Add xmss_fast starting point before BDS
This commit is contained in:
Joost Rijneveld
父節點
100a9e57e3
當前提交
1511c0bdf7
1
.gitignore
vendored
1
.gitignore
vendored
@ -2,6 +2,7 @@ test/test_chacha
|
||||
test/test_wots
|
||||
test/test_horst
|
||||
test/test_xmss
|
||||
test/test_xmss_fast
|
||||
test/test_xmssmt
|
||||
test/speed
|
||||
test/gen_testvectors
|
||||
4
Makefile
4
Makefile
@ -4,6 +4,7 @@ CFLAGS = -Wall -g -O3
|
||||
all: test/test_chacha \
|
||||
test/test_wots \
|
||||
test/test_xmss \
|
||||
test/test_xmss_fast \
|
||||
test/test_xmssmt
|
||||
|
||||
test/test_chacha: chacha.c prg.c randombytes.c test/test_chacha.c chacha.h prg.h randombytes.h
|
||||
@ -15,6 +16,9 @@ test/test_wots: chacha.c hash.c prg.c randombytes.c wots.c xmss_commons.c test/t
|
||||
test/test_xmss: chacha.c hash.c prg.c randombytes.c wots.c xmss.c xmss_commons.c test/test_xmss.c chacha.h hash.h prg.h randombytes.h wots.h xmss.h xmss_commons.h
|
||||
$(CC) $(CFLAGS) chacha.c hash.c prg.c randombytes.c wots.c xmss.c xmss_commons.c test/test_xmss.c -o $@ -lcrypto -lm
|
||||
|
||||
test/test_xmss_fast: chacha.c hash.c prg.c randombytes.c wots.c xmss_fast.c xmss_commons.c test/test_xmss_fast.c chacha.h hash.h prg.h randombytes.h wots.h xmss_fast.h xmss_commons.h
|
||||
$(CC) $(CFLAGS) chacha.c hash.c prg.c randombytes.c wots.c xmss_fast.c xmss_commons.c test/test_xmss_fast.c -o $@ -lcrypto -lm
|
||||
|
||||
test/test_xmssmt: chacha.c hash.c prg.c randombytes.c wots.c xmss.c xmss_commons.c test/test_xmssmt.c chacha.h hash.h prg.h randombytes.h wots.h xmss.h xmss_commons.h
|
||||
$(CC) $(CFLAGS) chacha.c hash.c prg.c randombytes.c wots.c xmss.c xmss_commons.c test/test_xmssmt.c -o $@ -lcrypto -lm
|
||||
|
||||
|
||||
88
test/test_xmss_fast.c
Normal file
88
test/test_xmss_fast.c
Normal file
@ -0,0 +1,88 @@
|
||||
#include <stdio.h>
|
||||
#include <string.h>
|
||||
|
||||
#include "../xmss.h"
|
||||
|
||||
#define MLEN 3491
|
||||
#define SIGNATURES 50
|
||||
|
||||
|
||||
unsigned char sk[100];
|
||||
unsigned char pk[64];
|
||||
unsigned char mi[MLEN];
|
||||
unsigned long long smlen;
|
||||
unsigned long long mlen;
|
||||
|
||||
int main()
|
||||
{
|
||||
int r;
|
||||
unsigned long long i;
|
||||
int m = 32;
|
||||
int n = 32;
|
||||
int h = 8;
|
||||
int w = 16;
|
||||
|
||||
xmss_params p;
|
||||
xmss_params *params = &p;
|
||||
xmss_set_params(params, m, n, h, w);
|
||||
unsigned long long signature_length = 4+m+params->wots_par.keysize+h*n;
|
||||
unsigned char mo[MLEN+signature_length];
|
||||
unsigned char sm[MLEN+signature_length];
|
||||
|
||||
FILE *urandom = fopen("/dev/urandom", "r");
|
||||
for(i=0;i<MLEN;i++) mi[i] = fgetc(urandom);
|
||||
|
||||
printf("keypair\n");
|
||||
xmss_keypair(pk, sk, params);
|
||||
// check pub_seed in SK
|
||||
for(i=0;i<n;i++)
|
||||
{
|
||||
if(pk[n+i] != sk[4+m+n+i]) printf("pk.pub_seed != sk.pub_seed %llu",i);
|
||||
}
|
||||
|
||||
// check index
|
||||
unsigned long idx = ((unsigned long)sk[0] << 24) | ((unsigned long)sk[1] << 16) | ((unsigned long)sk[2] << 8) | sk[3];
|
||||
if(idx) printf("\nidx != 0 %lu\n",idx);
|
||||
|
||||
for(i=0;i<SIGNATURES;i++){
|
||||
printf("sign\n");
|
||||
xmss_sign(sk, sm, &smlen, mi, MLEN, params);
|
||||
idx = ((unsigned long)sm[0] << 24) | ((unsigned long)sm[1] << 16) | ((unsigned long)sm[2] << 8) | sm[3];
|
||||
printf("\nidx = %lu\n",idx);
|
||||
|
||||
}
|
||||
|
||||
r = memcmp(mi, sm+signature_length,MLEN);
|
||||
printf("%d\n", r);
|
||||
|
||||
/* Test valid signature */
|
||||
printf("verify\n");
|
||||
r = xmss_sign_open(mo, &mlen, sm, smlen, pk, params);
|
||||
printf("%d\n", r);
|
||||
r = memcmp(mi,mo,MLEN);
|
||||
printf("%d\n", r);
|
||||
printf("%llu\n", MLEN-mlen);
|
||||
|
||||
/* Test with modified message */
|
||||
sm[52] ^= 1;
|
||||
r = xmss_sign_open(mo, &mlen, sm, smlen, pk, params);
|
||||
printf("%d\n", r+1);
|
||||
r = memcmp(mi,mo,MLEN);
|
||||
printf("%d\n", (r!=0) - 1);
|
||||
printf("%llu\n", mlen+1);
|
||||
|
||||
/* Test with modified signature */
|
||||
sm[260] ^= 1;
|
||||
sm[52] ^= 1;
|
||||
sm[2] ^= 1;
|
||||
r = xmss_sign_open(mo, &mlen, sm, smlen, pk, params);
|
||||
printf("%d\n", r+1);
|
||||
r = memcmp(mi,mo,MLEN);
|
||||
printf("%d\n", (r!=0) - 1);
|
||||
printf("%llu\n", mlen+1);
|
||||
|
||||
fclose(urandom);
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
856
xmss_fast.c
Normal file
856
xmss_fast.c
Normal file
@ -0,0 +1,856 @@
|
||||
/*
|
||||
xmss.c version 20150811
|
||||
Andreas Hülsing
|
||||
Public domain.
