rsa: Split the rsa-verify to separate the modular exponentiation

Public exponentiation which is required in rsa verify functionality is
tightly integrated with verification code in rsa_verify.c. The patch
splits the file into twp separating the modular exponentiation.

1. rsa-verify.c
- The file parses device tree keys node to fill a keyprop structure.
The keyprop structure can then be converted to implementation specific
format.
(struct rsa_pub_key for sw implementation)
- The parsed device tree node is then passed to a generic rsa_mod_exp
function.

2. rsa-mod-exp.c
Move the software specific functions related to modular exponentiation
from rsa-verify.c to this file.

Signed-off-by: Ruchika Gupta <ruchika.gupta@freescale.com>
CC: Simon Glass <sjg@chromium.org>
Acked-by: Simon Glass <sjg@chromium.org>
This commit is contained in:
Ruchika Gupta 2015-01-23 16:01:50 +05:30 committed by Simon Glass
parent 49cad54788
commit fc2f4246b4
5 changed files with 405 additions and 277 deletions

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@ -0,0 +1,43 @@
/*
* Copyright (c) 2014, Ruchika Gupta.
*
* SPDX-License-Identifier: GPL-2.0+
*/
#ifndef _RSA_MOD_EXP_H
#define _RSA_MOD_EXP_H
#include <errno.h>
#include <image.h>
/**
* struct key_prop - holder for a public key properties
*
* The struct has pointers to modulus (Typically called N),
* The inverse, R^2, exponent. These can be typecasted and
* used as byte arrays or converted to the required format
* as per requirement of RSA implementation.
*/
struct key_prop {
const void *rr; /* R^2 can be treated as byte array */
const void *modulus; /* modulus as byte array */
const void *public_exponent; /* public exponent as byte array */
uint32_t n0inv; /* -1 / modulus[0] mod 2^32 */
int num_bits; /* Key length in bits */
uint32_t exp_len; /* Exponent length in number of uint8_t */
};
/**
* rsa_mod_exp_sw() - Perform RSA Modular Exponentiation in sw
*
* Operation: out[] = sig ^ exponent % modulus
*
* @sig: RSA PKCS1.5 signature
* @sig_len: Length of signature in number of bytes
* @node: Node with RSA key elements like modulus, exponent, R^2, n0inv
* @out: Result in form of byte array
*/
int rsa_mod_exp_sw(const uint8_t *sig, uint32_t sig_len,
struct key_prop *node, uint8_t *out);
#endif

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@ -7,4 +7,4 @@
# SPDX-License-Identifier: GPL-2.0+
#
obj-$(CONFIG_FIT_SIGNATURE) += rsa-verify.o rsa-checksum.o
obj-$(CONFIG_FIT_SIGNATURE) += rsa-verify.o rsa-checksum.o rsa-mod-exp.o

