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/*
* rsa.c: implementation of RSA with PKCS#1 padding
*/
/*
* This file is Free Software. It was originally written for secnet.
*
* Copyright 1995-2003 Stephen Early
* Copyright 2002-2014 Ian Jackson
* Copyright 2001 Simon Tatham
* Copyright 2013 Mark Wooding
*
* You may redistribute secnet as a whole and/or modify it under the
* terms of the GNU General Public License as published by the Free
* Software Foundation; either version 3, or (at your option) any
* later version.
*
* You may redistribute this file and/or modify it under the terms of
* the GNU General Public License as published by the Free Software
* Foundation; either version 2, or (at your option) any later
* version.
*
* This software is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this software; if not, see
* https://www.gnu.org/licenses/gpl.html.
*/
#include <stdio.h>
#include <string.h>
#include <gmp.h>
#include "secnet.h"
#include "util.h"
#include "unaligned.h"
#define AUTHFILE_ID_STRING "SSH PRIVATE KEY FILE FORMAT 1.1\n"
#define mpp(s,n) do { char *p = mpz_get_str(NULL,16,n); printf("%s 0x%sL\n", s, p); free(p); } while (0)
struct rsacommon {
uint8_t *hashbuf;
};
#define FREE(b) ({ free((b)); (b)=0; })
struct load_ctx {
void (*verror)(struct load_ctx *l, struct cloc loc,
FILE *maybe_f,
const char *message, va_list args);
bool_t (*postreadcheck)(struct load_ctx *l, FILE *f);
const char *what;
dict_t *deprdict; /* used only to look up hash */
struct cloc loc;
union {
struct {
struct log_if *log;
} tryload;
} u;
};
static void load_err(struct load_ctx *l,
const struct cloc *maybe_loc, FILE *maybe_f,
const char *fmt, ...)
{
va_list al;
va_start(al,fmt);
l->verror(l, maybe_loc ? *maybe_loc : l->loc, maybe_f,fmt,al);
va_end(al);
}
FORMAT(printf,4,0)
static void verror_tryload(struct load_ctx *l, struct cloc loc,
FILE *maybe_f,
const char *message, va_list args)
{
int class=M_ERR;
slilog_part(l->u.tryload.log,class,"%s: ",l->what);
vslilog(l->u.tryload.log,class,message,args);
}
static void verror_cfgfatal(struct load_ctx *l, struct cloc loc,
FILE *maybe_f,
const char *message, va_list args)
{
vcfgfatal_maybefile(maybe_f,l->loc,l->what,message,args,"");
}
struct rsapriv {
closure_t cl;
struct sigprivkey_if ops;
struct cloc loc;
struct rsacommon common;
MP_INT n;
MP_INT p, dp;
MP_INT q, dq;
MP_INT w;
};
#define RSAPUB_BNS(each) \
each(0,e,"public exponent") \
each(1,n,"modulus")
#define RSAPUB_LOADCORE_PASSBN(ix,en,what) \
en##s, en##_loc,
#define RSAPUB_INIT_ST_BN( ix,en,what) mpz_init (&st->en);
#define RSAPUB_CLEAR_ST_BN(ix,en,what) mpz_clear(&st->en);
struct rsapub {
closure_t cl;
struct sigpubkey_if ops;
struct cloc loc;
struct rsacommon common;
MP_INT e;
MP_INT n;
};
/* Sign data. NB data must be smaller than modulus */
#define RSA_MAX_MODBYTES 2048
/* The largest modulus I've seen is 15360 bits, which works out at 1920
* bytes. Using keys this big is quite implausible, but it doesn't cost us
* much to support them.
*/
static const char *hexchars="0123456789abcdef";
static void rsa_sethash(struct load_ctx *l,
struct rsacommon *c,
const struct hash_if **in_ops)
{
struct hash_if *hash=0;
if (l->deprdict)
hash=find_cl_if(l->deprdict,"hash",CL_HASH,False,"site",l->loc);
if (!hash)
hash=sha1_hash_if;
c->hashbuf=safe_malloc(hash->hlen, "generate_msg");
*in_ops=hash;
}
static void rsacommon_dispose(struct rsacommon *c)
{
free(c->hashbuf);
}
static void emsa_pkcs1(MP_INT *n, MP_INT *m,
const uint8_t *data, int32_t datalen)
{
char buff[2*RSA_MAX_MODBYTES + 1];
int msize, i;
/* RSA PKCS#1 v1.5 signature padding:
*
* <------------ msize hex digits ---------->
*
* 00 01 ff ff .... ff ff 00 vv vv vv .... vv
*
* <--- datalen -->
* bytes
* = datalen*2 hex digits
*
* NB that according to PKCS#1 v1.5 we're supposed to include a
* hash function OID in the data. We don't do that (because we
* don't have the hash function OID to hand here), thus violating
* the spec in a way that affects interop but not security.
