library/constant_time.c

/**
 *  Constant-time functions
 *
 *  Copyright The Mbed TLS Contributors
 *  SPDX-License-Identifier: Apache-2.0
 *
 *  Licensed under the Apache License, Version 2.0 (the "License"); you may
 *  not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *  http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
 *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 */

/*
 * The following functions are implemented without using comparison operators, as those
 * might be translated to branches by some compilers on some platforms.
 */

#include "common.h"
#include "constant_time_internal.h"
#include "mbedtls/constant_time.h"
#include "mbedtls/error.h"
#include "mbedtls/platform_util.h"

#if defined(MBEDTLS_BIGNUM_C)
#include "mbedtls/bignum.h"
#endif

#if defined(MBEDTLS_SSL_TLS_C)
#include "mbedtls/ssl_internal.h"
#endif

#if defined(MBEDTLS_RSA_C)
#include "mbedtls/rsa.h"
#endif

#if defined(MBEDTLS_BASE64_C)
#include "constant_time_invasive.h"
#endif

#include <string.h>

int mbedtls_ct_memcmp(const void *a,
                      const void *b,
                      size_t n)
{
    size_t i;
    volatile const unsigned char *A = (volatile const unsigned char *) a;
    volatile const unsigned char *B = (volatile const unsigned char *) b;
    volatile unsigned char diff = 0;

    for (i = 0; i < n; i++) {
        /* Read volatile data in order before computing diff.
         * This avoids IAR compiler warning:
         * 'the order of volatile accesses is undefined ..' */
        unsigned char x = A[i], y = B[i];
        diff |= x ^ y;
    }

    return (int) diff;
}

unsigned mbedtls_ct_uint_mask(unsigned value)
{
    /* MSVC has a warning about unary minus on unsigned, but this is
     * well-defined and precisely what we want to do here */
#if defined(_MSC_VER)
#pragma warning( push )
#pragma warning( disable : 4146 )
#endif
    return -((value | -value) >> (sizeof(value) * 8 - 1));
#if defined(_MSC_VER)
#pragma warning( pop )
#endif
}

#if defined(MBEDTLS_SSL_SOME_MODES_USE_MAC)

size_t mbedtls_ct_size_mask(size_t value)
{
    /* MSVC has a warning about unary minus on unsigned integer types,
     * but this is well-defined and precisely what we want to do here. */
#if defined(_MSC_VER)
#pragma warning( push )
#pragma warning( disable : 4146 )
#endif
    return -((value | -value) >> (sizeof(value) * 8 - 1));
#if defined(_MSC_VER)
#pragma warning( pop )
#endif
}

#endif /* MBEDTLS_SSL_SOME_MODES_USE_MAC */

#if defined(MBEDTLS_BIGNUM_C)

mbedtls_mpi_uint mbedtls_ct_mpi_uint_mask(mbedtls_mpi_uint value)
{
    /* MSVC has a warning about unary minus on unsigned, but this is
     * well-defined and precisely what we want to do here */
#if defined(_MSC_VER)
#pragma warning( push )
#pragma warning( disable : 4146 )
#endif
    return -((value | -value) >> (sizeof(value) * 8 - 1));
#if defined(_MSC_VER)
#pragma warning( pop )
#endif
}

#endif /* MBEDTLS_BIGNUM_C */

#if defined(MBEDTLS_SSL_SOME_SUITES_USE_TLS_CBC)

/** Constant-flow mask generation for "less than" comparison:
 * - if \p x < \p y, return all-bits 1, that is (size_t) -1
 * - otherwise, return all bits 0, that is 0
 *
 * This function can be used to write constant-time code by replacing branches
 * with bit operations using masks.
 *
 * \param x     The first value to analyze.
 * \param y     The second value to analyze.
 *
 * \return      All-bits-one if \p x is less than \p y, otherwise zero.
 */
static size_t mbedtls_ct_size_mask_lt(size_t x,
                                      size_t y)
{
    /* This has the most significant bit set if and only if x < y */
    const size_t sub = x - y;

    /* sub1 = (x < y) ? 1 : 0 */
    const size_t sub1 = sub >> (sizeof(sub) * 8 - 1);

