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