*
* -iwj 17.9.2002
*/
msize=mpz_sizeinbase(n, 16);
if (datalen*2+6>=msize) {
fatal("rsa: message too big");
}
strcpy(buff,"0001");
for (i=0; i<datalen; i++) {
buff[msize+(-datalen+i)*2]=hexchars[(data[i]&0xf0)>>4];
buff[msize+(-datalen+i)*2+1]=hexchars[data[i]&0xf];
}
buff[msize-datalen*2-2]= '0';
buff[msize-datalen*2-1]= '0';
for (i=4; i<msize-datalen*2-2; i++)
buff[i]='f';
buff[msize]=0;
mpz_set_str(m, buff, 16);
}
static bool_t rsa_sign(void *sst, uint8_t *data, int32_t datalen,
struct buffer_if *msg)
{
struct rsapriv *st=sst;
MP_INT a, b, u, v, tmp, tmp2;
string_t signature = 0;
bool_t ok;
mpz_init(&a);
mpz_init(&b);
hash_hash(st->ops.hash,data,datalen,st->common.hashbuf);
/* Construct the message representative. */
emsa_pkcs1(&st->n, &a, st->common.hashbuf, st->ops.hash->hlen);
/*
* Produce an RSA signature (a^d mod n) using the Chinese
* Remainder Theorem. We compute:
*
* u = a^dp mod p (== a^d mod p, since dp == d mod (p-1))
* v = a^dq mod q (== a^d mod q, similarly)
*
* We also know w == iqmp * q, which has the property that w ==
* 0 mod q and w == 1 mod p. So (1-w) has the reverse property
* (congruent to 0 mod p and to 1 mod q). Hence we now compute
*
* b = w * u + (1-w) * v
* = w * (u-v) + v
*
* so that b is congruent to a^d both mod p and mod q. Hence b,
* reduced mod n, is the required signature.
*/
mpz_init(&tmp);
mpz_init(&tmp2);
mpz_init(&u);
mpz_init(&v);
mpz_powm_sec(&u, &a, &st->dp, &st->p);
mpz_powm_sec(&v, &a, &st->dq, &st->q);
mpz_sub(&tmp, &u, &v);
mpz_mul(&tmp2, &tmp, &st->w);
mpz_add(&tmp, &tmp2, &v);
mpz_mod(&b, &tmp, &st->n);
mpz_clear(&tmp);
mpz_clear(&tmp2);
mpz_clear(&u);
mpz_clear(&v);
signature=write_mpstring(&b);
uint8_t *op = buf_append(msg,2);
if (!op) { ok=False; goto out; }
size_t l = strlen(signature);
assert(l < 65536);
put_uint16(op, l);
op = buf_append(msg,l);
if (!op) { ok=False; goto out; }
memcpy(op, signature, l);
ok = True;
out:
free(signature);
mpz_clear(&b);
mpz_clear(&a);
return ok;
}
static bool_t rsa_sig_unpick(void *sst, struct buffer_if *msg,
struct alg_msg_data *sig)
{
uint8_t *lp = buf_unprepend(msg, 2);
if (!lp) return False;
sig->len = get_uint16(lp);
sig->start = buf_unprepend(msg, sig->len);
if (!sig->start) return False;
/* In `rsa_sig_check' below, we assume that we can write a nul
* terminator following the signature. Make sure there's enough space.
