In the current implementation of FIT_SIGNATURE, five parameters for a RSA public key are required while only two of them are essential. (See rsa-mod-exp.h and uImage.FIT/signature.txt) This is a result of considering relatively limited computer power and resources on embedded systems, while such a assumption may not be quite practical for other use cases.
In this patch, added is a function, rsa_gen_key_prop(), which will generate additional parameters for other uses, in particular UEFI secure boot, on the fly.
Note: the current code uses some "big number" routines from BearSSL for the calculation.
Signed-off-by: AKASHI Takahiro takahiro.akashi@linaro.org --- include/u-boot/rsa-mod-exp.h | 23 ++ lib/rsa/Kconfig | 1 + lib/rsa/Makefile | 1 + lib/rsa/rsa-keyprop.c | 725 +++++++++++++++++++++++++++++++++++ 4 files changed, 750 insertions(+) create mode 100644 lib/rsa/rsa-keyprop.c
diff --git a/include/u-boot/rsa-mod-exp.h b/include/u-boot/rsa-mod-exp.h index 8a428c4b6a1a..1da8af1bb83d 100644 --- a/include/u-boot/rsa-mod-exp.h +++ b/include/u-boot/rsa-mod-exp.h @@ -26,6 +26,29 @@ struct key_prop { uint32_t exp_len; /* Exponent length in number of uint8_t */ };
+/** + * rsa_gen_key_prop() - Generate key properties of RSA public key + * @key: Specifies key data in DER format + * @keylen: Length of @key + * @prop: Generated key property + * + * This function takes a blob of encoded RSA public key data in DER + * format, parse it and generate all the relevant properties + * in key_prop structure. + * Return a pointer to struct key_prop in @prop on success. + * + * Return: 0 on success, negative on error + */ +int rsa_gen_key_prop(const void *key, uint32_t keylen, struct key_prop **proc); + +/** + * rsa_free_key_prop() - Free key properties + * @prop: Pointer to struct key_prop + * + * This function frees all the memories allocated by rsa_gen_key_prop(). + */ +void rsa_free_key_prop(struct key_prop *prop); + /** * rsa_mod_exp_sw() - Perform RSA Modular Exponentiation in sw * diff --git a/lib/rsa/Kconfig b/lib/rsa/Kconfig index 71e4c06bf883..d1d6f6cf64a3 100644 --- a/lib/rsa/Kconfig +++ b/lib/rsa/Kconfig @@ -33,6 +33,7 @@ config RSA_VERIFY config RSA_VERIFY_WITH_PKEY bool "Execute RSA verification without key parameters from FDT" depends on RSA + imply RSA_PUBLIC_KEY_PARSER help The standard RSA-signature verification code (FIT_SIGNATURE) uses pre-calculated key properties, that are stored in fdt blob, in diff --git a/lib/rsa/Makefile b/lib/rsa/Makefile index c07305188e0c..14ed3cb4012b 100644 --- a/lib/rsa/Makefile +++ b/lib/rsa/Makefile @@ -6,4 +6,5 @@ # Wolfgang Denk, DENX Software Engineering, wd@denx.de.