|
||||
*/
|
||||
|
||||
#include "xmss.h"
|
||||
#include <stdlib.h>
|
||||
#include <string.h>
|
||||
#include <stdint.h>
|
||||
#include <math.h>
|
||||
|
||||
#include "randombytes.h"
|
||||
#include "wots.h"
|
||||
#include "hash.h"
|
||||
#include "prg.h"
|
||||
#include "xmss_commons.h"
|
||||
|
||||
// For testing
|
||||
#include "stdio.h"
|
||||
|
||||
/**
|
||||
* Macros used to manipulate the respective fields
|
||||
* in the 16byte hash address
|
||||
*/
|
||||
#define SET_LAYER_ADDRESS(a, v) {\
|
||||
a[6] = (a[6] & 3) | ((v << 2) & 255);\
|
||||
a[5] = (a[5] & 252) | ((v >> 6) & 255);}
|
||||
|
||||
#define SET_TREE_ADDRESS(a, v) {\
|
||||
a[9] = (a[9] & 3) | ((v << 2) & 255);\
|
||||
a[8] = (v >> 6) & 255;\
|
||||
a[7] = (v >> 14) & 255;\
|
||||
a[6] = (a[6] & 252) | ((v >> 22) & 255);}
|
||||
|
||||
#define SET_OTS_BIT(a, b) {\
|
||||
a[9] = (a[9] & 253) | (b << 1);}
|
||||
|
||||
#define SET_OTS_ADDRESS(a, v) {\
|
||||
a[12] = (a[12] & 1) | ((v << 1) & 255);\
|
||||
a[11] = (v >> 7) & 255;\
|
||||
a[10] = (v >> 15) & 255;\
|
||||
a[9] = (a[9] & 254) | ((v >> 23) & 1);}
|
||||
|
||||
#define ZEROISE_OTS_ADDR(a) {\
|
||||
a[12] = (a[12] & 254);\
|
||||
a[13] = 0;\
|
||||
a[14] = 0;\
|
||||
a[15] = 0;}
|
||||
|
||||
#define SET_LTREE_BIT(a, b) {\
|
||||
a[9] = (a[9] & 254) | b;}
|
||||
|
||||
#define SET_LTREE_ADDRESS(a, v) {\
|
||||
a[12] = v & 255;\
|
||||
a[11] = (v >> 8) & 255;\
|
||||
a[10] = (v >> 16) & 255;}
|
||||
|
||||
#define SET_LTREE_TREE_HEIGHT(a, v) {\
|
||||
a[13] = (a[13] & 3) | ((v << 2) & 255);}
|
||||
|
||||
#define SET_LTREE_TREE_INDEX(a, v) {\
|
||||
a[15] = (a[15] & 3) | ((v << 2) & 255);\
|
||||
a[14] = (v >> 6) & 255;\
|
||||
a[13] = (a[13] & 252) | ((v >> 14) & 3);}
|
||||
|
||||
#define SET_NODE_PADDING(a) {\
|
||||
a[10] = 0;\
|
||||
a[11] = a[11] & 3;}
|
||||
|
||||
#define SET_NODE_TREE_HEIGHT(a, v) {\
|
||||
a[12] = (a[12] & 3) | ((v << 2) & 255);\
|
||||
a[11] = (a[11] & 252) | ((v >> 6) & 3);}
|
||||
|
||||
#define SET_NODE_TREE_INDEX(a, v) {\
|
||||
a[15] = (a[15] & 3) | ((v << 2) & 255);\
|
||||
a[14] = (v >> 6) & 255;\
|
||||
a[13] = (v >> 14) & 255;\
|
||||
a[12] = (a[12] & 252) | ((v >> 22) & 3);}
|
||||
|
||||
|
||||
/**
|
||||
* Used for pseudorandom keygeneration,
|
||||
* generates the seed for the WOTS keypair at address addr
|
||||
*/
|
||||
static void get_seed(unsigned char seed[32], const unsigned char *sk_seed, unsigned char addr[16])
|
||||
{
|
||||
// Make sure that chain addr, hash addr, and key bit are 0!
|
||||
ZEROISE_OTS_ADDR(addr);
|
||||
// Generate pseudorandom value
|
||||
prg_with_counter(seed, 32, sk_seed, 32, addr);
|
||||
}
|
||||
|
||||
/**
|
||||
* Initialize xmss params struct
|
||||
* parameter names are the same as in the draft
|
||||
*/
|
||||
void xmss_set_params(xmss_params *params, int m, int n, int h, int w)
|
||||
{
|
||||
params->h = h;
|
||||
params->m = m;
|
||||
params->n = n;
|
||||
wots_params wots_par;
|
||||
wots_set_params(&wots_par, m, n, w);
|
||||
params->wots_par = wots_par;
|
||||
}
|
||||
|
||||
/**
|
||||
* Initialize xmssmt_params struct
|
||||
* parameter names are the same as in the draft
|
||||
*
|
||||
* Especially h is the total tree height, i.e. the XMSS trees have height h/d
|
||||
*/
|
||||
void xmssmt_set_params(xmssmt_params *params, int m, int n, int h, int d, int w)
|
||||
{
|
||||
if(h % d){
|
||||
fprintf(stderr, "d must devide h without remainder!\n");
|
||||
return;
|
||||
}
|
||||
params->h = h;
|
||||
params->d = d;
|
||||
params->m = m;
|
||||
params->n = n;
|
||||
params->index_len = (h + 7) / 8;
|
||||
xmss_params xmss_par;
|
||||
xmss_set_params(&xmss_par, m, n, (h/d), w);
|
||||
params->xmss_par = xmss_par;
|
||||
}
|
||||
|
||||
/**
|
||||
* Computes a leaf from a WOTS public key using an L-tree.
