crypto/engine/eng_rsax.c

/* crypto/engine/eng_rsax.c */
/* Copyright (c) 2010-2010 Intel Corp.
 *   Author: Vinodh.Gopal@intel.com
 *           Jim Guilford
 *           Erdinc.Ozturk@intel.com
 *           Maxim.Perminov@intel.com
 *           Ying.Huang@intel.com
 *
 * More information about algorithm used can be found at:
 *   http://www.cse.buffalo.edu/srds2009/escs2009_submission_Gopal.pdf
 */
/* ====================================================================
 * Copyright (c) 1999-2001 The OpenSSL Project.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in
 *    the documentation and/or other materials provided with the
 *    distribution.
 *
 * 3. All advertising materials mentioning features or use of this
 *    software must display the following acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    licensing@OpenSSL.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
 * OF THE POSSIBILITY OF SUCH DAMAGE.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 */

#include <openssl/opensslconf.h>

#include <stdio.h>
#include <string.h>
#include <openssl/crypto.h>
#include <openssl/buffer.h>
#include <openssl/engine.h>
#ifndef OPENSSL_NO_RSA
# include <openssl/rsa.h>
#endif
#include <openssl/bn.h>
#include <openssl/err.h>

/* RSAX is available **ONLY* on x86_64 CPUs */
#undef COMPILE_RSAX

#if (defined(__x86_64) || defined(__x86_64__) || \
     defined(_M_AMD64) || defined (_M_X64)) && !defined(OPENSSL_NO_ASM)
# define COMPILE_RSAX
static ENGINE *ENGINE_rsax(void);
#endif

void ENGINE_load_rsax(void)
{
/* On non-x86 CPUs it just returns. */
#ifdef COMPILE_RSAX
    ENGINE *toadd = ENGINE_rsax();
    if (!toadd)
        return;
    ENGINE_add(toadd);
    ENGINE_free(toadd);
    ERR_clear_error();
#endif
}

#ifdef COMPILE_RSAX
# define E_RSAX_LIB_NAME "rsax engine"

static int e_rsax_destroy(ENGINE *e);
static int e_rsax_init(ENGINE *e);
static int e_rsax_finish(ENGINE *e);
static int e_rsax_ctrl(ENGINE *e, int cmd, long i, void *p, void (*f) (void));

# ifndef OPENSSL_NO_RSA
/* RSA stuff */
static int e_rsax_rsa_mod_exp(BIGNUM *r, const BIGNUM *I, RSA *rsa,
                              BN_CTX *ctx);
static int e_rsax_rsa_finish(RSA *r);
# endif

static const ENGINE_CMD_DEFN e_rsax_cmd_defns[] = {
    {0, NULL, NULL, 0}
};

# ifndef OPENSSL_NO_RSA
/* Our internal RSA_METHOD that we provide pointers to */
static RSA_METHOD e_rsax_rsa = {
    "Intel RSA-X method",
    NULL,
    NULL,
    NULL,
    NULL,
    e_rsax_rsa_mod_exp,
    NULL,
    NULL,
    e_rsax_rsa_finish,
    RSA_FLAG_CACHE_PUBLIC | RSA_FLAG_CACHE_PRIVATE,
    NULL,
    NULL,
    NULL
};
# endif

/* Constants used when creating the ENGINE */
static const char *engine_e_rsax_id = "rsax";
static const char *engine_e_rsax_name = "RSAX engine support";

/* This internal function is used by ENGINE_rsax() */
static int bind_helper(ENGINE *e)
{
# ifndef OPENSSL_NO_RSA
    const RSA_METHOD *meth1;
# endif
    if (!ENGINE_set_id(e, engine_e_rsax_id) ||
        !ENGINE_set_name(e, engine_e_rsax_name) ||
# ifndef OPENSSL_NO_RSA
        !ENGINE_set_RSA(e, &e_rsax_rsa) ||
# endif
        !ENGINE_set_destroy_function(e, e_rsax_destroy) ||
        !ENGINE_set_init_function(e, e_rsax_init) ||
        !ENGINE_set_finish_function(e, e_rsax_finish) ||
        !ENGINE_set_ctrl_function(e, e_rsax_ctrl) ||
        !ENGINE_set_cmd_defns(e, e_rsax_cmd_defns))
        return 0;

