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- // 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;
- int rlen, i, ret = 0;
- *prop = calloc(sizeof(**prop), 1);
- if (!(*prop)) {
- ret = -ENOMEM;
- goto out;
- }
- ret = rsa_parse_pub_key(&rsa_key, key, keylen);
- if (ret)
- goto out;
- /* 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 out;
- }
- memcpy((void *)(*prop)->modulus, &rsa_key.n[i], rsa_key.n_sz - i);
- n = calloc(sizeof(uint32_t), 1 + ((*prop)->num_bits >> 5));
- rr = calloc(sizeof(uint32_t), 1 + (((*prop)->num_bits * 2) >> 5));
- rrtmp = calloc(sizeof(uint32_t), 2 + (((*prop)->num_bits * 2) >> 5));
- if (!n || !rr || !rrtmp) {
- ret = -ENOMEM;
- goto out;
- }
- /* exponent */
- (*prop)->public_exponent = calloc(1, sizeof(uint64_t));
- if (!(*prop)->public_exponent) {
- ret = -ENOMEM;
- goto out;
- }
- memcpy((void *)(*prop)->public_exponent + sizeof(uint64_t)
- - rsa_key.e_sz,
- rsa_key.e, rsa_key.e_sz);
- (*prop)->exp_len = sizeof(uint64_t);
- /* 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 out;
- }
- br_i32_encode((void *)(*prop)->rr, rlen, rr);
- out:
- free(n);
- free(rr);
- free(rrtmp);
- if (ret < 0)
- rsa_free_key_prop(*prop);
- return ret;
- }
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