*/
if (msg->start >= msg->base + msg->alloclen)
return False;
return True;
}
static sig_checksig_fn rsa_sig_check;
static bool_t rsa_sig_check(void *sst, uint8_t *data, int32_t datalen,
const struct alg_msg_data *sig)
{
struct rsapub *st=sst;
MP_INT a, b, c;
bool_t ok;
mpz_init(&a);
mpz_init(&b);
mpz_init(&c);
hash_hash(st->ops.hash,data,datalen,st->common.hashbuf);
emsa_pkcs1(&st->n, &a, st->common.hashbuf, st->ops.hash->hlen);
/* Terminate signature with a '0' - already checked that this will fit */
int save = sig->start[sig->len];
sig->start[sig->len] = 0;
mpz_set_str(&b, sig->start, 16);
sig->start[sig->len] = save;
mpz_powm(&c, &b, &st->e, &st->n);
ok=(mpz_cmp(&a, &c)==0);
mpz_clear(&c);
mpz_clear(&b);
mpz_clear(&a);
return ok;
}
static void rsapub_dispose(void *sst) {
struct rsapub *st=sst;
if (!st) return;
RSAPUB_BNS(RSAPUB_CLEAR_ST_BN)
rsacommon_dispose(&st->common);
free(st);
}
#define RSAPUB_LOADCORE_DEFBN(ix,en,what) \
const char *en##s, struct cloc en##_loc,
#define LDPUBFATAL(lc,...) ({ \
load_err(l,(lc),0,__VA_ARGS__); \
goto error_out; \
})
static struct rsapub *rsa_loadpub_core(RSAPUB_BNS(RSAPUB_LOADCORE_DEFBN)
struct load_ctx *l)
{
struct rsapub *st;
NEW(st);
st->cl.description="rsapub";
st->cl.type=CL_SIGPUBKEY;
st->cl.apply=NULL;
st->cl.interface=&st->ops;
st->ops.st=st;
st->common.hashbuf=NULL;
st->ops.unpick=rsa_sig_unpick;
st->ops.check=rsa_sig_check;
st->ops.hash=0;
st->ops.dispose=rsapub_dispose;
st->loc=l->loc;
RSAPUB_BNS(RSAPUB_INIT_ST_BN)
#define RSAPUB_LOADCORE_GETBN(ix,en,what) \
if (mpz_init_set_str(&st->en,en##s,10)!=0) { \
LDPUBFATAL(&en##_loc, what " \"%s\" is not a " \
"decimal number string",en##s); \
} \
if (mpz_sizeinbase(&st->en, 256) > RSA_MAX_MODBYTES) { \
LDPUBFATAL(&en##_loc, "implausibly large " what); \
}
RSAPUB_BNS(RSAPUB_LOADCORE_GETBN)
rsa_sethash(l,&st->common,&st->ops.hash);
return st;
error_out:
rsapub_dispose(st);
return 0;
}
static list_t *rsapub_apply(closure_t *self, struct cloc loc, dict_t *context,
list_t *args)
{
struct load_ctx l[1];
l->verror=verror_cfgfatal;
l->postreadcheck=0;
l->what="rsa-public";
l->deprdict=context;
l->loc=loc;
#define RSAPUB_APPLY_GETBN(ix,en,what) \
item_t *en##i; \
const char *en##s; \
en##i=list_elem(args,ix); \
if (!en##i) \
cfgfatal(loc,"rsa-public", \
"you must provide an encryption key\n"); \
struct cloc en##_loc=en##i->loc; \
if (en##i->type!=t_string) \
cfgfatal(en##_loc,"rsa-public", \
"first argument must be a string\n"); \
en##s=en##i->data.string;
RSAPUB_BNS(RSAPUB_APPLY_GETBN)
struct rsapub *st=rsa_loadpub_core(RSAPUB_BNS(RSAPUB_LOADCORE_PASSBN)
l);
return new_closure(&st->cl);
}
bool_t rsa1_loadpub(const struct sigscheme_info *algo,
struct buffer_if *pubkeydata,
struct sigpubkey_if **sigpub_r,
closure_t **closure_r,
struct log_if *log, struct cloc loc)
{
struct rsapub *st=0;
struct load_ctx l[1];
l->verror=verror_tryload;
l->postreadcheck=0;
l->what="rsa1_loadpub";
l->deprdict=0;
l->loc=loc;
l->u.tryload.log=log;
char *nul=buf_append(pubkeydata,1);