    /* mask = (x < y) ? 0xff... : 0x00... */
    const size_t mask = mbedtls_ct_size_mask(sub1);

    return mask;
}

size_t mbedtls_ct_size_mask_ge(size_t x,
                               size_t y)
{
    return ~mbedtls_ct_size_mask_lt(x, y);
}

#endif /* MBEDTLS_SSL_SOME_SUITES_USE_TLS_CBC */

#if defined(MBEDTLS_BASE64_C)

/* Return 0xff if low <= c <= high, 0 otherwise.
 *
 * Constant flow with respect to c.
 */
MBEDTLS_STATIC_TESTABLE
unsigned char mbedtls_ct_uchar_mask_of_range(unsigned char low,
                                             unsigned char high,
                                             unsigned char c)
{
    /* low_mask is: 0 if low <= c, 0x...ff if low > c */
    unsigned low_mask = ((unsigned) c - low) >> 8;
    /* high_mask is: 0 if c <= high, 0x...ff if c > high */
    unsigned high_mask = ((unsigned) high - c) >> 8;
    return ~(low_mask | high_mask) & 0xff;
}

#endif /* MBEDTLS_BASE64_C */

unsigned mbedtls_ct_size_bool_eq(size_t x,
                                 size_t y)
{
    /* diff = 0 if x == y, non-zero otherwise */
    const size_t diff = x ^ y;

    /* MSVC has a warning about unary minus on unsigned integer types,
     * but this is well-defined and precisely what we want to do here. */
#if defined(_MSC_VER)
#pragma warning( push )
#pragma warning( disable : 4146 )
#endif

    /* diff_msb's most significant bit is equal to x != y */
    const size_t diff_msb = (diff | (size_t) -diff);

#if defined(_MSC_VER)
#pragma warning( pop )
#endif

    /* diff1 = (x != y) ? 1 : 0 */
    const unsigned diff1 = diff_msb >> (sizeof(diff_msb) * 8 - 1);

    return 1 ^ diff1;
}

#if defined(MBEDTLS_PKCS1_V15) && defined(MBEDTLS_RSA_C) && !defined(MBEDTLS_RSA_ALT)

/** Constant-flow "greater than" comparison:
 * return x > y
 *
 * This is equivalent to \p x > \p y, but is likely to be compiled
 * to code using bitwise operation rather than a branch.
 *
 * \param x     The first value to analyze.
 * \param y     The second value to analyze.
 *
 * \return      1 if \p x greater than \p y, otherwise 0.
 */
static unsigned mbedtls_ct_size_gt(size_t x,
                                   size_t y)
{
    /* Return the sign bit (1 for negative) of (y - x). */
    return (y - x) >> (sizeof(size_t) * 8 - 1);
}

#endif /* MBEDTLS_PKCS1_V15 && MBEDTLS_RSA_C && ! MBEDTLS_RSA_ALT */

#if defined(MBEDTLS_BIGNUM_C)

unsigned mbedtls_ct_mpi_uint_lt(const mbedtls_mpi_uint x,
                                const mbedtls_mpi_uint y)
{
    mbedtls_mpi_uint ret;
    mbedtls_mpi_uint cond;

    /*
     * Check if the most significant bits (MSB) of the operands are different.
     */
    cond = (x ^ y);
    /*
     * If the MSB are the same then the difference x-y will be negative (and
     * have its MSB set to 1 during conversion to unsigned) if and only if x<y.
     */
    ret = (x - y) & ~cond;
    /*
     * If the MSB are different, then the operand with the MSB of 1 is the
     * bigger. (That is if y has MSB of 1, then x<y is true and it is false if
     * the MSB of y is 0.)
     */
    ret |= y & cond;


    ret = ret >> (sizeof(mbedtls_mpi_uint) * 8 - 1);

    return (unsigned) ret;
}

#endif /* MBEDTLS_BIGNUM_C */

unsigned mbedtls_ct_uint_if(unsigned condition,
                            unsigned if1,
                            unsigned if0)
{
    unsigned mask = mbedtls_ct_uint_mask(condition);
    return (mask & if1) | (~mask & if0);
}

#if defined(MBEDTLS_BIGNUM_C)

void mbedtls_ct_mpi_uint_cond_assign(size_t n,
                                     mbedtls_mpi_uint *dest,
                                     const mbedtls_mpi_uint *src,
                                     unsigned char condition)
{
    size_t i;