|
||||
*/
|
||||
static void l_tree(unsigned char *leaf, unsigned char *wots_pk, const xmss_params *params, const unsigned char *pub_seed, unsigned char addr[16])
|
||||
{
|
||||
unsigned int l = params->wots_par.len;
|
||||
unsigned int n = params->n;
|
||||
unsigned long i = 0;
|
||||
unsigned int height = 0;
|
||||
|
||||
//ADRS.setTreeHeight(0);
|
||||
SET_LTREE_TREE_HEIGHT(addr,height);
|
||||
unsigned long bound;
|
||||
while ( l > 1 )
|
||||
{
|
||||
bound = l >> 1; //floor(l / 2);
|
||||
for ( i = 0; i < bound; i = i + 1 ) {
|
||||
//ADRS.setTreeIndex(i);
|
||||
SET_LTREE_TREE_INDEX(addr,i);
|
||||
//wots_pk[i] = RAND_HASH(pk[2i], pk[2i + 1], SEED, ADRS);
|
||||
hash_2n_n(wots_pk+i*n,wots_pk+i*2*n, pub_seed, addr, n);
|
||||
}
|
||||
//if ( l % 2 == 1 ) {
|
||||
if(l&1)
|
||||
{
|
||||
//pk[floor(l / 2) + 1] = pk[l];
|
||||
memcpy(wots_pk+(l>>1)*n,wots_pk+(l-1)*n, n);
|
||||
//l = ceil(l / 2);
|
||||
l=(l>>1)+1;
|
||||
}
|
||||
else
|
||||
{
|
||||
//l = ceil(l / 2);
|
||||
l=(l>>1);
|
||||
}
|
||||
//ADRS.setTreeHeight(ADRS.getTreeHeight() + 1);
|
||||
height++;
|
||||
SET_LTREE_TREE_HEIGHT(addr,height);
|
||||
}
|
||||
//return pk[0];
|
||||
memcpy(leaf,wots_pk,n);
|
||||
}
|
||||
|
||||
/**
|
||||
* Computes the leaf at a given address. First generates the WOTS key pair, then computes leaf using l_tree. As this happens position independent, we only require that addr encodes the right ltree-address.
|
||||
*/
|
||||
static void gen_leaf_wots(unsigned char *leaf, const unsigned char *sk_seed, const xmss_params *params, const unsigned char *pub_seed, unsigned char ltree_addr[16], unsigned char ots_addr[16])
|
||||
{
|
||||
unsigned char seed[32];
|
||||
unsigned char pk[params->wots_par.keysize];
|
||||
|
||||
get_seed(seed, sk_seed, ots_addr);
|
||||
wots_pkgen(pk, seed, &(params->wots_par), pub_seed, ots_addr);
|
||||
|
||||
l_tree(leaf, pk, params, pub_seed, ltree_addr);
|
||||
}
|
||||
|
||||
/**
|
||||
* Merkle's TreeHash algorithm. The address only needs to initialize the first 78 bits of addr. Everything else will be set by treehash.
|
||||
* Currently only used for key generation.
|
||||
*
|
||||
*/
|
||||
static void treehash(unsigned char *node, int height, int index, const unsigned char *sk_seed, const xmss_params *params, const unsigned char *pub_seed, const unsigned char addr[16])
|
||||
{
|
||||
|
||||
unsigned int idx = index;
|
||||
unsigned int n = params->n;
|
||||
// use three different addresses because at this point we use all three formats in parallel
|
||||
unsigned char ots_addr[16];
|
||||
unsigned char ltree_addr[16];
|
||||
unsigned char node_addr[16];
|
||||
memcpy(ots_addr, addr, 10);
|
||||
SET_OTS_BIT(ots_addr, 1);
|
||||
memcpy(ltree_addr, addr, 10);
|
||||
SET_OTS_BIT(ltree_addr, 0);
|
||||
SET_LTREE_BIT(ltree_addr, 1);
|
||||
memcpy(node_addr, ltree_addr, 10);
|
||||
SET_LTREE_BIT(node_addr, 0);
|
||||
SET_NODE_PADDING(node_addr);
|
||||
|
||||
int lastnode,i;
|
||||
unsigned char stack[(height+1)*n];
|
||||
unsigned int stacklevels[height+1];
|
||||
unsigned int stackoffset=0;
|
||||
|
||||
lastnode = idx+(1<<height);
|
||||
|
||||
for(;idx<lastnode;idx++)
|
||||
{
|
||||
SET_LTREE_ADDRESS(ltree_addr,idx);
|
||||
SET_OTS_ADDRESS(ots_addr,idx);
|
||||
gen_leaf_wots(stack+stackoffset*n,sk_seed,params, pub_seed, ltree_addr, ots_addr);
|
||||
stacklevels[stackoffset] = 0;
|
||||
stackoffset++;
|
||||
while(stackoffset>1 && stacklevels[stackoffset-1] == stacklevels[stackoffset-2])
|
||||
{
|
||||
SET_NODE_TREE_HEIGHT(node_addr,stacklevels[stackoffset-1]);
|
||||
SET_NODE_TREE_INDEX(node_addr, (idx >> (stacklevels[stackoffset-1]+1)));
|
||||
hash_2n_n(stack+(stackoffset-2)*n,stack+(stackoffset-2)*n, pub_seed,
|
||||
node_addr, n);
|
||||
stacklevels[stackoffset-2]++;
|
||||
stackoffset--;
|
||||
}
|
||||
}
|
||||
for(i=0;i<n;i++)
|
||||
node[i] = stack[i];
|
||||
}
|
||||
|
||||
/**
|
||||
* Computes a root node given a leaf and an authapth
|
||||
*/
|
||||
static void validate_authpath(unsigned char *root, const unsigned char *leaf, unsigned long leafidx, const unsigned char *authpath, const xmss_params *params, const unsigned char *pub_seed, unsigned char addr[16])
|
||||
{
|
||||
unsigned int n = params->n;
|
||||
|
||||
int i,j;
|
||||
unsigned char buffer[2*n];
|
||||
|
||||
// If leafidx is odd (last bit = 1), current path element is a right child and authpath has to go to the left.