303
lib/rsa/rsa-mod-exp.c Normal file
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@ -0,0 +1,303 @@
/*
* Copyright (c) 2013, Google Inc.
*
* SPDX-License-Identifier: GPL-2.0+
*/
#ifndef USE_HOSTCC
#include <common.h>
#include <fdtdec.h>
#include <asm/types.h>
#include <asm/byteorder.h>
#include <asm/errno.h>
#include <asm/types.h>
#include <asm/unaligned.h>
#else
#include "fdt_host.h"
#include "mkimage.h"
#include <fdt_support.h>
#endif
#include <u-boot/rsa.h>
#include <u-boot/rsa-mod-exp.h>
#define UINT64_MULT32(v, multby) (((uint64_t)(v)) * ((uint32_t)(multby)))
#define get_unaligned_be32(a) fdt32_to_cpu(*(uint32_t *)a)
#define put_unaligned_be32(a, b) (*(uint32_t *)(b) = cpu_to_fdt32(a))
/* Default public exponent for backward compatibility */
#define RSA_DEFAULT_PUBEXP 65537
/**
* 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[])
{
int i;
for (i = (int)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);
}
/**
* num_pub_exponent_bits() - Number of bits in the public exponent
*
* @key: RSA key
* @num_bits: Storage for the number of public exponent bits
*/
static int num_public_exponent_bits(const struct rsa_public_key *key,
int *num_bits)
{
uint64_t exponent;
int exponent_bits;
const uint max_bits = (sizeof(exponent) * 8);
exponent = key->exponent;
exponent_bits = 0;
if (!exponent) {
*num_bits = exponent_bits;
return 0;
}
for (exponent_bits = 1; exponent_bits < max_bits + 1; ++exponent_bits)
if (!(exponent >>= 1)) {
*num_bits = exponent_bits;
return 0;
}
return -EINVAL;
}
/**
* is_public_exponent_bit_set() - Check if a bit in the public exponent is set
*
* @key: RSA key
* @pos: The bit position to check
*/
static int is_public_exponent_bit_set(const struct rsa_public_key *key,
int pos)
{
return key->exponent & (1ULL << pos);
}
/**
* 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;
int j, k;
/* 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];
uint32_t a_scaled[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);
if (0 != num_public_exponent_bits(key, &k))
return -EINVAL;
if (k < 2) {
debug("Public exponent is too short (%d bits, minimum 2)\n",
k);
return -EINVAL;
}
if (!is_public_exponent_bit_set(key, 0)) {
debug("LSB of RSA public exponent must be set.\n");
return -EINVAL;
}
/* the bit at e[k-1] is 1 by definition, so start with: C := M */
montgomery_mul(key, acc, val, key->rr); /* acc = a * RR / R mod n */
/* retain scaled version for intermediate use */
memcpy(a_scaled, acc, key->len * sizeof(a_scaled[0]));
for (j = k - 2; j > 0; --j) {
montgomery_mul(key, tmp, acc, acc); /* tmp = acc^2 / R mod n */
if (is_public_exponent_bit_set(key, j)) {
/* acc = tmp * val / R mod n */
montgomery_mul(key, acc, tmp, a_scaled);
} else {
/* e[j] == 0, copy tmp back to acc for next operation */
memcpy(acc, tmp, key->len * sizeof(acc[0]));
}
}
/* the bit at e[0] is always 1 */
montgomery_mul(key, tmp, acc, acc); /* tmp = acc^2 / R mod n */
montgomery_mul(key, acc, tmp, val); /* acc = tmp * a / R mod M */
memcpy(result, acc, key->len * sizeof(result[0]));
/* 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 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]);
}
int rsa_mod_exp_sw(const uint8_t *sig, uint32_t sig_len,
struct key_prop *prop, uint8_t *out)
{
struct rsa_public_key key;
int ret;
if (!prop) {
debug("%s: Skipping invalid prop", __func__);
return -EBADF;
}
key.n0inv = prop->n0inv;
key.len = prop->num_bits;
if (!prop->public_exponent)
key.exponent = RSA_DEFAULT_PUBEXP;
else
key.exponent =
fdt64_to_cpu(*((uint64_t *)(prop->public_exponent)));
if (!key.len || !prop->modulus || !prop->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, (uint32_t *)prop->modulus, key.len);
rsa_convert_big_endian(key.rr, (uint32_t *)prop->rr, key.len);
if (!key.modulus || !key.rr) {
debug("%s: Out of memory", __func__);
return -ENOMEM;
}
uint32_t buf[sig_len / sizeof(uint32_t)];
memcpy(buf, sig, sig_len);
ret = pow_mod(&key, buf);
if (ret)
return ret;
memcpy(out, buf, sig_len);
return 0;
}