    /* MSVC has a warning about unary minus on unsigned integer types,
     * but this is well-defined and precisely what we want to do here. */
#if defined(_MSC_VER)
#pragma warning( push )
#pragma warning( disable : 4146 )
#endif

    /* all-bits 1 if condition is 1, all-bits 0 if condition is 0 */
    const mbedtls_mpi_uint mask = -condition;

#if defined(_MSC_VER)
#pragma warning( pop )
#endif

    for (i = 0; i < n; i++) {
        dest[i] = (src[i] & mask) | (dest[i] & ~mask);
    }
}

#endif /* MBEDTLS_BIGNUM_C */

#if defined(MBEDTLS_BASE64_C)

unsigned char mbedtls_ct_base64_enc_char(unsigned char value)
{
    unsigned char digit = 0;
    /* For each range of values, if value is in that range, mask digit with
     * the corresponding value. Since value can only be in a single range,
     * only at most one masking will change digit. */
    digit |= mbedtls_ct_uchar_mask_of_range(0, 25, value) & ('A' + value);
    digit |= mbedtls_ct_uchar_mask_of_range(26, 51, value) & ('a' + value - 26);
    digit |= mbedtls_ct_uchar_mask_of_range(52, 61, value) & ('0' + value - 52);
    digit |= mbedtls_ct_uchar_mask_of_range(62, 62, value) & '+';
    digit |= mbedtls_ct_uchar_mask_of_range(63, 63, value) & '/';
    return digit;
}

signed char mbedtls_ct_base64_dec_value(unsigned char c)
{
    unsigned char val = 0;
    /* For each range of digits, if c is in that range, mask val with
     * the corresponding value. Since c can only be in a single range,
     * only at most one masking will change val. Set val to one plus
     * the desired value so that it stays 0 if c is in none of the ranges. */
    val |= mbedtls_ct_uchar_mask_of_range('A', 'Z', c) & (c - 'A' +  0 + 1);
    val |= mbedtls_ct_uchar_mask_of_range('a', 'z', c) & (c - 'a' + 26 + 1);
    val |= mbedtls_ct_uchar_mask_of_range('0', '9', c) & (c - '0' + 52 + 1);
    val |= mbedtls_ct_uchar_mask_of_range('+', '+', c) & (c - '+' + 62 + 1);
    val |= mbedtls_ct_uchar_mask_of_range('/', '/', c) & (c - '/' + 63 + 1);
    /* At this point, val is 0 if c is an invalid digit and v+1 if c is
     * a digit with the value v. */
    return val - 1;
}

#endif /* MBEDTLS_BASE64_C */

#if defined(MBEDTLS_PKCS1_V15) && defined(MBEDTLS_RSA_C) && !defined(MBEDTLS_RSA_ALT)

/** Shift some data towards the left inside a buffer.
 *
 * `mbedtls_ct_mem_move_to_left(start, total, offset)` is functionally
 * equivalent to
 * ```
 * memmove(start, start + offset, total - offset);
 * memset(start + offset, 0, total - offset);
 * ```
 * but it strives to use a memory access pattern (and thus total timing)
 * that does not depend on \p offset. This timing independence comes at
 * the expense of performance.
 *
 * \param start     Pointer to the start of the buffer.
 * \param total     Total size of the buffer.
 * \param offset    Offset from which to copy \p total - \p offset bytes.
 */
static void mbedtls_ct_mem_move_to_left(void *start,
                                        size_t total,
                                        size_t offset)
{
    volatile unsigned char *buf = start;
    size_t i, n;
    if (total == 0) {
        return;
    }
    for (i = 0; i < total; i++) {
        unsigned no_op = mbedtls_ct_size_gt(total - offset, i);
        /* The first `total - offset` passes are a no-op. The last
         * `offset` passes shift the data one byte to the left and
         * zero out the last byte. */
        for (n = 0; n < total - 1; n++) {
            unsigned char current = buf[n];
            unsigned char next = buf[n+1];
            buf[n] = mbedtls_ct_uint_if(no_op, current, next);
        }
        buf[total-1] = mbedtls_ct_uint_if(no_op, buf[total-1], 0);
    }
}