|
||||
// Otherwise, it is the other way around
|
||||
if(leafidx&1)
|
||||
{
|
||||
for(j=0;j<n;j++)
|
||||
buffer[n+j] = leaf[j];
|
||||
for(j=0;j<n;j++)
|
||||
buffer[j] = authpath[j];
|
||||
}
|
||||
else
|
||||
{
|
||||
for(j=0;j<n;j++)
|
||||
buffer[j] = leaf[j];
|
||||
for(j=0;j<n;j++)
|
||||
buffer[n+j] = authpath[j];
|
||||
}
|
||||
authpath += n;
|
||||
|
||||
for(i=0;i<params->h-1;i++)
|
||||
{
|
||||
SET_NODE_TREE_HEIGHT(addr,i);
|
||||
leafidx >>= 1;
|
||||
SET_NODE_TREE_INDEX(addr, leafidx);
|
||||
if(leafidx&1)
|
||||
{
|
||||
hash_2n_n(buffer+n,buffer,pub_seed, addr, n);
|
||||
for(j=0;j<n;j++)
|
||||
buffer[j] = authpath[j];
|
||||
}
|
||||
else
|
||||
{
|
||||
hash_2n_n(buffer,buffer,pub_seed, addr, n);
|
||||
for(j=0;j<n;j++)
|
||||
buffer[j+n] = authpath[j];
|
||||
}
|
||||
authpath += n;
|
||||
}
|
||||
SET_NODE_TREE_HEIGHT(addr, (params->h-1));
|
||||
leafidx >>= 1;
|
||||
SET_NODE_TREE_INDEX(addr, leafidx);
|
||||
hash_2n_n(root,buffer,pub_seed,addr,n);
|
||||
}
|
||||
|
||||
/**
|
||||
* Computes the authpath and the root. This method is using a lot of space as we build the whole tree and then select the authpath nodes.
|
||||
* For more efficient algorithms see e.g. the chapter on hash-based signatures in Bernstein, Buchmann, Dahmen. "Post-quantum Cryptography", Springer 2009.
|
||||
* It returns the authpath in "authpath" with the node on level 0 at index 0.
|
||||
*/
|
||||
static void compute_authpath_wots(unsigned char *root, unsigned char *authpath, unsigned long leaf_idx, const unsigned char *sk_seed, const xmss_params *params, unsigned char *pub_seed, unsigned char addr[16])
|
||||
{
|
||||
unsigned int i, j, level;
|
||||
int n = params->n;
|
||||
int h = params->h;
|
||||
|
||||
unsigned char tree[2*(1<<h)*n];
|
||||
|
||||
unsigned char ots_addr[16];
|
||||
unsigned char ltree_addr[16];
|
||||
unsigned char node_addr[16];
|
||||
|
||||
memcpy(ots_addr, addr, 10);
|
||||
SET_OTS_BIT(ots_addr, 1);
|
||||
memcpy(ltree_addr, addr, 10);
|
||||
SET_OTS_BIT(ltree_addr, 0);
|
||||
SET_LTREE_BIT(ltree_addr, 1);
|
||||
memcpy(node_addr, ltree_addr, 10);
|
||||
SET_LTREE_BIT(node_addr, 0);
|
||||
SET_NODE_PADDING(node_addr);
|
||||
|
||||
|
||||
// Compute all leaves
|
||||
for(i = 0; i < (1<<h); i++)
|
||||
{
|
||||
SET_LTREE_ADDRESS(ltree_addr,i);
|
||||
SET_OTS_ADDRESS(ots_addr,i);
|
||||
gen_leaf_wots(tree+((1<<h)*n + i*n), sk_seed, params, pub_seed, ltree_addr, ots_addr);
|
||||
}
|
||||
|
||||
|
||||
level = 0;
|
||||
// Compute tree:
|
||||
// Outer loop: For each inner layer
|
||||
for (i = (1<<h); i > 0; i>>=1)
|
||||
{
|
||||
SET_NODE_TREE_HEIGHT(node_addr, level);
|
||||
// Inner loop: for each pair of sibling nodes
|
||||
for (j = 0; j < i; j+=2)
|
||||
{
|
||||
SET_NODE_TREE_INDEX(node_addr, j>>1);
|
||||
hash_2n_n(tree + (i>>1)*n + (j>>1) * n, tree + i*n + j*n, pub_seed, node_addr, n);
|
||||
}
|
||||
level++;
|
||||
}
|
||||
|
||||
// copy authpath
|
||||
for(i=0;i<h;i++)
|
||||
memcpy(authpath + i*n, tree + ((1<<h)>>i)*n + ((leaf_idx >> i) ^ 1) * n, n);
|
||||
|
||||
// copy root
|
||||
memcpy(root, tree+n, n);
|
||||
}
|
||||
|
||||
|
||||
/*
|
||||
* Generates a XMSS key pair for a given parameter set.
|
||||
* Format sk: [(32bit) idx || SK_SEED || SK_PRF || PUB_SEED]
|
||||
* Format pk: [root || PUB_SEED] omitting algo oid.
|
||||
*/
|
||||
int xmss_keypair(unsigned char *pk, unsigned char *sk, xmss_params *params)
|
||||
{
|
||||
unsigned int n = params->n;
|
||||
unsigned int m = params->m;
|
||||
// Set idx = 0
|
||||
sk[0] = 0;
|
||||
sk[1] = 0;
|
||||
sk[2] = 0;
|
||||
sk[3] = 0;
|
||||
// Init SK_SEED (n byte), SK_PRF (m byte), and PUB_SEED (n byte)
|
||||
randombytes(sk+4,2*n+m);
|
||||
// Copy PUB_SEED to public key
|
||||
memcpy(pk+n, sk+4+n+m,n);
|
||||
|
||||
unsigned char addr[16] = {0,0,0,0};
|
||||
// Compute root
|
||||
treehash(pk, params->h, 0, sk+4, params, sk+4+n+m, addr);
|
||||
return 0;
|
||||
}
|
||||
|
||||
/**
|
||||
* Signs a message.
|
||||
* Returns
|
||||
* 1. an array containing the signature followed by the message AND
|
||||
* 2. an updated secret key!
|
||||
*
|
||||
*/
|
||||
int xmss_sign(unsigned char *sk, unsigned char *sig_msg, unsigned long long *sig_msg_len, const unsigned char *msg, unsigned long long msglen, const xmss_params *params)
|
||||
{
|
||||
unsigned int n = params->n;
|
||||
unsigned int m = params->m;
|
||||
|
||||
// Extract SK
|
||||
unsigned long idx = ((unsigned long)sk[0] << 24) | ((unsigned long)sk[1] << 16) | ((unsigned long)sk[2] << 8) | sk[3];
|
||||
unsigned char sk_seed[n];
|
||||
memcpy(sk_seed,sk+4,n);
|
||||
unsigned char sk_prf[m];
|
||||
memcpy(sk_prf,sk+4+n,m);
|
||||
unsigned char pub_seed[n];
|
||||
memcpy(pub_seed,sk+4+n+m,n);
|
||||
|
||||
// Update SK
|
||||
sk[0] = ((idx + 1) >> 24) & 255;
|
||||
sk[1] = ((idx + 1) >> 16) & 255;
|
||||
sk[2] = ((idx + 1) >> 8) & 255;
|
||||
sk[3] = (idx + 1) & 255;
|
||||
// -- Secret key for this non-forward-secure version is now updated.