if (!nul) LDPUBFATAL(0,"rsa1 public key data too long for extra nul");
*nul=0;
const char *delim=" \t\n";
char *saveptr;
/*unused*/ strtok_r(pubkeydata->start,delim,&saveptr);
#define RSAPUB_TRYLOAD_GETBN(ix,en,what) \
struct cloc en##_loc=loc; \
const char *en##s=strtok_r(0,delim,&saveptr); \
if (!en##s) LDPUBFATAL(0,"end of pubkey data looking for " what);
RSAPUB_BNS(RSAPUB_TRYLOAD_GETBN);
st=rsa_loadpub_core(RSAPUB_BNS(RSAPUB_LOADCORE_PASSBN) l);
if (!st) goto error_out;
*sigpub_r=&st->ops;
*closure_r=&st->cl;
return True;
error_out:
rsapub_dispose(st);
return False;
}
#define LDFATAL(...) ({ load_err(l,0,0,__VA_ARGS__); goto error_out; })
#define LDFATAL_FILE(...) ({ load_err(l,0,f,__VA_ARGS__); goto error_out; })
#define KEYFILE_GET(is) ({ \
uint##is##_t keyfile_get_tmp=keyfile_get_##is(l,f); \
if (!l->postreadcheck(l,f)) goto error_out; \
keyfile_get_tmp; \
})
static uint32_t keyfile_get_32(struct load_ctx *l, FILE *f)
{
uint32_t r;
r=fgetc(f)<<24;
r|=fgetc(f)<<16;
r|=fgetc(f)<<8;
r|=fgetc(f);
return r;
}
static uint16_t keyfile_get_16(struct load_ctx *l, FILE *f)
{
uint16_t r;
r=fgetc(f)<<8;
r|=fgetc(f);
return r;
}
static void rsapriv_dispose(void *sst)
{
struct rsapriv *st=sst;
mpz_clear(&st->n);
mpz_clear(&st->p); mpz_clear(&st->dp);
mpz_clear(&st->q); mpz_clear(&st->dq);
mpz_clear(&st->w);
rsacommon_dispose(&st->common);
free(st);
}
static struct rsapriv *rsa_loadpriv_core(struct load_ctx *l,
FILE *f, struct cloc loc,
bool_t do_validity_check)
{
struct rsapriv *st=0;
long length;
uint8_t *b=0, *c=0;
int cipher_type;
MP_INT e,d,iqmp,tmp,tmp2,tmp3;
bool_t valid;
mpz_init(&e);
mpz_init(&d);
mpz_init(&iqmp);
mpz_init(&tmp);
mpz_init(&tmp2);
mpz_init(&tmp3);
NEW(st);
st->cl.description="rsapriv";
st->cl.type=CL_SIGPRIVKEY;
st->cl.apply=NULL;
st->cl.interface=&st->ops;
st->ops.st=st;
st->common.hashbuf=NULL;
st->ops.sign=rsa_sign;
st->ops.hash=0;
st->ops.dispose=rsapriv_dispose;
st->loc=loc;
mpz_init(&st->n);
mpz_init(&st->q);
mpz_init(&st->p);
mpz_init(&st->dp);
mpz_init(&st->dq);
mpz_init(&st->w);
if (!f) {
assert(just_check_config);
goto assume_valid;
}
/* Check that the ID string is correct */
length=strlen(AUTHFILE_ID_STRING)+1;
b=safe_malloc(length,"rsapriv_apply");
if (fread(b,length,1,f)!=1 || memcmp(b,AUTHFILE_ID_STRING,length)!=0) {
LDFATAL_FILE("failed to read magic ID"
" string from SSH1 private keyfile\n");
}
FREE(b);
cipher_type=fgetc(f);
KEYFILE_GET(32); /* "Reserved data" */
if (cipher_type != 0) {
LDFATAL("we don't support encrypted keyfiles\n");
}
/* Read the public key */
KEYFILE_GET(32); /* Not sure what this is */
length=(KEYFILE_GET(16)+7)/8;
if (length>RSA_MAX_MODBYTES) {
LDFATAL("implausible length %ld for modulus\n",
length);
}
b=safe_malloc(length,"rsapriv_apply");
if (fread(b,length,1,f) != 1) {
LDFATAL_FILE("error reading modulus\n");
}
read_mpbin(&st->n,b,length);
FREE(b);
length=(KEYFILE_GET(16)+7)/8;
if (length>RSA_MAX_MODBYTES) {
LDFATAL("implausible length %ld for e\n",length);
}