# ifndef OPENSSL_NO_RSA
    meth1 = RSA_PKCS1_SSLeay();
    e_rsax_rsa.rsa_pub_enc = meth1->rsa_pub_enc;
    e_rsax_rsa.rsa_pub_dec = meth1->rsa_pub_dec;
    e_rsax_rsa.rsa_priv_enc = meth1->rsa_priv_enc;
    e_rsax_rsa.rsa_priv_dec = meth1->rsa_priv_dec;
    e_rsax_rsa.bn_mod_exp = meth1->bn_mod_exp;
# endif
    return 1;
}

static ENGINE *ENGINE_rsax(void)
{
    ENGINE *ret = ENGINE_new();
    if (!ret)
        return NULL;
    if (!bind_helper(ret)) {
        ENGINE_free(ret);
        return NULL;
    }
    return ret;
}

# ifndef OPENSSL_NO_RSA
/* Used to attach our own key-data to an RSA structure */
static int rsax_ex_data_idx = -1;
# endif

static int e_rsax_destroy(ENGINE *e)
{
    return 1;
}

/* (de)initialisation functions. */
static int e_rsax_init(ENGINE *e)
{
# ifndef OPENSSL_NO_RSA
    if (rsax_ex_data_idx == -1)
        rsax_ex_data_idx = RSA_get_ex_new_index(0, NULL, NULL, NULL, NULL);
# endif
    if (rsax_ex_data_idx == -1)
        return 0;
    return 1;
}

static int e_rsax_finish(ENGINE *e)
{
    return 1;
}

static int e_rsax_ctrl(ENGINE *e, int cmd, long i, void *p, void (*f) (void))
{
    int to_return = 1;

    switch (cmd) {
        /* The command isn't understood by this engine */
    default:
        to_return = 0;
        break;
    }

    return to_return;
}

# ifndef OPENSSL_NO_RSA

#  ifdef _WIN32
typedef unsigned __int64 UINT64;
#  else
typedef unsigned long long UINT64;
#  endif
typedef unsigned short UINT16;

/*
 * Table t is interleaved in the following manner: The order in memory is
 * t[0][0], t[0][1], ..., t[0][7], t[1][0], ... A particular 512-bit value is
 * stored in t[][index] rather than the more normal t[index][]; i.e. the
 * qwords of a particular entry in t are not adjacent in memory
 */

/* Init BIGNUM b from the interleaved UINT64 array */
static int interleaved_array_to_bn_512(BIGNUM *b, UINT64 *array);

/*
 * Extract array elements from BIGNUM b To set the whole array from b, call
 * with n=8
 */
static int bn_extract_to_array_512(const BIGNUM *b, unsigned int n,
                                   UINT64 *array);

struct mod_ctx_512 {
    UINT64 t[8][8];
    UINT64 m[8];
    UINT64 m1[8];               /* 2^278 % m */
    UINT64 m2[8];               /* 2^640 % m */
    UINT64 k1[2];               /* (- 1/m) % 2^128 */
};

static int mod_exp_pre_compute_data_512(UINT64 *m, struct mod_ctx_512 *data);

void mod_exp_512(UINT64 *result, /* 512 bits, 8 qwords */
                 UINT64 *g,     /* 512 bits, 8 qwords */
                 UINT64 *exp,   /* 512 bits, 8 qwords */
                 struct mod_ctx_512 *data);

typedef struct st_e_rsax_mod_ctx {
    UINT64 type;
    union {
        struct mod_ctx_512 b512;
    } ctx;

} E_RSAX_MOD_CTX;

static E_RSAX_MOD_CTX *e_rsax_get_ctx(RSA *rsa, int idx, BIGNUM *m)
{
    E_RSAX_MOD_CTX *hptr;

    if (idx < 0 || idx > 2)
        return NULL;

    hptr = RSA_get_ex_data(rsa, rsax_ex_data_idx);
    if (!hptr) {
        hptr = OPENSSL_malloc(3 * sizeof(E_RSAX_MOD_CTX));
        if (!hptr)
            return NULL;
        hptr[2].type = hptr[1].type = hptr[0].type = 0;
        RSA_set_ex_data(rsa, rsax_ex_data_idx, hptr);
    }

    if (hptr[idx].type == (UINT64)BN_num_bits(m))
        return hptr + idx;

    if (BN_num_bits(m) == 512) {
        UINT64 _m[8];
        bn_extract_to_array_512(m, 8, _m);
        memset(&hptr[idx].ctx.b512, 0, sizeof(struct mod_ctx_512));
        mod_exp_pre_compute_data_512(_m, &hptr[idx].ctx.b512);
    }

    hptr[idx].type = BN_num_bits(m);
    return hptr + idx;
}

static int e_rsax_rsa_finish(RSA *rsa)
{
    E_RSAX_MOD_CTX *hptr = RSA_get_ex_data(rsa, rsax_ex_data_idx);
    if (hptr) {
        OPENSSL_free(hptr);
        RSA_set_ex_data(rsa, rsax_ex_data_idx, NULL);
    }
    if (rsa->_method_mod_n)
        BN_MONT_CTX_free(rsa->_method_mod_n);
    if (rsa->_method_mod_p)
        BN_MONT_CTX_free(rsa->_method_mod_p);
    if (rsa->_method_mod_q)
        BN_MONT_CTX_free(rsa->_method_mod_q);
    return 1;
}

static int e_rsax_bn_mod_exp(BIGNUM *r, const BIGNUM *g, const BIGNUM *e,
                             const BIGNUM *m, BN_CTX *ctx,
                             BN_MONT_CTX *in_mont,
                             E_RSAX_MOD_CTX *rsax_mod_ctx)
{
    if (rsax_mod_ctx && BN_get_flags(e, BN_FLG_CONSTTIME) != 0) {
        if (BN_num_bits(m) == 512) {
            UINT64 _r[8];
            UINT64 _g[8];
            UINT64 _e[8];

            /* Init the arrays from the BIGNUMs */
            bn_extract_to_array_512(g, 8, _g);
            bn_extract_to_array_512(e, 8, _e);

            mod_exp_512(_r, _g, _e, &rsax_mod_ctx->ctx.b512);
            /* Return the result in the BIGNUM */
            interleaved_array_to_bn_512(r, _r);
            return 1;
        }
    }

    return BN_mod_exp_mont(r, g, e, m, ctx, in_mont);
}

/*
 * Declares for the Intel CIAP 512-bit / CRT / 1024 bit RSA modular
 * exponentiation routine precalculations and a structure to hold the
 * necessary values.  These files are meant to live in crypto/rsa/ in the
 * target openssl.
 */

/*
 * Local method: extracts a piece from a BIGNUM, to fit it into
 * an array. Call with n=8 to extract an entire 512-bit BIGNUM
 */
static int bn_extract_to_array_512(const BIGNUM *b, unsigned int n,
                                   UINT64 *array)
{
    int i;
    UINT64 tmp;
    unsigned char bn_buff[64];
    memset(bn_buff, 0, 64);
    if (BN_num_bytes(b) > 64) {
        printf("Can't support this byte size\n");
        return 0;
    }
    if (BN_num_bytes(b) != 0) {
        if (!BN_bn2bin(b, bn_buff + (64 - BN_num_bytes(b)))) {
            printf("Error's in bn2bin\n");
            /* We have to error, here */
            return 0;
        }
    }
    while (n-- > 0) {
        array[n] = 0;
        for (i = 7; i >= 0; i--) {
            tmp = bn_buff[63 - (n * 8 + i)];
            array[n] |= tmp << (8 * i);
        }
    }
    return 1;
}

/* Init a 512-bit BIGNUM from the UINT64*_ (8 * 64) interleaved array */
static int interleaved_array_to_bn_512(BIGNUM *b, UINT64 *array)
{
    unsigned char tmp[64];
    int n = 8;
    int i;
    while (n-- > 0) {
        for (i = 7; i >= 0; i--) {
            tmp[63 - (n * 8 + i)] = (unsigned char)(array[n] >> (8 * i));
    }}
    BN_bin2bn(tmp, 64, b);
    return 0;
}

/* The main 512bit precompute call */
static int mod_exp_pre_compute_data_512(UINT64 *m, struct mod_ctx_512 *data)
{
    BIGNUM two_768, two_640, two_128, two_512, tmp, _m, tmp2;

    /* We need a BN_CTX for the modulo functions */
    BN_CTX *ctx;
    /* Some tmps */
    UINT64 _t[8];
    int i, j, ret = 0;

    /* Init _m with m */
    BN_init(&_m);
    interleaved_array_to_bn_512(&_m, m);
    memset(_t, 0, 64);

    /* Inits */
    BN_init(&two_768);
    BN_init(&two_640);
    BN_init(&two_128);
    BN_init(&two_512);
    BN_init(&tmp);
    BN_init(&tmp2);

    /* Create our context */
    if ((ctx = BN_CTX_new()) == NULL) {
        goto err;
    }
    BN_CTX_start(ctx);

    /*
     * For production, if you care, these only need to be set once,
     * and may be made constants.
     */
    BN_lshift(&two_768, BN_value_one(), 768);
    BN_lshift(&two_640, BN_value_one(), 640);
    BN_lshift(&two_128, BN_value_one(), 128);
    BN_lshift(&two_512, BN_value_one(), 512);

    if (0 == (m[7] & 0x8000000000000000)) {
        goto err;
    }
    if (0 == (m[0] & 0x1)) {    /* Odd modulus required for Mont */
        goto err;
    }

    /* Precompute m1 */
    BN_mod(&tmp, &two_768, &_m, ctx);
    if (!bn_extract_to_array_512(&tmp, 8, &data->m1[0])) {
        goto err;
    }

    /* Precompute m2 */
    BN_mod(&tmp, &two_640, &_m, ctx);
    if (!bn_extract_to_array_512(&tmp, 8, &data->m2[0])) {
        goto err;
    }

    /*
     * Precompute k1, a 128b number = ((-1)* m-1 ) mod 2128; k1 should
     * be non-negative.
     */
    BN_mod_inverse(&tmp, &_m, &two_128, ctx);
    if (!BN_is_zero(&tmp)) {
        BN_sub(&tmp, &two_128, &tmp);
    }
    if (!bn_extract_to_array_512(&tmp, 2, &data->k1[0])) {
        goto err;
    }

    /* Precompute t */
    for (i = 0; i < 8; i++) {
        BN_zero(&tmp);
        if (i & 1) {
            BN_add(&tmp, &two_512, &tmp);
        }
        if (i & 2) {
            BN_add(&tmp, &two_512, &tmp);
        }
        if (i & 4) {
            BN_add(&tmp, &two_640, &tmp);
        }

        BN_nnmod(&tmp2, &tmp, &_m, ctx);
        if (!bn_extract_to_array_512(&tmp2, 8, _t)) {
            goto err;
        }
        for (j = 0; j < 8; j++)
            data->t[j][i] = _t[j];
    }

    /* Precompute m */
    for (i = 0; i < 8; i++) {
        data->m[i] = m[i];
    }

    ret = 1;

 err:
    /* Cleanup */
    if (ctx != NULL) {
        BN_CTX_end(ctx);
        BN_CTX_free(ctx);
    }
    BN_free(&two_768);
    BN_free(&two_640);
    BN_free(&two_128);
    BN_free(&two_512);
    BN_free(&tmp);
    BN_free(&tmp2);
    BN_free(&_m);

    return ret;
}

static int e_rsax_rsa_mod_exp(BIGNUM *r0, const BIGNUM *I, RSA *rsa,
                              BN_CTX *ctx)
{
    BIGNUM *r1, *m1, *vrfy;
    BIGNUM local_dmp1, local_dmq1, local_c, local_r1;
    BIGNUM *dmp1, *dmq1, *c, *pr1;
    int ret = 0;

    BN_CTX_start(ctx);
    r1 = BN_CTX_get(ctx);
    m1 = BN_CTX_get(ctx);
    vrfy = BN_CTX_get(ctx);

    {
        BIGNUM local_p, local_q;
        BIGNUM *p = NULL, *q = NULL;
        int error = 0;

        /*
         * Make sure BN_mod_inverse in Montgomery intialization uses the
         * BN_FLG_CONSTTIME flag (unless RSA_FLAG_NO_CONSTTIME is set)
         */
        if (!(rsa->flags & RSA_FLAG_NO_CONSTTIME)) {
            BN_init(&local_p);
            p = &local_p;
            BN_with_flags(p, rsa->p, BN_FLG_CONSTTIME);

            BN_init(&local_q);
            q = &local_q;
            BN_with_flags(q, rsa->q, BN_FLG_CONSTTIME);
        } else {
            p = rsa->p;
            q = rsa->q;
        }

        if (rsa->flags & RSA_FLAG_CACHE_PRIVATE) {
            if (!BN_MONT_CTX_set_locked
                (&rsa->_method_mod_p, CRYPTO_LOCK_RSA, p, ctx))
                error = 1;
            if (!BN_MONT_CTX_set_locked
                (&rsa->_method_mod_q, CRYPTO_LOCK_RSA, q, ctx))
                error = 1;
        }

        /* clean up */
        if (!(rsa->flags & RSA_FLAG_NO_CONSTTIME)) {
            BN_free(&local_p);
            BN_free(&local_q);
        }
        if (error)
            goto err;
    }

    if (rsa->flags & RSA_FLAG_CACHE_PUBLIC)
        if (!BN_MONT_CTX_set_locked
            (&rsa->_method_mod_n, CRYPTO_LOCK_RSA, rsa->n, ctx))
            goto err;

    /* compute I mod q */
    if (!(rsa->flags & RSA_FLAG_NO_CONSTTIME)) {
        c = &local_c;
        BN_with_flags(c, I, BN_FLG_CONSTTIME);
        if (!BN_mod(r1, c, rsa->q, ctx))
            goto err;
    } else {
        if (!BN_mod(r1, I, rsa->q, ctx))
            goto err;
    }

    /* compute r1^dmq1 mod q */
    if (!(rsa->flags & RSA_FLAG_NO_CONSTTIME)) {
        dmq1 = &local_dmq1;
        BN_with_flags(dmq1, rsa->dmq1, BN_FLG_CONSTTIME);
    } else
        dmq1 = rsa->dmq1;

    if (!e_rsax_bn_mod_exp(m1, r1, dmq1, rsa->q, ctx,
                           rsa->_method_mod_q, e_rsax_get_ctx(rsa, 0,
                                                              rsa->q)))
        goto err;

    /* compute I mod p */
    if (!(rsa->flags & RSA_FLAG_NO_CONSTTIME)) {
        c = &local_c;
        BN_with_flags(c, I, BN_FLG_CONSTTIME);
        if (!BN_mod(r1, c, rsa->p, ctx))
            goto err;
    } else {
        if (!BN_mod(r1, I, rsa->p, ctx))
            goto err;
    }

    /* compute r1^dmp1 mod p */
    if (!(rsa->flags & RSA_FLAG_NO_CONSTTIME)) {
        dmp1 = &local_dmp1;
        BN_with_flags(dmp1, rsa->dmp1, BN_FLG_CONSTTIME);
    } else
        dmp1 = rsa->dmp1;

    if (!e_rsax_bn_mod_exp(r0, r1, dmp1, rsa->p, ctx,
                           rsa->_method_mod_p, e_rsax_get_ctx(rsa, 1,
                                                              rsa->p)))
        goto err;

    if (!BN_sub(r0, r0, m1))
        goto err;
    /*
     * This will help stop the size of r0 increasing, which does affect the
     * multiply if it optimised for a power of 2 size
     */
    if (BN_is_negative(r0))
        if (!BN_add(r0, r0, rsa->p))
            goto err;

    if (!BN_mul(r1, r0, rsa->iqmp, ctx))
        goto err;

    /* Turn BN_FLG_CONSTTIME flag on before division operation */
    if (!(rsa->flags & RSA_FLAG_NO_CONSTTIME)) {
        pr1 = &local_r1;
        BN_with_flags(pr1, r1, BN_FLG_CONSTTIME);
    } else
        pr1 = r1;
    if (!BN_mod(r0, pr1, rsa->p, ctx))
        goto err;

    /*
     * If p < q it is occasionally possible for the correction of adding 'p'
     * if r0 is negative above to leave the result still negative. This can
     * break the private key operations: the following second correction
     * should *always* correct this rare occurrence. This will *never* happen
     * with OpenSSL generated keys because they ensure p > q [steve]
     */
    if (BN_is_negative(r0))
        if (!BN_add(r0, r0, rsa->p))
            goto err;
    if (!BN_mul(r1, r0, rsa->q, ctx))
        goto err;
    if (!BN_add(r0, r1, m1))
        goto err;

    if (rsa->e && rsa->n) {
        if (!e_rsax_bn_mod_exp
            (vrfy, r0, rsa->e, rsa->n, ctx, rsa->_method_mod_n,
             e_rsax_get_ctx(rsa, 2, rsa->n)))
            goto err;

        /*
         * If 'I' was greater than (or equal to) rsa->n, the operation will
         * be equivalent to using 'I mod n'. However, the result of the
         * verify will *always* be less than 'n' so we don't check for
         * absolute equality, just congruency.
         */
        if (!BN_sub(vrfy, vrfy, I))
            goto err;
        if (!BN_mod(vrfy, vrfy, rsa->n, ctx))
            goto err;
        if (BN_is_negative(vrfy))
            if (!BN_add(vrfy, vrfy, rsa->n))
                goto err;
        if (!BN_is_zero(vrfy)) {
            /*
             * 'I' and 'vrfy' aren't congruent mod n. Don't leak
             * miscalculated CRT output, just do a raw (slower) mod_exp and
             * return that instead.
             */

            BIGNUM local_d;
            BIGNUM *d = NULL;

            if (!(rsa->flags & RSA_FLAG_NO_CONSTTIME)) {
                d = &local_d;
                BN_with_flags(d, rsa->d, BN_FLG_CONSTTIME);
            } else
                d = rsa->d;
            if (!e_rsax_bn_mod_exp(r0, I, d, rsa->n, ctx,
                                   rsa->_method_mod_n, e_rsax_get_ctx(rsa, 2,
                                                                      rsa->n)))
                goto err;
        }
    }
    ret = 1;

 err:
    BN_CTX_end(ctx);

    return ret;
}
# endif                         /* !OPENSSL_NO_RSA */
#endif                          /* !COMPILE_RSAX */