obj-$(CONFIG_$(SPL_)RSA_VERIFY) += rsa-verify.o rsa-checksum.o +obj-$(CONFIG_RSA_VERIFY_WITH_PKEY) += rsa-keyprop.o obj-$(CONFIG_RSA_SOFTWARE_EXP) += rsa-mod-exp.o diff --git a/lib/rsa/rsa-keyprop.c b/lib/rsa/rsa-keyprop.c new file mode 100644 index 000000000000..9464df009343 --- /dev/null +++ b/lib/rsa/rsa-keyprop.c @@ -0,0 +1,725 @@ +// SPDX-License-Identifier: GPL-2.0+ and MIT +/* + * RSA library - generate parameters for a public key + * + * Copyright (c) 2019 Linaro Limited + * Author: AKASHI Takahiro + * + * Big number routines in this file come from BearSSL: + * Copyright (c) 2016 Thomas Pornin pornin@bolet.org + */ + +#include <common.h> +#include <image.h> +#include <malloc.h> +#include <asm/byteorder.h> +#include <crypto/internal/rsa.h> +#include <u-boot/rsa-mod-exp.h> + +/** + * br_dec16be() - Convert 16-bit big-endian integer to native + * @src: Pointer to data + * Return: Native-endian integer + */ +static unsigned br_dec16be(const void *src) +{ + return be16_to_cpup(src); +} + +/** + * br_dec32be() - Convert 32-bit big-endian integer to native + * @src: Pointer to data + * Return: Native-endian integer + */ +static uint32_t br_dec32be(const void *src) +{ + return be32_to_cpup(src); +} + +/** + * br_enc32be() - Convert native 32-bit integer to big-endian + * @dst: Pointer to buffer to store big-endian integer in + * @x: Native 32-bit integer + */ +static void br_enc32be(void *dst, uint32_t x) +{ + __be32 tmp; + + tmp = cpu_to_be32(x); + memcpy(dst, &tmp, sizeof(tmp)); +} + +/* from BearSSL's src/inner.h */ + +/* + * Negate a boolean. + */ +static uint32_t NOT(uint32_t ctl) +{ + return ctl ^ 1; +} + +/* + * Multiplexer: returns x if ctl == 1, y if ctl == 0. + */ +static uint32_t MUX(uint32_t ctl, uint32_t x, uint32_t y) +{ + return y ^ (-ctl & (x ^ y)); +} + +/* + * Equality check: returns 1 if x == y, 0 otherwise. + */ +static uint32_t EQ(uint32_t x, uint32_t y) +{ + uint32_t q; + + q = x ^ y; + return NOT((q | -q) >> 31); +} + +/* + * Inequality check: returns 1 if x != y, 0 otherwise. + */ +static uint32_t NEQ(uint32_t x, uint32_t y) +{ + uint32_t q; + + q = x ^ y; + return (q | -q) >> 31; +} + +/* + * Comparison: returns 1 if x > y, 0 otherwise. + */ +static uint32_t GT(uint32_t x, uint32_t y) +{ + /* + * If both x < 2^31 and y < 2^31, then y-x will have its high + * bit set if x > y, cleared otherwise. + * + * If either x >= 2^31 or y >= 2^31 (but not both), then the + * result is the high bit of x. + * + * If both x >= 2^31 and y >= 2^31, then we can virtually + * subtract 2^31 from both, and we are back to the first case. + * Since (y-2^31)-(x-2^31) = y-x, the subtraction is already + * fine. + */ + uint32_t z; + + z = y - x; + return (z ^ ((x ^ y) & (x ^ z))) >> 31; +} + +/* + * Compute the bit length of a 32-bit integer. Returned value is between 0 + * and 32 (inclusive). + */ +static uint32_t BIT_LENGTH(uint32_t x) +{ + uint32_t k, c; + + k = NEQ(x, 0); + c = GT(x, 0xFFFF); x = MUX(c, x >> 16, x); k += c << 4; + c = GT(x, 0x00FF); x = MUX(c, x >> 8, x); k += c << 3; + c = GT(x, 0x000F); x = MUX(c, x >> 4, x); k += c << 2; + c = GT(x, 0x0003); x = MUX(c, x >> 2, x); k += c << 1; + k += GT(x, 0x0001); + return k; +} + +#define GE(x, y) NOT(GT(y, x)) +#define LT(x, y) GT(y, x) +#define MUL(x, y) ((uint64_t)(x) * (uint64_t)(y)) + +/* + * Integers 'i32' + * -------------- + * + * The 'i32' functions implement computations on big integers using + * an internal representation as an array of 32-bit integers. For + * an array x[]: + * -- x[0] contains the "announced bit length" of the integer + * -- x[1], x[2]... contain the value in little-endian order (x[1] + * contains the least significant 32 bits) + * + * Multiplications rely on the elementary 32x32->64 multiplication. + * + * The announced bit length specifies the number of bits that are + * significant in the subsequent 32-bit words. Unused bits in the + * last (most significant) word are set to 0; subsequent words are + * uninitialized and need not exist at all. + * + * The execution time and memory access patterns of all computations + * depend on the announced bit length, but not on the actual word + * values. For modular integers, the announced bit length of any integer + * modulo n is equal to the actual bit length of n; thus, computations + * on modular integers are "constant-time" (only the modulus length may + * leak). + */ + +/* + * Extract one word from an integer. The offset is counted in bits. + * The word MUST entirely fit within the word elements corresponding + * to the announced bit length of a[]. + */ +static uint32_t br_i32_word(const uint32_t *a, uint32_t off) +{ + size_t u; + unsigned j; + + u = (size_t)(off >> 5) + 1; + j = (unsigned)off & 31; + if (j == 0) { + return a[u]; + } else { + return (a[u] >> j) | (a[u + 1] << (32 - j)); + } +} + +/* from BearSSL's src/int/i32_bitlen.c */ + +/* + * Compute the actual bit length of an integer. The argument x should + * point to the first (least significant) value word of the integer. + * The len 'xlen' contains the number of 32-bit words to access. + * + * CT: value or length of x does not leak. + */ +static uint32_t br_i32_bit_length(uint32_t *x, size_t xlen) +{ + uint32_t tw, twk; + + tw = 0; + twk = 0; + while (xlen -- > 0) { + uint32_t w, c; + + c = EQ(tw, 0); + w = x[xlen]; + tw = MUX(c, w, tw); + twk = MUX(c, (uint32_t)xlen, twk); + } + return (twk << 5) + BIT_LENGTH(tw); +} + +/* from BearSSL's src/int/i32_decode.c */ + +/* + * Decode an integer from its big-endian unsigned representation. The + * "true" bit length of the integer is computed, but all words of x[] + * corresponding to the full 'len' bytes of the source are set. + * + * CT: value or length of x does not leak. + */ +static void br_i32_decode(uint32_t *x, const void *src, size_t len) +{ + const unsigned char *buf; + size_t u, v; + + buf = src; + u = len; + v = 1; + for (;;) { + if (u < 4) { + uint32_t w; + + if (u < 2) { + if (u == 0) { + break; + } else { + w = buf[0]; + } + } else { + if (u == 2) { + w = br_dec16be(buf); + } else { + w = ((uint32_t)buf[0] << 16) + | br_dec16be(buf + 1); + } + } + x[v ++] = w; + break; + } else { + u -= 4; + x[v ++] = br_dec32be(buf + u); + } + } + x[0] = br_i32_bit_length(x + 1, v - 1); +} + +/* from BearSSL's src/int/i32_encode.c */ + +/* + * Encode an integer into its big-endian unsigned representation. The + * output length in bytes is provided (parameter 'len'); if the length + * is too short then the integer is appropriately truncated; if it is + * too long then the extra bytes are set to 0. + */ +static void br_i32_encode(void *dst, size_t len, const uint32_t *x) +{ + unsigned char *buf; + size_t k; + + buf = dst; + + /* + * Compute the announced size of x in bytes; extra bytes are + * filled with zeros. + */ + k = (x[0] + 7) >> 3; + while (len > k) { + *buf ++ = 0; + len --; + } + + /* + * Now we use k as index within x[]. That index starts at 1; + * we initialize it to the topmost complete word, and process + * any remaining incomplete word. + */ + k = (len + 3) >> 2; + switch (len & 3) { + case 3: + *buf ++ = x[k] >> 16; + /* fall through */ + case 2: + *buf ++ = x[k] >> 8; + /* fall through */ + case 1: + *buf ++ = x[k]; + k --; + } + + /* + * Encode all complete words. + */ + while (k > 0) { + br_enc32be(buf, x[k]); + k --; + buf += 4; + } +} + +/* from BearSSL's src/int/i32_ninv32.c */ + +/* + * Compute -(1/x) mod 2^32. If x is even, then this function returns 0. + */ +static uint32_t br_i32_ninv32(uint32_t x) +{ + uint32_t y; + + y = 2 - x; + y *= 2 - y * x; + y *= 2 - y * x; + y *= 2 - y * x; + y *= 2 - y * x; + return MUX(x & 1, -y, 0); +} + +/* from BearSSL's src/int/i32_add.c */ + +/* + * Add b[] to a[] and return the carry (0 or 1). If ctl is 0, then a[] + * is unmodified, but the carry is still computed and returned. The + * arrays a[] and b[] MUST have the same announced bit length. + * + * a[] and b[] MAY be the same array, but partial overlap is not allowed. + */ +static uint32_t br_i32_add(uint32_t *a, const uint32_t *b, uint32_t ctl) +{ + uint32_t cc; + size_t u, m; + + cc = 0; + m = (a[0] + 63) >> 5; + for (u = 1; u < m; u ++) { + uint32_t aw, bw, naw; + + aw = a[u]; + bw = b[u]; + naw = aw + bw + cc; + + /* + * Carry is 1 if naw < aw. Carry is also 1 if naw == aw + * AND the carry was already 1. + */ + cc = (cc & EQ(naw, aw)) | LT(naw, aw); + a[u] = MUX(ctl, naw, aw); + } + return cc; +} + +/* from BearSSL's src/int/i32_sub.c */ + +/* + * Subtract b[] from a[] and return the carry (0 or 1). If ctl is 0, + * then a[] is unmodified, but the carry is still computed and returned. + * The arrays a[] and b[] MUST have the same announced bit length. + * + * a[] and b[] MAY be the same array, but partial overlap is not allowed. + */ +static uint32_t br_i32_sub(uint32_t *a, const uint32_t *b, uint32_t ctl) +{ + uint32_t cc; + size_t u, m; + + cc = 0; + m = (a[0] + 63) >> 5; + for (u = 1; u < m; u ++) { + uint32_t aw, bw, naw; + + aw = a[u]; + bw = b[u]; + naw = aw - bw - cc; + + /* + * Carry is 1 if naw > aw. Carry is 1 also if naw == aw + * AND the carry was already 1. + */ + cc = (cc & EQ(naw, aw)) | GT(naw, aw); + a[u] = MUX(ctl, naw, aw); + } + return cc; +} + +/* from BearSSL's src/int/i32_div32.c */ + +/* + * Constant-time division. The dividend hi:lo is divided by the + * divisor d; the quotient is returned and the remainder is written + * in *r. If hi == d, then the quotient does not fit on 32 bits; + * returned value is thus truncated. If hi > d, returned values are + * indeterminate. + */ +static uint32_t br_divrem(uint32_t hi, uint32_t lo, uint32_t d, uint32_t *r) +{ + /* TODO: optimize this */ + uint32_t q; + uint32_t ch, cf; + int k; + + q = 0; + ch = EQ(hi, d); + hi = MUX(ch, 0, hi); + for (k = 31; k > 0; k --) { + int j; + uint32_t w, ctl, hi2, lo2; + + j = 32 - k; + w = (hi << j) | (lo >> k); + ctl = GE(w, d) | (hi >> k); + hi2 = (w - d) >> j; + lo2 = lo - (d << k); + hi = MUX(ctl, hi2, hi); + lo = MUX(ctl, lo2, lo); + q |= ctl << k; + } + cf = GE(lo, d) | hi; + q |= cf; + *r = MUX(cf, lo - d, lo); + return q; +} + +/* + * Wrapper for br_divrem(); the remainder is returned, and the quotient + * is discarded. + */ +static uint32_t br_rem(uint32_t hi, uint32_t lo, uint32_t d) +{ + uint32_t r; + + br_divrem(hi, lo, d, &r); + return r; +} + +/* + * Wrapper for br_divrem(); the quotient is returned, and the remainder + * is discarded. + */ +static uint32_t br_div(uint32_t hi, uint32_t lo, uint32_t d) +{ + uint32_t r; + + return br_divrem(hi, lo, d, &r); +} + +/* from BearSSL's src/int/i32_muladd.c */ + +/* + * Multiply x[] by 2^32 and then add integer z, modulo m[]. This + * function assumes that x[] and m[] have the same announced bit + * length, and the announced bit length of m[] matches its true + * bit length. + * + * x[] and m[] MUST be distinct arrays. + * + * CT: only the common announced bit length of x and m leaks, not + * the values of x, z or m. + */ +static void br_i32_muladd_small(uint32_t *x, uint32_t z, const uint32_t *m) +{ + uint32_t m_bitlen; + size_t u, mlen; + uint32_t a0, a1, b0, hi, g, q, tb; + uint32_t chf, clow, under, over; + uint64_t cc; + + /* + * We can test on the modulus bit length since we accept to + * leak that length. + */ + m_bitlen = m[0]; + if (m_bitlen == 0) { + return; + } + if (m_bitlen <= 32) { + x[1] = br_rem(x[1], z, m[1]); + return; + } + mlen = (m_bitlen + 31) >> 5; + + /* + * Principle: we estimate the quotient (x*2^32+z)/m by + * doing a 64/32 division with the high words. + * + * Let: + * w = 2^32 + * a = (w*a0 + a1) * w^N + a2 + * b = b0 * w^N + b2 + * such that: + * 0 <= a0 < w + * 0 <= a1 < w + * 0 <= a2 < w^N + * w/2 <= b0 < w + * 0 <= b2 < w^N + * a < w*b + * I.e. the two top words of a are a0:a1, the top word of b is + * b0, we ensured that b0 is "full" (high bit set), and a is + * such that the quotient q = a/b fits on one word (0 <= q < w). + * + * If a = b*q + r (with 0 <= r < q), we can estimate q by + * doing an Euclidean division on the top words: + * a0*w+a1 = b0*u + v (with 0 <= v < w) + * Then the following holds: + * 0 <= u <= w + * u-2 <= q <= u + */ + a0 = br_i32_word(x, m_bitlen - 32); + hi = x[mlen]; + memmove(x + 2, x + 1, (mlen - 1) * sizeof *x); + x[1] = z; + a1 = br_i32_word(x, m_bitlen - 32); + b0 = br_i32_word(m, m_bitlen - 32); + + /* + * We estimate a divisor q. If the quotient returned by br_div() + * is g: + * -- If a0 == b0 then g == 0; we want q = 0xFFFFFFFF. + * -- Otherwise: + * -- if g == 0 then we set q = 0; + * -- otherwise, we set q = g - 1. + * The properties described above then ensure that the true + * quotient is q-1, q or q+1. + */ + g = br_div(a0, a1, b0); + q = MUX(EQ(a0, b0), 0xFFFFFFFF, MUX(EQ(g, 0), 0, g - 1)); + + /* + * We subtract q*m from x (with the extra high word of value 'hi'). + * Since q may be off by 1 (in either direction), we may have to + * add or subtract m afterwards. + * + * The 'tb' flag will be true (1) at the end of the loop if the + * result is greater than or equal to the modulus (not counting + * 'hi' or the carry). + */ + cc = 0; + tb = 1; + for (u = 1; u <= mlen; u ++) { + uint32_t mw, zw, xw, nxw; + uint64_t zl; + + mw = m[u]; + zl = MUL(mw, q) + cc; + cc = (uint32_t)(zl >> 32); + zw = (uint32_t)zl; + xw = x[u]; + nxw = xw - zw; + cc += (uint64_t)GT(nxw, xw); + x[u] = nxw; + tb = MUX(EQ(nxw, mw), tb, GT(nxw, mw)); + } + + /* + * If we underestimated q, then either cc < hi (one extra bit + * beyond the top array word), or cc == hi and tb is true (no + * extra bit, but the result is not lower than the modulus). In + * these cases we must subtract m once. + * + * Otherwise, we may have overestimated, which will show as + * cc > hi (thus a negative result). Correction is adding m once. + */ + chf = (uint32_t)(cc >> 32); + clow = (uint32_t)cc; + over = chf | GT(clow, hi); + under = ~over & (tb | (~chf & LT(clow, hi))); + br_i32_add(x, m, over); + br_i32_sub(x, m, under); +} + +/* from BearSSL's src/int/i32_reduce.c */ + +/* + * Reduce an integer (a[]) modulo another (m[]). The result is written + * in x[] and its announced bit length is set to be equal to that of m[]. + * + * x[] MUST be distinct from a[] and m[]. + * + * CT: only announced bit lengths leak, not values of x, a or m. + */ +static void br_i32_reduce(uint32_t *x, const uint32_t *a, const uint32_t *m) +{ + uint32_t m_bitlen, a_bitlen; + size_t mlen, alen, u; + + m_bitlen = m[0]; + mlen = (m_bitlen + 31) >> 5; + + x[0] = m_bitlen; + if (m_bitlen == 0) { + return; + } + + /* + * If the source is shorter, then simply copy all words from a[] + * and zero out the upper words. + */ + a_bitlen = a[0]; + alen = (a_bitlen + 31) >> 5; + if (a_bitlen < m_bitlen) { + memcpy(x + 1, a + 1, alen * sizeof *a); + for (u = alen; u < mlen; u ++) { + x[u + 1] = 0; + } + return; + } + + /* + * The source length is at least equal to that of the modulus. + * We must thus copy N-1 words, and input the remaining words + * one by one. + */ + memcpy(x + 1, a + 2 + (alen - mlen), (mlen - 1) * sizeof *a); + x[mlen] = 0; + for (u = 1 + alen - mlen; u > 0; u --) { + br_i32_muladd_small(x, a[u], m); + } +} + +/** + * rsa_free_key_prop() - Free key properties + * @prop: Pointer to struct key_prop + * + * This function frees all the memories allocated by rsa_gen_key_prop(). + */ +void rsa_free_key_prop(struct key_prop *prop) +{ + if (!prop) + return; + + free((void *)prop->modulus); + free((void *)prop->public_exponent); + free((void *)prop->rr); + + free(prop); +} + +/** + * rsa_gen_key_prop() - Generate key properties of RSA public key + * @key: Specifies key data in DER format + * @keylen: Length of @key + * @prop: Generated key property + * + * This function takes a blob of encoded RSA public key data in DER + * format, parse it and generate all the relevant properties + * in key_prop structure. + * Return a pointer to struct key_prop in @prop on success. + * + * Return: 0 on success, negative on error + */ +int rsa_gen_key_prop(const void *key, uint32_t keylen, struct key_prop **prop) +{ + struct rsa_key rsa_key; + uint32_t *n = NULL, *rr = NULL, *rrtmp = NULL; + const int max_rsa_size = 4096; + int rlen, i, ret; + + *prop = calloc(sizeof(**prop), 1); + n = calloc(sizeof(uint32_t), 1 + (max_rsa_size >> 5)); + rr = calloc(sizeof(uint32_t), 1 + (max_rsa_size >> 5)); + rrtmp = calloc(sizeof(uint32_t), 1 + (max_rsa_size >> 5)); + if (!(*prop) || !n || !rr || !rrtmp) { + ret = -ENOMEM; + goto err; + } + + ret = rsa_parse_pub_key(&rsa_key, key, keylen); + if (ret) + goto err; + + /* modulus */ + /* removing leading 0's */ + for (i = 0; i < rsa_key.n_sz && !rsa_key.n[i]; i++) + ; + (*prop)->num_bits = (rsa_key.n_sz - i) * 8; + (*prop)->modulus = malloc(rsa_key.n_sz - i); + if (!(*prop)->modulus) { + ret = -ENOMEM; + goto err; + } + memcpy((void *)(*prop)->modulus, &rsa_key.n[i], rsa_key.n_sz - i); + + /* exponent */ + (*prop)->public_exponent = calloc(1, sizeof(uint64_t)); + if (!(*prop)->public_exponent) { + ret = -ENOMEM; + goto err; + } + memcpy((void *)(*prop)->public_exponent + sizeof(uint64_t) + - rsa_key.e_sz, + rsa_key.e, rsa_key.e_sz); + (*prop)->exp_len = rsa_key.e_sz; + + /* n0 inverse */ + br_i32_decode(n, &rsa_key.n[i], rsa_key.n_sz - i); + (*prop)->n0inv = br_i32_ninv32(n[1]); + + /* R^2 mod n; R = 2^(num_bits) */ + rlen = (*prop)->num_bits * 2; /* #bits of R^2 = (2^num_bits)^2 */ + rr[0] = 0; + *(uint8_t *)&rr[0] = (1 << (rlen % 8)); + for (i = 1; i < (((rlen + 31) >> 5) + 1); i++) + rr[i] = 0; + br_i32_decode(rrtmp, rr, ((rlen + 7) >> 3) + 1); + br_i32_reduce(rr, rrtmp, n); + + rlen = ((*prop)->num_bits + 7) >> 3; /* #bytes of R^2 mod n */ + (*prop)->rr = malloc(rlen); + if (!(*prop)->rr) { + ret = -ENOMEM; + goto err; + } + br_i32_encode((void *)(*prop)->rr, rlen, rr); + + return 0; + +err: + free(n); + free(rr); + free(rrtmp); + rsa_free_key_prop(*prop); + return ret; +}