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@ -17,230 +17,26 @@
#include "mkimage.h"
#include <fdt_support.h>
#endif
#include <u-boot/rsa-mod-exp.h>
#include <u-boot/rsa.h>
#include <u-boot/sha1.h>
#include <u-boot/sha256.h>
#define UINT64_MULT32(v, multby) (((uint64_t)(v)) * ((uint32_t)(multby)))
#define get_unaligned_be32(a) fdt32_to_cpu(*(uint32_t *)a)
#define put_unaligned_be32(a, b) (*(uint32_t *)(b) = cpu_to_fdt32(a))
/* Default public exponent for backward compatibility */
#define RSA_DEFAULT_PUBEXP 65537
/**
* subtract_modulus() - subtract modulus from the given value
* rsa_verify_key() - Verify a signature against some data using RSA Key
*
* @key: Key containing modulus to subtract
* @num: Number to subtract modulus from, as little endian word array
* Verify a RSA PKCS1.5 signature against an expected hash using
* the RSA Key properties in prop structure.
*
* @prop: Specifies key
* @sig: Signature
* @sig_len: Number of bytes in signature
* @hash: Pointer to the expected hash
* @algo: Checksum algo structure having information on RSA padding etc.
* @return 0 if verified, -ve on error
*/
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[])
{
int i;
for (i = (int)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);
}
/**
* num_pub_exponent_bits() - Number of bits in the public exponent
*
* @key: RSA key
* @num_bits: Storage for the number of public exponent bits
*/
static int num_public_exponent_bits(const struct rsa_public_key *key,
int *num_bits)
{
uint64_t exponent;
int exponent_bits;
const uint max_bits = (sizeof(exponent) * 8);
exponent = key->exponent;
exponent_bits = 0;
if (!exponent) {
*num_bits = exponent_bits;
return 0;
}
for (exponent_bits = 1; exponent_bits < max_bits + 1; ++exponent_bits)
if (!(exponent >>= 1)) {
*num_bits = exponent_bits;
return 0;
}
return -EINVAL;
}
/**
* is_public_exponent_bit_set() - Check if a bit in the public exponent is set
*
* @key: RSA key
* @pos: The bit position to check
*/
static int is_public_exponent_bit_set(const struct rsa_public_key *key,
int pos)
{
return key->exponent & (1ULL << pos);
}
/**
* 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;
int j, k;
/* 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];
uint32_t a_scaled[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);
if (0 != num_public_exponent_bits(key, &k))
return -EINVAL;
if (k < 2) {
debug("Public exponent is too short (%d bits, minimum 2)\n",
k);
return -EINVAL;
}
if (!is_public_exponent_bit_set(key, 0)) {
debug("LSB of RSA public exponent must be set.\n");
return -EINVAL;
}
/* the bit at e[k-1] is 1 by definition, so start with: C := M */
montgomery_mul(key, acc, val, key->rr); /* acc = a * RR / R mod n */
/* retain scaled version for intermediate use */
memcpy(a_scaled, acc, key->len * sizeof(a_scaled[0]));
for (j = k - 2; j > 0; --j) {
montgomery_mul(key, tmp, acc, acc); /* tmp = acc^2 / R mod n */
if (is_public_exponent_bit_set(key, j)) {
/* acc = tmp * val / R mod n */
montgomery_mul(key, acc, tmp, a_scaled);
} else {
/* e[j] == 0, copy tmp back to acc for next operation */
memcpy(acc, tmp, key->len * sizeof(acc[0]));
}
}
/* the bit at e[0] is always 1 */
montgomery_mul(key, tmp, acc, acc); /* tmp = acc^2 / R mod n */
montgomery_mul(key, acc, tmp, val); /* acc = tmp * a / R mod M */
memcpy(result, acc, key->len * sizeof(result[0]));
/* 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,
static int rsa_verify_key(struct key_prop *prop, const uint8_t *sig,