#endif /* MBEDTLS_PKCS1_V15 && MBEDTLS_RSA_C && ! MBEDTLS_RSA_ALT */

#if defined(MBEDTLS_SSL_SOME_MODES_USE_MAC)
void mbedtls_ct_memcpy_if_eq(unsigned char *dest,
                             const unsigned char *src,
                             size_t len,
                             size_t c1,
                             size_t c2)
{
    /* mask = c1 == c2 ? 0xff : 0x00 */
    const size_t equal = mbedtls_ct_size_bool_eq(c1, c2);
    const unsigned char mask = (unsigned char) mbedtls_ct_size_mask(equal);

    /* dest[i] = c1 == c2 ? src[i] : dest[i] */
    for (size_t i = 0; i < len; i++) {
        dest[i] = (src[i] & mask) | (dest[i] & ~mask);
    }
}

void mbedtls_ct_memcpy_offset(unsigned char *dest,
                              const unsigned char *src,
                              size_t offset,
                              size_t offset_min,
                              size_t offset_max,
                              size_t len)
{
    size_t offsetval;

    for (offsetval = offset_min; offsetval <= offset_max; offsetval++) {
        mbedtls_ct_memcpy_if_eq(dest, src + offsetval, len,
                                offsetval, offset);
    }
}

int mbedtls_ct_hmac(mbedtls_md_context_t *ctx,
                    const unsigned char *add_data,
                    size_t add_data_len,
                    const unsigned char *data,
                    size_t data_len_secret,
                    size_t min_data_len,
                    size_t max_data_len,
                    unsigned char *output)
{
    /*
     * This function breaks the HMAC abstraction and uses the md_clone()
     * extension to the MD API in order to get constant-flow behaviour.
     *
     * HMAC(msg) is defined as HASH(okey + HASH(ikey + msg)) where + means
     * concatenation, and okey/ikey are the XOR of the key with some fixed bit
     * patterns (see RFC 2104, sec. 2), which are stored in ctx->hmac_ctx.
     *
     * We'll first compute inner_hash = HASH(ikey + msg) by hashing up to
     * minlen, then cloning the context, and for each byte up to maxlen
     * finishing up the hash computation, keeping only the correct result.
     *
     * Then we only need to compute HASH(okey + inner_hash) and we're done.
     */
    const mbedtls_md_type_t md_alg = mbedtls_md_get_type(ctx->md_info);
    /* TLS 1.0-1.2 only support SHA-384, SHA-256, SHA-1, MD-5,
     * all of which have the same block size except SHA-384. */
    const size_t block_size = md_alg == MBEDTLS_MD_SHA384 ? 128 : 64;
    const unsigned char * const ikey = ctx->hmac_ctx;
    const unsigned char * const okey = ikey + block_size;
    const size_t hash_size = mbedtls_md_get_size(ctx->md_info);

    unsigned char aux_out[MBEDTLS_MD_MAX_SIZE];
    mbedtls_md_context_t aux;
    size_t offset;
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;

    mbedtls_md_init(&aux);

#define MD_CHK(func_call) \
    do {                    \
        ret = (func_call);  \
        if (ret != 0)      \
        goto cleanup;   \
    } while (0)

    MD_CHK(mbedtls_md_setup(&aux, ctx->md_info, 0));

    /* After hmac_start() of hmac_reset(), ikey has already been hashed,
     * so we can start directly with the message */
    MD_CHK(mbedtls_md_update(ctx, add_data, add_data_len));
    MD_CHK(mbedtls_md_update(ctx, data, min_data_len));

    /* Fill the hash buffer in advance with something that is
     * not a valid hash (barring an attack on the hash and
     * deliberately-crafted input), in case the caller doesn't
     * check the return status properly. */
    memset(output, '!', hash_size);

    /* For each possible length, compute the hash up to that point */
    for (offset = min_data_len; offset <= max_data_len; offset++) {
        MD_CHK(mbedtls_md_clone(&aux, ctx));
        MD_CHK(mbedtls_md_finish(&aux, aux_out));
        /* Keep only the correct inner_hash in the output buffer */
        mbedtls_ct_memcpy_if_eq(output, aux_out, hash_size,
                                offset, data_len_secret);

        if (offset < max_data_len) {
            MD_CHK(mbedtls_md_update(ctx, data + offset, 1));
        }
    }