|
||||
// -- A productive implementation should use a file handle instead and write the updated secret key at this point!
|
||||
|
||||
// Init working params
|
||||
unsigned long long i;
|
||||
unsigned char R[m];
|
||||
unsigned char msg_h[m];
|
||||
unsigned char root[n];
|
||||
unsigned char ots_seed[n];
|
||||
unsigned char ots_addr[16] = {0,0,0,0};
|
||||
|
||||
// ---------------------------------
|
||||
// Message Hashing
|
||||
// ---------------------------------
|
||||
|
||||
// Message Hash:
|
||||
// First compute pseudorandom key
|
||||
prf_m(R, msg, msglen, sk_prf, m);
|
||||
// Then use it for message digest
|
||||
hash_m(msg_h, msg, msglen, R, m, m);
|
||||
|
||||
// Start collecting signature
|
||||
*sig_msg_len = 0;
|
||||
|
||||
// Copy index to signature
|
||||
sig_msg[0] = (idx >> 24) & 255;
|
||||
sig_msg[1] = (idx >> 16) & 255;
|
||||
sig_msg[2] = (idx >> 8) & 255;
|
||||
sig_msg[3] = idx & 255;
|
||||
|
||||
sig_msg += 4;
|
||||
*sig_msg_len += 4;
|
||||
|
||||
// Copy R to signature
|
||||
for(i=0; i<m; i++)
|
||||
sig_msg[i] = R[i];
|
||||
|
||||
sig_msg += m;
|
||||
*sig_msg_len += m;
|
||||
|
||||
// ----------------------------------
|
||||
// Now we start to "really sign"
|
||||
// ----------------------------------
|
||||
|
||||
// Prepare Address
|
||||
SET_OTS_BIT(ots_addr,1);
|
||||
SET_OTS_ADDRESS(ots_addr,idx);
|
||||
|
||||
// Compute seed for OTS key pair
|
||||
get_seed(ots_seed, sk_seed, ots_addr);
|
||||
|
||||
// Compute WOTS signature
|
||||
wots_sign(sig_msg, msg_h, ots_seed, &(params->wots_par), pub_seed, ots_addr);
|
||||
|
||||
sig_msg += params->wots_par.keysize;
|
||||
*sig_msg_len += params->wots_par.keysize;
|
||||
|
||||
compute_authpath_wots(root, sig_msg, idx, sk_seed, params, pub_seed, ots_addr);
|
||||
sig_msg += params->h*n;
|
||||
*sig_msg_len += params->h*n;
|
||||
|
||||
//Whipe secret elements?
|
||||
//zerobytes(tsk, CRYPTO_SECRETKEYBYTES);
|
||||
|
||||
memcpy(sig_msg,msg,msglen);
|
||||
*sig_msg_len += msglen;
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
/**
|
||||
* Verifies a given message signature pair under a given public key.
|
||||
*/
|
||||
int xmss_sign_open(unsigned char *msg, unsigned long long *msglen, const unsigned char *sig_msg, unsigned long long sig_msg_len, const unsigned char *pk, const xmss_params *params)
|
||||
{
|
||||
unsigned int n = params->n;
|
||||
unsigned int m = params->m;
|
||||
|
||||
unsigned long long i, m_len;
|
||||
unsigned long idx=0;
|
||||
unsigned char wots_pk[params->wots_par.keysize];
|
||||
unsigned char pkhash[n];
|
||||
unsigned char root[n];
|
||||
unsigned char msg_h[m];
|
||||
|
||||
unsigned char pub_seed[n];
|
||||
memcpy(pub_seed,pk+n,n);
|
||||
|
||||
// Init addresses
|
||||
unsigned char ots_addr[16] = {0,0,0,0};
|
||||
unsigned char ltree_addr[16];
|
||||
unsigned char node_addr[16];
|
||||
|
||||
SET_OTS_BIT(ots_addr, 1);
|
||||
|
||||
memcpy(ltree_addr, ots_addr, 10);
|
||||
SET_OTS_BIT(ltree_addr, 0);
|
||||
SET_LTREE_BIT(ltree_addr, 1);
|
||||
|
||||
memcpy(node_addr, ltree_addr, 10);
|
||||
SET_LTREE_BIT(node_addr, 0);
|
||||
SET_NODE_PADDING(node_addr);
|
||||
|
||||
// Extract index
|
||||
idx = ((unsigned long)sig_msg[0] << 24) | ((unsigned long)sig_msg[1] << 16) | ((unsigned long)sig_msg[2] << 8) | sig_msg[3];
|
||||
printf("verify:: idx = %lu\n",idx);
|
||||
sig_msg += 4;
|
||||
sig_msg_len -= 4;
|
||||
|
||||
// hash message (recall, R is now on pole position at sig_msg
|
||||
unsigned long long tmp_sig_len = m+params->wots_par.keysize+params->h*n;
|
||||
m_len = sig_msg_len - tmp_sig_len;
|
||||
hash_m(msg_h, sig_msg + tmp_sig_len, m_len, sig_msg, m, m);
|
||||
|
||||
sig_msg += m;
|
||||
sig_msg_len -= m;
|
||||
|
||||
//-----------------------
|
||||
// Verify signature
|
||||
//-----------------------
|
||||
|
||||
// Prepare Address
|
||||
SET_OTS_ADDRESS(ots_addr,idx);
|
||||
// Check WOTS signature
|
||||
wots_pkFromSig(wots_pk, sig_msg, msg_h, &(params->wots_par), pub_seed, ots_addr);
|
||||
|
||||
sig_msg += params->wots_par.keysize;
|
||||
sig_msg_len -= params->wots_par.keysize;
|
||||
|
||||
// Compute Ltree
|
||||
SET_LTREE_ADDRESS(ltree_addr, idx);
|
||||
l_tree(pkhash, wots_pk, params, pub_seed, ltree_addr);
|
||||
|
||||
// Compute root
|
||||
validate_authpath(root, pkhash, idx, sig_msg, params, pub_seed, node_addr);
|
||||
|
||||
sig_msg += params->h*n;
|
||||
sig_msg_len -= params->h*n;
|
||||
|
||||
for(i=0;i<n;i++)
|
||||
if(root[i] != pk[i])
|
||||
goto fail;
|
||||
|
||||
*msglen = sig_msg_len;
|
||||
for(i=0;i<*msglen;i++)
|
||||
msg[i] = sig_msg[i];
|
||||
|
||||
return 0;
|
||||
|
||||
|
||||
fail:
|
||||
*msglen = sig_msg_len;
|
||||
for(i=0;i<*msglen;i++)
|
||||
msg[i] = 0;
|
||||
*msglen = -1;
|
||||
return -1;
|
||||
}
|
||||
|
||||
/*
|
||||
* Generates a XMSSMT key pair for a given parameter set.