const uint32_t sig_len, const uint8_t *hash,
struct checksum_algo *algo)
{
@ -248,10 +44,10 @@ static int rsa_verify_key(const struct rsa_public_key *key, const uint8_t *sig,
int pad_len;
int ret;
if (!key || !sig || !hash || !algo)
if (!prop || !sig || !hash || !algo)
return -EIO;
if (sig_len != (key->len * sizeof(uint32_t))) {
if (sig_len != (prop->num_bits / 8)) {
debug("Signature is of incorrect length %d\n", sig_len);
return -EINVAL;
}
@ -265,13 +61,13 @@ static int rsa_verify_key(const struct rsa_public_key *key, const uint8_t *sig,
return -EINVAL;
}
uint32_t buf[sig_len / sizeof(uint32_t)];
uint8_t buf[sig_len];
memcpy(buf, sig, sig_len);
ret = pow_mod(key, buf);
if (ret)
ret = rsa_mod_exp_sw(sig, sig_len, prop, buf);
if (ret) {
debug("Error in Modular exponentation\n");
return ret;
}
padding = algo->rsa_padding;
pad_len = algo->pad_len - algo->checksum_len;
@ -291,74 +87,59 @@ static int rsa_verify_key(const struct rsa_public_key *key, const uint8_t *sig,
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]);
}
/**
* rsa_verify_with_keynode() - Verify a signature against some data using
* information in node with prperties of RSA Key like modulus, exponent etc.
*
* Parse sign-node and fill a key_prop structure with properties of the
* key. Verify a RSA PKCS1.5 signature against an expected hash using
* the properties parsed
*
* @info: Specifies key and FIT information
* @hash: Pointer to the expected hash
* @sig: Signature
* @sig_len: Number of bytes in signature
* @node: Node having the RSA Key properties
* @return 0 if verified, -ve on error
*/
static int rsa_verify_with_keynode(struct image_sign_info *info,
const void *hash, uint8_t *sig, uint sig_len, int node)
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;
const uint64_t *public_exponent;
struct key_prop prop;
int length;
int ret;
int ret = 0;
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);
public_exponent = fdt_getprop(blob, node, "rsa,exponent", &length);
if (!public_exponent || length < sizeof(*public_exponent))
key.exponent = RSA_DEFAULT_PUBEXP;
else
key.exponent = fdt64_to_cpu(*public_exponent);
modulus = fdt_getprop(blob, node, "rsa,modulus", NULL);
rr = fdt_getprop(blob, node, "rsa,r-squared", NULL);
if (!key.len || !modulus || !rr) {
prop.num_bits = fdtdec_get_int(blob, node, "rsa,num-bits", 0);
prop.n0inv = fdtdec_get_int(blob, node, "rsa,n0-inverse", 0);
prop.public_exponent = fdt_getprop(blob, node, "rsa,exponent", &length);
if (!prop.public_exponent || length < sizeof(uint64_t))
prop.public_exponent = NULL;
prop.exp_len = sizeof(uint64_t);
prop.modulus = fdt_getprop(blob, node, "rsa,modulus", NULL);
prop.rr = fdt_getprop(blob, node, "rsa,r-squared", NULL);
if (!prop.num_bits || !prop.modulus) {
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];
ret = rsa_verify_key(&prop, sig, sig_len, hash, info->algo->checksum);
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, info->algo->checksum);
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)

View File

@ -60,7 +60,8 @@ FIT_SIG_OBJS-$(CONFIG_FIT_SIGNATURE) := common/image-sig.o
LIBFDT_OBJS := $(addprefix lib/libfdt/, \
fdt.o fdt_ro.o fdt_rw.o fdt_strerror.o fdt_wip.o)
RSA_OBJS-$(CONFIG_FIT_SIGNATURE) := $(addprefix lib/rsa/, \
rsa-sign.o rsa-verify.o rsa-checksum.o)
rsa-sign.o rsa-verify.o rsa-checksum.o \
rsa-mod-exp.o)
# common objs for dumpimage and mkimage
dumpimage-mkimage-objs := aisimage.o \