    /* The context needs to finish() before it starts() again */
    MD_CHK(mbedtls_md_finish(ctx, aux_out));

    /* Now compute HASH(okey + inner_hash) */
    MD_CHK(mbedtls_md_starts(ctx));
    MD_CHK(mbedtls_md_update(ctx, okey, block_size));
    MD_CHK(mbedtls_md_update(ctx, output, hash_size));
    MD_CHK(mbedtls_md_finish(ctx, output));

    /* Done, get ready for next time */
    MD_CHK(mbedtls_md_hmac_reset(ctx));

#undef MD_CHK

cleanup:
    mbedtls_md_free(&aux);
    return ret;
}

#endif /* MBEDTLS_SSL_SOME_MODES_USE_MAC */

#if defined(MBEDTLS_BIGNUM_C)

#define MPI_VALIDATE_RET(cond)                                       \
    MBEDTLS_INTERNAL_VALIDATE_RET(cond, MBEDTLS_ERR_MPI_BAD_INPUT_DATA)

/*
 * Conditionally assign X = Y, without leaking information
 * about whether the assignment was made or not.
 * (Leaking information about the respective sizes of X and Y is ok however.)
 */
#if defined(_MSC_VER) && defined(_M_ARM64) && (_MSC_FULL_VER < 193131103)
/*
 * MSVC miscompiles this function if it's inlined prior to Visual Studio 2022 version 17.1. See:
 * https://developercommunity.visualstudio.com/t/c-compiler-miscompiles-part-of-mbedtls-library-on/1646989
 */
__declspec(noinline)
#endif
int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X,
                                 const mbedtls_mpi *Y,
                                 unsigned char assign)
{
    int ret = 0;
    size_t i;
    mbedtls_mpi_uint limb_mask;
    MPI_VALIDATE_RET(X != NULL);
    MPI_VALIDATE_RET(Y != NULL);

    /* all-bits 1 if assign is 1, all-bits 0 if assign is 0 */
    limb_mask = mbedtls_ct_mpi_uint_mask(assign);;

    MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, Y->n));

    X->s = (int) mbedtls_ct_uint_if(assign, Y->s, X->s);

    mbedtls_ct_mpi_uint_cond_assign(Y->n, X->p, Y->p, assign);

    for (i = Y->n; i < X->n; i++) {
        X->p[i] &= ~limb_mask;
    }

cleanup:
    return ret;
}

/*
 * Conditionally swap X and Y, without leaking information
 * about whether the swap was made or not.
 * Here it is not ok to simply swap the pointers, which would lead to
 * different memory access patterns when X and Y are used afterwards.
 */
int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X,
                               mbedtls_mpi *Y,
                               unsigned char swap)
{
    int ret, s;
    size_t i;
    mbedtls_mpi_uint limb_mask;
    mbedtls_mpi_uint tmp;
    MPI_VALIDATE_RET(X != NULL);
    MPI_VALIDATE_RET(Y != NULL);

    if (X == Y) {
        return 0;
    }

    /* all-bits 1 if swap is 1, all-bits 0 if swap is 0 */
    limb_mask = mbedtls_ct_mpi_uint_mask(swap);

    MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, Y->n));
    MBEDTLS_MPI_CHK(mbedtls_mpi_grow(Y, X->n));

    s = X->s;
    X->s = (int) mbedtls_ct_uint_if(swap, Y->s, X->s);
    Y->s = (int) mbedtls_ct_uint_if(swap, s, Y->s);


    for (i = 0; i < X->n; i++) {
        tmp = X->p[i];
        X->p[i] = (X->p[i] & ~limb_mask) | (Y->p[i] & limb_mask);
        Y->p[i] = (Y->p[i] & ~limb_mask) | (tmp & limb_mask);
    }

cleanup:
    return ret;
}

/*
 * Compare signed values in constant time
 */
int mbedtls_mpi_lt_mpi_ct(const mbedtls_mpi *X,
                          const mbedtls_mpi *Y,
                          unsigned *ret)
{
    size_t i;
    /* The value of any of these variables is either 0 or 1 at all times. */
    unsigned cond, done, X_is_negative, Y_is_negative;