|
||||
* Format sk: [(ceil(h/8) bit) idx || SK_SEED || SK_PRF || PUB_SEED]
|
||||
* Format pk: [root || PUB_SEED] omitting algo oid.
|
||||
*/
|
||||
int xmssmt_keypair(unsigned char *pk, unsigned char *sk, xmssmt_params *params)
|
||||
{
|
||||
unsigned int n = params->n;
|
||||
unsigned int m = params->m;
|
||||
unsigned int i;
|
||||
// Set idx = 0
|
||||
for (i = 0; i < params->index_len; i++){
|
||||
sk[i] = 0;
|
||||
}
|
||||
// Init SK_SEED (n byte), SK_PRF (m byte), and PUB_SEED (n byte)
|
||||
randombytes(sk+params->index_len,2*n+m);
|
||||
// Copy PUB_SEED to public key
|
||||
memcpy(pk+n, sk+params->index_len+n+m,n);
|
||||
|
||||
// Set address to point on the single tree on layer d-1
|
||||
unsigned char addr[16] = {0,0,0,0};
|
||||
SET_LAYER_ADDRESS(addr, (params->d-1));
|
||||
|
||||
// Compute root
|
||||
treehash(pk, params->xmss_par.h, 0, sk+params->index_len, &(params->xmss_par), pk+n, addr);
|
||||
return 0;
|
||||
}
|
||||
|
||||
/**
|
||||
* Signs a message.
|
||||
* Returns
|
||||
* 1. an array containing the signature followed by the message AND
|
||||
* 2. an updated secret key!
|
||||
*
|
||||
*/
|
||||
int xmssmt_sign(unsigned char *sk, unsigned char *sig_msg, unsigned long long *sig_msg_len, const unsigned char *msg, unsigned long long msglen, const xmssmt_params *params)
|
||||
{
|
||||
unsigned int n = params->n;
|
||||
unsigned int m = params->m;
|
||||
unsigned int tree_h = params->xmss_par.h;
|
||||
unsigned int idx_len = params->index_len;
|
||||
unsigned long long idx_tree;
|
||||
unsigned long long idx_leaf;
|
||||
unsigned long long i;
|
||||
|
||||
unsigned char sk_seed[n];
|
||||
unsigned char sk_prf[m];
|
||||
unsigned char pub_seed[n];
|
||||
// Init working params
|
||||
unsigned char R[m];
|
||||
unsigned char msg_h[m];
|
||||
unsigned char root[n];
|
||||
unsigned char ots_seed[n];
|
||||
unsigned char ots_addr[16] = {0,0,0,0};
|
||||
|
||||
// Extract SK
|
||||
unsigned long long idx = 0;
|
||||
for(i = 0; i < idx_len; i++){
|
||||
idx |= ((unsigned long long)sk[i]) << 8*(idx_len - 1 - i);
|
||||
}
|
||||
|
||||
memcpy(sk_seed,sk+idx_len,n);
|
||||
memcpy(sk_prf,sk+idx_len+n,m);
|
||||
memcpy(pub_seed,sk+idx_len+n+m,n);
|
||||
|
||||
// Update SK
|
||||
for(i = 0; i < idx_len; i++){
|
||||
sk[i] = ((idx + 1) >> 8*(idx_len - 1 - i)) & 255;
|
||||
}
|
||||
// -- Secret key for this non-forward-secure version is now updated.
|
||||
// -- A productive implementation should use a file handle instead and write the updated secret key at this point!
|
||||
|
||||
|
||||
// ---------------------------------
|
||||
// Message Hashing
|
||||
// ---------------------------------
|
||||
|
||||
// Message Hash:
|
||||
// First compute pseudorandom key
|
||||
prf_m(R, msg, msglen, sk_prf, m);
|
||||
// Then use it for message digest
|
||||
hash_m(msg_h, msg, msglen, R, m, m);
|
||||
|
||||
// Start collecting signature
|
||||
*sig_msg_len = 0;
|
||||
|
||||
// Copy index to signature
|
||||
for(i = 0; i < idx_len; i++){
|
||||
sig_msg[i] = (idx >> 8*(idx_len - 1 - i)) & 255;
|
||||
}
|
||||
|
||||
sig_msg += idx_len;
|
||||
*sig_msg_len += idx_len;
|
||||
|
||||
// Copy R to signature
|
||||
for(i=0; i<m; i++)
|
||||
sig_msg[i] = R[i];
|
||||
|
||||
sig_msg += m;
|
||||
*sig_msg_len += m;
|
||||
|
||||
// ----------------------------------
|
||||
// Now we start to "really sign"
|
||||
// ----------------------------------
|
||||
|
||||
// Handle lowest layer separately as it is slightly different...
|
||||
|
||||
// Prepare Address
|
||||
SET_OTS_BIT(ots_addr,1);
|
||||
idx_tree = idx >> tree_h;
|
||||
idx_leaf = (idx & ((1 << tree_h)-1));
|
||||
SET_LAYER_ADDRESS(ots_addr,0);
|
||||
SET_TREE_ADDRESS(ots_addr, idx_tree);
|
||||
SET_OTS_ADDRESS(ots_addr, idx_leaf);
|
||||
|
||||
// Compute seed for OTS key pair
|
||||
get_seed(ots_seed, sk_seed, ots_addr);
|
||||
|
||||
// Compute WOTS signature
|
||||
wots_sign(sig_msg, msg_h, ots_seed, &(params->xmss_par.wots_par), pub_seed, ots_addr);
|
||||
|
||||
sig_msg += params->xmss_par.wots_par.keysize;
|
||||
*sig_msg_len += params->xmss_par.wots_par.keysize;
|
||||
|
||||
compute_authpath_wots(root, sig_msg, idx_leaf, sk_seed, &(params->xmss_par), pub_seed, ots_addr);
|
||||
sig_msg += tree_h*n;
|
||||
*sig_msg_len += tree_h*n;
|
||||
|
||||
// Now loop over remaining layers...