b=safe_malloc(length,"rsapriv_apply");
if (fread(b,length,1,f)!=1) {
LDFATAL_FILE("error reading e\n");
}
read_mpbin(&e,b,length);
FREE(b);
length=KEYFILE_GET(32);
if (length>1024) {
LDFATAL("implausibly long (%ld) key comment\n",
length);
}
c=safe_malloc(length+1,"rsapriv_apply");
if (fread(c,length,1,f)!=1) {
LDFATAL_FILE("error reading key comment\n");
}
c[length]=0;
/* Check that the next two pairs of characters are identical - the
keyfile is not encrypted, so they should be */
if (KEYFILE_GET(16) != KEYFILE_GET(16)) {
LDFATAL("corrupt keyfile\n");
}
/* Read d */
length=(KEYFILE_GET(16)+7)/8;
if (length>RSA_MAX_MODBYTES) {
LDFATAL("implausibly long (%ld) decryption key\n",
length);
}
b=safe_malloc(length,"rsapriv_apply");
if (fread(b,length,1,f)!=1) {
LDFATAL_FILE("error reading decryption key\n");
}
read_mpbin(&d,b,length);
FREE(b);
/* Read iqmp (inverse of q mod p) */
length=(KEYFILE_GET(16)+7)/8;
if (length>RSA_MAX_MODBYTES) {
LDFATAL("implausibly long (%ld)"
" iqmp auxiliary value\n", length);
}
b=safe_malloc(length,"rsapriv_apply");
if (fread(b,length,1,f)!=1) {
LDFATAL_FILE("error reading decryption key\n");
}
read_mpbin(&iqmp,b,length);
FREE(b);
/* Read q (the smaller of the two primes) */
length=(KEYFILE_GET(16)+7)/8;
if (length>RSA_MAX_MODBYTES) {
LDFATAL("implausibly long (%ld) q value\n",
length);
}
b=safe_malloc(length,"rsapriv_apply");
if (fread(b,length,1,f)!=1) {
LDFATAL_FILE("error reading q value\n");
}
read_mpbin(&st->q,b,length);
FREE(b);
/* Read p (the larger of the two primes) */
length=(KEYFILE_GET(16)+7)/8;
if (length>RSA_MAX_MODBYTES) {
LDFATAL("implausibly long (%ld) p value\n",
length);
}
b=safe_malloc(length,"rsapriv_apply");
if (fread(b,length,1,f)!=1) {
LDFATAL_FILE("error reading p value\n");
}
read_mpbin(&st->p,b,length);
FREE(b);
if (ferror(f)) {
fatal_perror("rsa-private (%s:%d): ferror",loc.file,loc.line);
}
rsa_sethash(l,&st->common,&st->ops.hash);
/*
* Now verify the validity of the key, and set up the auxiliary
* values for fast CRT signing.
*/
valid=False;
if (do_validity_check) {
/* Verify that p*q is equal to n. */
mpz_mul(&tmp, &st->p, &st->q);
if (mpz_cmp(&tmp, &st->n) != 0)
goto done_checks;
/*
* Verify that d*e is congruent to 1 mod (p-1), and mod
* (q-1). This is equivalent to it being congruent to 1 mod
* lambda(n) = lcm(p-1,q-1). The usual `textbook' condition,
* that d e == 1 (mod (p-1)(q-1)) is sufficient, but not
* actually necessary.
*/
mpz_mul(&tmp, &d, &e);
mpz_sub_ui(&tmp2, &st->p, 1);
mpz_mod(&tmp3, &tmp, &tmp2);
if (mpz_cmp_si(&tmp3, 1) != 0)
goto done_checks;
mpz_sub_ui(&tmp2, &st->q, 1);
mpz_mod(&tmp3, &tmp, &tmp2);
if (mpz_cmp_si(&tmp3, 1) != 0)
goto done_checks;
/* Verify that q*iqmp is congruent to 1 mod p. */
mpz_mul(&tmp, &st->q, &iqmp);
mpz_mod(&tmp2, &tmp, &st->p);
if (mpz_cmp_si(&tmp2, 1) != 0)
goto done_checks;
}
/* Now we know the key is valid (or we don't care). */
valid = True;
/*
* Now we compute auxiliary values dp, dq and w to allow us
* to use the CRT optimisation when signing.
*
* dp == d mod (p-1) so that a^dp == a^d mod p, for all a
* dq == d mod (q-1) similarly mod q
* w == iqmp * q so that w == 0 mod q, and w == 1 mod p
*/
mpz_sub_ui(&tmp, &st->p, 1);
mpz_mod(&st->dp, &d, &tmp);
mpz_sub_ui(&tmp, &st->q, 1);
mpz_mod(&st->dq, &d, &tmp);
mpz_mul(&st->w, &iqmp, &st->q);
done_checks:
if (!valid) {
LDFATAL("file does not contain a "
"valid RSA key!\n");
}
assume_valid:
out:
mpz_clear(&tmp);
mpz_clear(&tmp2);
mpz_clear(&tmp3);
FREE(b);
FREE(c);
mpz_clear(&e);
mpz_clear(&d);
mpz_clear(&iqmp);
return st;
error_out:
if (st) rsapriv_dispose(st);
st=0;
goto out;
}
static bool_t postreadcheck_tryload(struct load_ctx *l, FILE *f)
{
assert(!ferror(f));
if (feof(f)) { load_err(l,0,0,"eof mid-integer"); return False; }
return True;
}
bool_t rsa1_loadpriv(const struct sigscheme_info *algo,
struct buffer_if *privkeydata,
struct sigprivkey_if **sigpriv_r,
closure_t **closure_r,
struct log_if *log, struct cloc loc)
{
FILE *f=0;
struct rsapriv *st=0;
f=fmemopen(privkeydata->start,privkeydata->size,"r");
if (!f) {
slilog(log,M_ERR,"failed to fmemopen private key file\n");
goto error_out;
}
struct load_ctx l[1];
l->what="rsa1priv load";
l->verror=verror_tryload;
l->postreadcheck=postreadcheck_tryload;
l->deprdict=0;
l->loc=loc;
l->u.tryload.log=log;
st=rsa_loadpriv_core(l,f,loc,False);
if (!st) goto error_out;
goto out;
error_out:
FREE(st);
out:
if (f) fclose(f);
if (!st) return False;
*sigpriv_r=&st->ops;
*closure_r=&st->cl;
return True;
}
static bool_t postreadcheck_apply(struct load_ctx *l, FILE *f)
{
cfgfile_postreadcheck(l->loc,f);
return True;
}
static list_t *rsapriv_apply(closure_t *self, struct cloc loc, dict_t *context,
list_t *args)
{
struct rsapriv *st;
item_t *i;
cstring_t filename;
FILE *f;
struct load_ctx l[1];
l->what="rsa-private";
l->verror=verror_cfgfatal;
l->postreadcheck=postreadcheck_apply;
l->deprdict=context;
l->loc=loc;
/* Argument is filename pointing to SSH1 private key file */
i=list_elem(args,0);
if (i) {
if (i->type!=t_string) {
cfgfatal(i->loc,"rsa-private","first argument must be a string\n");
}
filename=i->data.string;
} else {
filename=NULL; /* Make compiler happy */
cfgfatal(i->loc,"rsa-private","you must provide a filename\n");
}
f=fopen(filename,"rb");
if (!f) {
if (just_check_config) {
Message(M_WARNING,"rsa-private (%s:%d): cannot open keyfile "
"\"%s\" (%s); assuming it's valid while we check the "
"rest of the configuration\n",
loc.file,loc.line,filename,strerror(errno));
return list_new();
} else {
fatal_perror("rsa-private (%s:%d): cannot open file \"%s\"",
loc.file,loc.line,filename);
}
}
bool_t do_validity_check=True;
i=list_elem(args,1);
if (i && i->type==t_bool && i->data.bool_==False) {
Message(M_INFO,"rsa-private (%s:%d): skipping RSA key validity "
"check\n",loc.file,loc.line);
do_validity_check=False;
}
st=rsa_loadpriv_core(l,f,loc,do_validity_check);
fclose(f);
return new_closure(&st->cl);
}
void rsa_module(dict_t *dict)
{
add_closure(dict,"rsa-private",rsapriv_apply);
add_closure(dict,"rsa-public",rsapub_apply);
}
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