    MPI_VALIDATE_RET(X != NULL);
    MPI_VALIDATE_RET(Y != NULL);
    MPI_VALIDATE_RET(ret != NULL);

    if (X->n != Y->n) {
        return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
    }

    /*
     * Set sign_N to 1 if N >= 0, 0 if N < 0.
     * We know that N->s == 1 if N >= 0 and N->s == -1 if N < 0.
     */
    X_is_negative = (X->s & 2) >> 1;
    Y_is_negative = (Y->s & 2) >> 1;

    /*
     * If the signs are different, then the positive operand is the bigger.
     * That is if X is negative (X_is_negative == 1), then X < Y is true and it
     * is false if X is positive (X_is_negative == 0).
     */
    cond = (X_is_negative ^ Y_is_negative);
    *ret = cond & X_is_negative;

    /*
     * This is a constant-time function. We might have the result, but we still
     * need to go through the loop. Record if we have the result already.
     */
    done = cond;

    for (i = X->n; i > 0; i--) {
        /*
         * If Y->p[i - 1] < X->p[i - 1] then X < Y is true if and only if both
         * X and Y are negative.
         *
         * Again even if we can make a decision, we just mark the result and
         * the fact that we are done and continue looping.
         */
        cond = mbedtls_ct_mpi_uint_lt(Y->p[i - 1], X->p[i - 1]);
        *ret |= cond & (1 - done) & X_is_negative;
        done |= cond;

        /*
         * If X->p[i - 1] < Y->p[i - 1] then X < Y is true if and only if both
         * X and Y are positive.
         *
         * Again even if we can make a decision, we just mark the result and
         * the fact that we are done and continue looping.
         */
        cond = mbedtls_ct_mpi_uint_lt(X->p[i - 1], Y->p[i - 1]);
        *ret |= cond & (1 - done) & (1 - X_is_negative);
        done |= cond;
    }

    return 0;
}

#endif /* MBEDTLS_BIGNUM_C */

#if defined(MBEDTLS_PKCS1_V15) && defined(MBEDTLS_RSA_C) && !defined(MBEDTLS_RSA_ALT)

int mbedtls_ct_rsaes_pkcs1_v15_unpadding(int mode,
                                         unsigned char *input,
                                         size_t ilen,
                                         unsigned char *output,
                                         size_t output_max_len,
                                         size_t *olen)
{
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
    size_t i, plaintext_max_size;

    /* The following variables take sensitive values: their value must
     * not leak into the observable behavior of the function other than
     * the designated outputs (output, olen, return value). Otherwise
     * this would open the execution of the function to
     * side-channel-based variants of the Bleichenbacher padding oracle
     * attack. Potential side channels include overall timing, memory
     * access patterns (especially visible to an adversary who has access
     * to a shared memory cache), and branches (especially visible to
     * an adversary who has access to a shared code cache or to a shared
     * branch predictor). */
    size_t pad_count = 0;
    unsigned bad = 0;
    unsigned char pad_done = 0;
    size_t plaintext_size = 0;
    unsigned output_too_large;

    plaintext_max_size = (output_max_len > ilen - 11) ? ilen - 11
                                                        : output_max_len;

    /* Check and get padding length in constant time and constant
     * memory trace. The first byte must be 0. */
    bad |= input[0];

    if (mode == MBEDTLS_RSA_PRIVATE) {
        /* Decode EME-PKCS1-v1_5 padding: 0x00 || 0x02 || PS || 0x00
         * where PS must be at least 8 nonzero bytes. */
        bad |= input[1] ^ MBEDTLS_RSA_CRYPT;

        /* Read the whole buffer. Set pad_done to nonzero if we find
         * the 0x00 byte and remember the padding length in pad_count. */
        for (i = 2; i < ilen; i++) {
            pad_done  |= ((input[i] | (unsigned char) -input[i]) >> 7) ^ 1;
            pad_count += ((pad_done | (unsigned char) -pad_done) >> 7) ^ 1;
        }
    } else {
        /* Decode EMSA-PKCS1-v1_5 padding: 0x00 || 0x01 || PS || 0x00
         * where PS must be at least 8 bytes with the value 0xFF. */
        bad |= input[1] ^ MBEDTLS_RSA_SIGN;