|
||||
unsigned int j;
|
||||
for(j = 1; j < params->d; j++){
|
||||
// Prepare Address
|
||||
idx_leaf = (idx_tree & ((1 << tree_h)-1));
|
||||
idx_tree = idx_tree >> tree_h;
|
||||
SET_LAYER_ADDRESS(ots_addr,j);
|
||||
SET_TREE_ADDRESS(ots_addr, idx_tree);
|
||||
SET_OTS_ADDRESS(ots_addr, idx_leaf);
|
||||
|
||||
// Compute seed for OTS key pair
|
||||
get_seed(ots_seed, sk_seed, ots_addr);
|
||||
|
||||
// Compute WOTS signature
|
||||
wots_sign(sig_msg, root, ots_seed, &(params->xmss_par.wots_par), pub_seed, ots_addr);
|
||||
|
||||
sig_msg += params->xmss_par.wots_par.keysize;
|
||||
*sig_msg_len += params->xmss_par.wots_par.keysize;
|
||||
|
||||
compute_authpath_wots(root, sig_msg, idx_leaf, sk_seed, &(params->xmss_par), pub_seed, ots_addr);
|
||||
sig_msg += tree_h*n;
|
||||
*sig_msg_len += tree_h*n;
|
||||
}
|
||||
|
||||
//Whipe secret elements?
|
||||
//zerobytes(tsk, CRYPTO_SECRETKEYBYTES);
|
||||
|
||||
memcpy(sig_msg,msg,msglen);
|
||||
*sig_msg_len += msglen;
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
/**
|
||||
* Verifies a given message signature pair under a given public key.
|
||||
*/
|
||||
int xmssmt_sign_open(unsigned char *msg, unsigned long long *msglen, const unsigned char *sig_msg, unsigned long long sig_msg_len, const unsigned char *pk, const xmssmt_params *params)
|
||||
{
|
||||
unsigned int n = params->n;
|
||||
unsigned int m = params->m;
|
||||
|
||||
unsigned int tree_h = params->xmss_par.h;
|
||||
unsigned int idx_len = params->index_len;
|
||||
unsigned long long idx_tree;
|
||||
unsigned long long idx_leaf;
|
||||
|
||||
unsigned long long i, m_len;
|
||||
unsigned long long idx=0;
|
||||
unsigned char wots_pk[params->xmss_par.wots_par.keysize];
|
||||
unsigned char pkhash[n];
|
||||
unsigned char root[n];
|
||||
unsigned char msg_h[m];
|
||||
|
||||
unsigned char pub_seed[n];
|
||||
memcpy(pub_seed,pk+n,n);
|
||||
|
||||
// Init addresses
|
||||
unsigned char ots_addr[16] = {0,0,0,0};
|
||||
unsigned char ltree_addr[16];
|
||||
unsigned char node_addr[16];
|
||||
|
||||
// Extract index
|
||||
for(i = 0; i < idx_len; i++){
|
||||
idx |= ((unsigned long long)sig_msg[i]) << (8*(idx_len - 1 - i));
|
||||
}
|
||||
printf("verify:: idx = %llu\n",idx);
|
||||
sig_msg += idx_len;
|
||||
sig_msg_len -= idx_len;
|
||||
|
||||
// hash message (recall, R is now on pole position at sig_msg
|
||||
unsigned long long tmp_sig_len = m+ (params->d * params->xmss_par.wots_par.keysize) + (params->h * n);
|
||||
m_len = sig_msg_len - tmp_sig_len;
|
||||
hash_m(msg_h, sig_msg + tmp_sig_len, m_len, sig_msg, m, m);
|
||||
|
||||
sig_msg += m;
|
||||
sig_msg_len -= m;
|
||||
|
||||
//-----------------------
|
||||
// Verify signature
|
||||
//-----------------------
|
||||
|
||||
// Prepare Address
|
||||
idx_tree = idx >> tree_h;
|
||||
idx_leaf = (idx & ((1 << tree_h)-1));
|
||||
SET_LAYER_ADDRESS(ots_addr,0);
|
||||
SET_TREE_ADDRESS(ots_addr, idx_tree);
|
||||
SET_OTS_BIT(ots_addr, 1);
|
||||
|
||||
memcpy(ltree_addr, ots_addr, 10);
|
||||
SET_OTS_BIT(ltree_addr, 0);
|
||||
SET_LTREE_BIT(ltree_addr, 1);
|
||||
|
||||
memcpy(node_addr, ltree_addr, 10);
|
||||
SET_LTREE_BIT(node_addr, 0);
|
||||
SET_NODE_PADDING(node_addr);
|
||||
|
||||
SET_OTS_ADDRESS(ots_addr,idx_leaf);
|
||||
|
||||
// Check WOTS signature
|
||||
wots_pkFromSig(wots_pk, sig_msg, msg_h, &(params->xmss_par.wots_par), pub_seed, ots_addr);
|
||||
|
||||
sig_msg += params->xmss_par.wots_par.keysize;
|
||||
sig_msg_len -= params->xmss_par.wots_par.keysize;
|
||||
|
||||
// Compute Ltree
|
||||
SET_LTREE_ADDRESS(ltree_addr, idx_leaf);
|
||||
l_tree(pkhash, wots_pk, &(params->xmss_par), pub_seed, ltree_addr);
|
||||
|
||||
// Compute root
|
||||
validate_authpath(root, pkhash, idx_leaf, sig_msg, &(params->xmss_par), pub_seed, node_addr);
|
||||
|
||||
sig_msg += tree_h*n;
|
||||
sig_msg_len -= tree_h*n;
|
||||
|
||||
for(i = 1; i < params->d; i++){
|
||||
// Prepare Address
|
||||
idx_leaf = (idx_tree & ((1 << tree_h)-1));
|
||||
idx_tree = idx_tree >> tree_h;
|
||||
|
||||
SET_LAYER_ADDRESS(ots_addr,i);
|
||||
SET_TREE_ADDRESS(ots_addr, idx_tree);
|
||||
SET_OTS_BIT(ots_addr, 1);
|
||||
|
||||
memcpy(ltree_addr, ots_addr, 10);
|
||||
SET_OTS_BIT(ltree_addr, 0);
|
||||
SET_LTREE_BIT(ltree_addr, 1);
|
||||
|
||||
memcpy(node_addr, ltree_addr, 10);
|
||||
SET_LTREE_BIT(node_addr, 0);
|
