\n");
+		return -EINVAL;
+	}
+
+	/* Check hash. */
+	if (memcmp((uint8_t *)buf + pad_len, hash, sig_len - pad_len)) {
+		debug("In RSAVerify(): Hash check failed!\n");
+		return -EACCES;
+	}
+
+	return 0;
+}
+
+static void rsa_convert_big_endian(uint32_t *dst, const uint32_t *src, int len)
+{
+	int i;
+
+	for (i = 0; i < len; i++)
+		dst[i] = fdt32_to_cpu(src[len - 1 - i]);
+}
+
+static int rsa_verify_with_keynode(struct image_sign_info *info,
+		const void *hash, uint8_t *sig, uint sig_len, int node)
+{
+	const void *blob = info->fdt_blob;
+	struct rsa_public_key key;
+	const void *modulus, *rr;
+	int ret;
+
+	if (node < 0) {
+		debug("%s: Skipping invalid node", __func__);
+		return -EBADF;
+	}
+	if (!fdt_getprop(blob, node, "rsa,n0-inverse", NULL)) {
+		debug("%s: Missing rsa,n0-inverse", __func__);
+		return -EFAULT;
+	}
+	key.len = fdtdec_get_int(blob, node, "rsa,num-bits", 0);
+	key.n0inv = fdtdec_get_int(blob, node, "rsa,n0-inverse", 0);
+	modulus = fdt_getprop(blob, node, "rsa,modulus", NULL);
+	rr = fdt_getprop(blob, node, "rsa,r-squared", NULL);
+	if (!key.len || !modulus || !rr) {
+		debug("%s: Missing RSA key info", __func__);
+		return -EFAULT;
+	}
+
+	/* Sanity check for stack size */
+	if (key.len > RSA_MAX_KEY_BITS || key.len < RSA_MIN_KEY_BITS) {
+		debug("RSA key bits %u outside allowed range %d..%d\n",
+		      key.len, RSA_MIN_KEY_BITS, RSA_MAX_KEY_BITS);
+		return -EFAULT;
+	}
+	key.len /= sizeof(uint32_t) * 8;
+	uint32_t key1[key.len], key2[key.len];
+
+	key.modulus = key1;
+	key.rr = key2;
+	rsa_convert_big_endian(key.modulus, modulus, key.len);
+	rsa_convert_big_endian(key.rr, rr, key.len);
+	if (!key.modulus || !key.rr) {
+		debug("%s: Out of memory", __func__);
+		return -ENOMEM;
+	}
+
+	debug("key length %d\n", key.len);
+	ret = rsa_verify_key(&key, sig, sig_len, hash);
+	if (ret) {
+		printf("%s: RSA failed to verify: %d\n", __func__, ret);
+		return ret;
+	}
+
+	return 0;
+}
+
+int rsa_verify(struct image_sign_info *info,
+	       const struct image_region region[], int region_count,
+	       uint8_t *sig, uint sig_len)
+{
+	const void *blob = info->fdt_blob;
+	uint8_t hash[SHA1_SUM_LEN];
+	int ndepth, noffset;
+	int sig_node, node;
+	char name[100];
+	sha1_context ctx;
+	int ret, i;
+
+	sig_node = fdt_subnode_offset(blob, 0, FIT_SIG_NODENAME);
+	if (sig_node < 0) {
+		debug("%s: No signature node found\n", __func__);
+		return -ENOENT;
+	}
+
+	sha1_starts(&ctx);
+	for (i = 0; i < region_count; i++)
+		sha1_update(&ctx, region[i].data, region[i].size);
+	sha1_finish(&ctx, hash);
+
+	/* See if we must use a particular key */
+	if (info->required_keynode != -1) {
+		ret = rsa_verify_with_keynode(info, hash, sig, sig_len,
+			info->required_keynode);
+		if (!ret)
+			return ret;
+	}
+
+	/* Look for a key that matches our hint */
+	snprintf(name, sizeof(name), "key-%s", info->keyname);
+	node = fdt_subnode_offset(blob, sig_node, name);
+	ret = rsa_verify_with_keynode(info, hash, sig, sig_len, node);
+	if (!ret)
+		return ret;
+
+	/* No luck, so try each of the keys in turn */
+	for (ndepth = 0, noffset = fdt_next_node(info->fit, sig_node, &ndepth);
+			(noffset >= 0) && (ndepth > 0);
+			noffset = fdt_next_node(info->fit, noffset, &ndepth)) {
+		if (ndepth == 1 && noffset != node) {
+			ret = rsa_verify_with_keynode(info, hash, sig, sig_len,
+						      noffset);
+			if (!ret)
+				break;
+		}
+	}
+
+	return ret;
+}

tools/Makefile

@@ -125,6 +125,9 @@ LIBFDT_OBJ_FILES-y += fdt_rw.o
 LIBFDT_OBJ_FILES-y += fdt_strerror.o
 LIBFDT_OBJ_FILES-y += fdt_wip.o
 
+# RSA objects
+RSA_OBJ_FILES-y += rsa-sign.o
+
 # Generated LCD/video logo
 LOGO_H = $(OBJTREE)/include/bmp_logo.h
 LOGO_DATA_H = $(OBJTREE)/include/bmp_logo_data.h
@@ -152,8 +155,10 @@ endif # !LOGO_BMP
 HOSTSRCS += $(addprefix $(SRCTREE)/,$(EXT_OBJ_FILES-y:.o=.c))
 HOSTSRCS += $(addprefix $(SRCTREE)/tools/,$(OBJ_FILES-y:.o=.c))
 HOSTSRCS += $(addprefix $(SRCTREE)/lib/libfdt/,$(LIBFDT_OBJ_FILES-y:.o=.c))
+HOSTSRCS += $(addprefix $(SRCTREE)/lib/rsa/,$(RSA_OBJ_FILES-y:.o=.c))
 BINS	:= $(addprefix $(obj),$(sort $(BIN_FILES-y)))
 LIBFDT_OBJS	:= $(addprefix $(obj),$(LIBFDT_OBJ_FILES-y))
+RSA_OBJS	:= $(addprefix $(obj),$(RSA_OBJ_FILES-y))
 
 # We cannot check CONFIG_FIT_SIGNATURE here since it is not set on the host
 FIT_SIG_OBJ_FILES	:= image-sig.o
@@ -228,8 +233,9 @@ $(obj)mkimage$(SFX):	$(obj)aisimage.o \
 			$(obj)omapimage.o \
 			$(obj)sha1.o \
 			$(obj)ublimage.o \
-			$(LIBFDT_OBJS)
-	$(HOSTCC) $(HOSTCFLAGS) $(HOSTLDFLAGS) -o $@ $^
+			$(LIBFDT_OBJS) \
+			$(RSA_OBJS)
+	$(HOSTCC) $(HOSTCFLAGS) $(HOSTLDFLAGS) -o $@ $^ $(HOSTLIBS)
 	$(HOSTSTRIP) $@
 
 $(obj)mk$(BOARD)spl$(SFX):	$(obj)mkexynosspl.o
@@ -265,6 +271,9 @@ $(obj)%.o: $(SRCTREE)/lib/%.c
 $(obj)%.o: $(SRCTREE)/lib/libfdt/%.c
 	$(HOSTCC) -g $(HOSTCFLAGS_NOPED) -c -o $@ $<
 
+$(obj)%.o: $(SRCTREE)/lib/rsa/%.c
+	$(HOSTCC) -g $(HOSTCFLAGS_NOPED) -c -o $@ $<
+
 subdirs:
 ifeq ($(TOOLSUBDIRS),)
 	@: