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- /*
- * Copyright 2023 The OpenSSL Project Authors. All Rights Reserved.
- *
- * Licensed under the Apache License 2.0 (the "License"). You may not use
- * this file except in compliance with the License. You can obtain a copy
- * in the file LICENSE in the source distribution or at
- * https://www.openssl.org/source/license.html
- */
- #include "crypto/rand.h"
- #include "internal/common.h"
- /*
- * Implementation an optimal random integer in a range function.
- *
- * Essentially it boils down to incrementally generating a fixed point
- * number on the interval [0, 1) and multiplying this number by the upper
- * range limit. Once it is certain what the fractional part contributes to
- * the integral part of the product, the algorithm has produced a definitive
- * result.
- *
- * Refer: https://github.com/apple/swift/pull/39143 for a fuller description
- * of the algorithm.
- */
- uint32_t ossl_rand_uniform_uint32(OSSL_LIB_CTX *ctx, uint32_t upper, int *err)
- {
- uint32_t i, f; /* integer and fractional parts */
- uint32_t f2, rand; /* extra fractional part and random material */
- uint64_t prod; /* temporary holding double width product */
- const int max_followup_iterations = 10;
- int j;
- if (!ossl_assert(upper > 0)) {
- *err = 0;
- return 0;
- }
- if (ossl_unlikely(upper == 1))
- return 0;
- /* Get 32 bits of entropy */
- if (RAND_bytes_ex(ctx, (unsigned char *)&rand, sizeof(rand), 0) <= 0) {
- *err = 1;
- return 0;
- }
- /*
- * We are generating a fixed point number on the interval [0, 1).
- * Multiplying this by the range gives us a number on [0, upper).
- * The high word of the multiplication result represents the integral
- * part we want. The lower word is the fractional part. We can early exit if
- * if the fractional part is small enough that no carry from the next lower
- * word can cause an overflow and carry into the integer part. This
- * happens when the fractional part is bounded by 2^32 - upper which
- * can be simplified to just -upper (as an unsigned integer).
- */
- prod = (uint64_t)upper * rand;
- i = prod >> 32;
- f = prod & 0xffffffff;
- if (ossl_likely(f <= 1 + ~upper)) /* 1+~upper == -upper but compilers whine */
- return i;
- /*
- * We're in the position where the carry from the next word *might* cause
- * a carry to the integral part. The process here is to generate the next
- * word, multiply it by the range and add that to the current word. If
- * it overflows, the carry propagates to the integer part (return i+1).
- * If it can no longer overflow regardless of further lower order bits,
- * we are done (return i). If there is still a chance of overflow, we
- * repeat the process with the next lower word.
- *
- * Each *bit* of randomness has a probability of one half of terminating
- * this process, so each each word beyond the first has a probability
- * of 2^-32 of not terminating the process. That is, we're extremely
- * likely to stop very rapidly.
- */
- for (j = 0; j < max_followup_iterations; j++) {
- if (RAND_bytes_ex(ctx, (unsigned char *)&rand, sizeof(rand), 0) <= 0) {
- *err = 1;
- return 0;
- }
- prod = (uint64_t)upper * rand;
- f2 = prod >> 32;
- f += f2;
- /* On overflow, add the carry to our result */
- if (f < f2)
- return i + 1;
- /* For not all 1 bits, there is no carry so return the result */
- if (ossl_likely(f != 0xffffffff))
- return i;
- /* setup for the next word of randomness */
- f = prod & 0xffffffff;
- }
- /*
- * If we get here, we've consumed 32 * max_followup_iterations + 32 bits
- * with no firm decision, this gives a bias with probability < 2^-(32*n),
- * which is likely acceptable.
- */
- return i;
- }
- uint32_t ossl_rand_range_uint32(OSSL_LIB_CTX *ctx, uint32_t lower, uint32_t upper,
- int *err)
- {
- if (!ossl_assert(lower < upper)) {
- *err = 1;
- return 0;
- }
- return lower + ossl_rand_uniform_uint32(ctx, upper - lower, err);
- }
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