||||
SET_NODE_PADDING(node_addr);
|
||||
|
||||
SET_OTS_ADDRESS(ots_addr,idx_leaf);
|
||||
|
||||
// Check WOTS signature
|
||||
wots_pkFromSig(wots_pk, sig_msg, root, &(params->xmss_par.wots_par), pub_seed, ots_addr);
|
||||
|
||||
sig_msg += params->xmss_par.wots_par.keysize;
|
||||
sig_msg_len -= params->xmss_par.wots_par.keysize;
|
||||
|
||||
// Compute Ltree
|
||||
SET_LTREE_ADDRESS(ltree_addr, idx_leaf);
|
||||
l_tree(pkhash, wots_pk, &(params->xmss_par), pub_seed, ltree_addr);
|
||||
|
||||
// Compute root
|
||||
validate_authpath(root, pkhash, idx_leaf, sig_msg, &(params->xmss_par), pub_seed, node_addr);
|
||||
|
||||
sig_msg += tree_h*n;
|
||||
sig_msg_len -= tree_h*n;
|
||||
|
||||
}
|
||||
|
||||
for(i=0;i<n;i++)
|
||||
if(root[i] != pk[i])
|
||||
goto fail;
|
||||
|
||||
*msglen = sig_msg_len;
|
||||
for(i=0;i<*msglen;i++)
|
||||
msg[i] = sig_msg[i];
|
||||
|
||||
return 0;
|
||||
|
||||
|
||||
fail:
|
||||
*msglen = sig_msg_len;
|
||||
for(i=0;i<*msglen;i++)
|
||||
msg[i] = 0;
|
||||
*msglen = -1;
|
||||
return -1;
|
||||
}
|
||||
84
xmss_fast.h
Normal file
84
xmss_fast.h
Normal file
@ -0,0 +1,84 @@
|
||||
/*
|
||||
xmss.h version 20150811
|
||||
Andreas Hülsing
|
||||
Public domain.
|
||||
*/
|
||||
|
||||
#include "wots.h"
|
||||
|
||||
#ifndef XMSS_H
|
||||
#define XMSS_H
|
||||
typedef struct{
|
||||
int level;
|
||||
unsigned long long subtree;
|
||||
int subleaf;
|
||||
} leafaddr;
|
||||
|
||||
typedef struct{
|
||||
wots_params wots_par;
|
||||
int n;
|
||||
int m;
|
||||
int h;
|
||||
} xmss_params;
|
||||
|
||||
typedef struct{
|
||||
xmss_params xmss_par;
|
||||
int n;
|
||||
int m;
|
||||
int h;
|
||||
int d;
|
||||
int index_len;
|
||||
} xmssmt_params;
|
||||
/**
|
||||
* Initializes parameter set.
|
||||
* Needed, for any of the other methods.
|
||||
*/
|
||||
void xmss_set_params(xmss_params *params, int m, int n, int h, int w);
|
||||
/**
|
||||
* Initialize xmssmt_params struct
|
||||
* parameter names are the same as in the draft
|
||||
*
|
||||
* Especially h is the total tree height, i.e. the XMSS trees have height h/d
|
||||
*/
|
||||
void xmssmt_set_params(xmssmt_params *params, int m, int n, int h, int d, int w);
|
||||
/**
|
||||
* Generates a XMSS key pair for a given parameter set.
|
||||
* Format sk: [(32bit) idx || SK_SEED || SK_PRF || PUB_SEED]
|
||||
* Format pk: [root || PUB_SEED] omitting algo oid.
|
||||
*/
|
||||
int xmss_keypair(unsigned char *pk, unsigned char *sk, xmss_params *params);
|
||||
/**
|
||||
* Signs a message.
|
||||
* Returns
|
||||
* 1. an array containing the signature followed by the message AND
|
||||
* 2. an updated secret key!
|
||||
*
|
||||
*/
|
||||
int xmss_sign(unsigned char *sk, unsigned char *sig_msg, unsigned long long *sig_msg_len, const unsigned char *msg,unsigned long long msglen, const xmss_params *params);
|
||||
/**
|
||||
* Verifies a given message signature pair under a given public key.
|
||||
*
|
||||
* Note: msg and msglen are pure outputs which carry the message in case verification succeeds. The (input) message is assumed to be within sig_msg which has the form (sig||msg).
|
||||
*/
|
||||
int xmss_sign_open(unsigned char *msg,unsigned long long *msglen, const unsigned char *sig_msg,unsigned long long sig_msg_len, const unsigned char *pk, const xmss_params *params);
|
||||
|
||||
/*
|
||||
* Generates a XMSSMT key pair for a given parameter set.
|
||||
* Format sk: [(ceil(h/8) bit) idx || SK_SEED || SK_PRF || PUB_SEED]
|
||||
* Format pk: [root || PUB_SEED] omitting algo oid.
|
||||
*/
|
||||
int xmssmt_keypair(unsigned char *pk, unsigned char *sk, xmssmt_params *params);
|
||||
/**
|
||||
* Signs a message.
|
||||
* Returns
|
||||
* 1. an array containing the signature followed by the message AND
|
||||
* 2. an updated secret key!
|
||||
*
|
||||
*/
|
||||
int xmssmt_sign(unsigned char *sk, unsigned char *sig_msg, unsigned long long *sig_msg_len, const unsigned char *msg, unsigned long long msglen, const xmssmt_params *params);
|
||||
/**
|
||||
* Verifies a given message signature pair under a given public key.
|
||||
*/
|
||||
int xmssmt_sign_open(unsigned char *msg, unsigned long long *msglen, const unsigned char *sig_msg, unsigned long long sig_msg_len, const unsigned char *pk, const xmssmt_params *params);
|
||||
#endif
|
||||
|
||||
Loading…
Reference in New Issue
Block a user