        /* Read the whole buffer. Set pad_done to nonzero if we find
         * the 0x00 byte and remember the padding length in pad_count.
         * If there's a non-0xff byte in the padding, the padding is bad. */
        for (i = 2; i < ilen; i++) {
            pad_done |= mbedtls_ct_uint_if(input[i], 0, 1);
            pad_count += mbedtls_ct_uint_if(pad_done, 0, 1);
            bad |= mbedtls_ct_uint_if(pad_done, 0, input[i] ^ 0xFF);
        }
    }

    /* If pad_done is still zero, there's no data, only unfinished padding. */
    bad |= mbedtls_ct_uint_if(pad_done, 0, 1);

    /* There must be at least 8 bytes of padding. */
    bad |= mbedtls_ct_size_gt(8, pad_count);

    /* If the padding is valid, set plaintext_size to the number of
     * remaining bytes after stripping the padding. If the padding
     * is invalid, avoid leaking this fact through the size of the
     * output: use the maximum message size that fits in the output
     * buffer. Do it without branches to avoid leaking the padding
     * validity through timing. RSA keys are small enough that all the
     * size_t values involved fit in unsigned int. */
    plaintext_size = mbedtls_ct_uint_if(
        bad, (unsigned) plaintext_max_size,
        (unsigned) (ilen - pad_count - 3));

    /* Set output_too_large to 0 if the plaintext fits in the output
     * buffer and to 1 otherwise. */
    output_too_large = mbedtls_ct_size_gt(plaintext_size,
                                          plaintext_max_size);

    /* Set ret without branches to avoid timing attacks. Return:
     * - INVALID_PADDING if the padding is bad (bad != 0).
     * - OUTPUT_TOO_LARGE if the padding is good but the decrypted
     *   plaintext does not fit in the output buffer.
     * - 0 if the padding is correct. */
    ret = -(int) mbedtls_ct_uint_if(
        bad, -MBEDTLS_ERR_RSA_INVALID_PADDING,
        mbedtls_ct_uint_if(output_too_large,
                           -MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE,
                           0));

    /* If the padding is bad or the plaintext is too large, zero the
     * data that we're about to copy to the output buffer.
     * We need to copy the same amount of data
     * from the same buffer whether the padding is good or not to
     * avoid leaking the padding validity through overall timing or
     * through memory or cache access patterns. */
    bad = mbedtls_ct_uint_mask(bad | output_too_large);
    for (i = 11; i < ilen; i++) {
        input[i] &= ~bad;
    }

    /* If the plaintext is too large, truncate it to the buffer size.
     * Copy anyway to avoid revealing the length through timing, because
     * revealing the length is as bad as revealing the padding validity
     * for a Bleichenbacher attack. */
    plaintext_size = mbedtls_ct_uint_if(output_too_large,
                                        (unsigned) plaintext_max_size,
                                        (unsigned) plaintext_size);

    /* Move the plaintext to the leftmost position where it can start in
     * the working buffer, i.e. make it start plaintext_max_size from
     * the end of the buffer. Do this with a memory access trace that
     * does not depend on the plaintext size. After this move, the
     * starting location of the plaintext is no longer sensitive
     * information. */
    mbedtls_ct_mem_move_to_left(input + ilen - plaintext_max_size,
                                plaintext_max_size,
                                plaintext_max_size - plaintext_size);

    /* Finally copy the decrypted plaintext plus trailing zeros into the output
     * buffer. If output_max_len is 0, then output may be an invalid pointer
     * and the result of memcpy() would be undefined; prevent undefined
     * behavior making sure to depend only on output_max_len (the size of the
     * user-provided output buffer), which is independent from plaintext
     * length, validity of padding, success of the decryption, and other
     * secrets. */
    if (output_max_len != 0) {
        memcpy(output, input + ilen - plaintext_max_size, plaintext_max_size);
    }

    /* Report the amount of data we copied to the output buffer. In case
     * of errors (bad padding or output too large), the value of *olen
     * when this function returns is not specified. Making it equivalent
     * to the good case limits the risks of leaking the padding validity. */
    *olen = plaintext_size;

    return ret;
}

#endif /* MBEDTLS_PKCS1_V15 && MBEDTLS_RSA_C && ! MBEDTLS_RSA_ALT */