main(int ac, char **av)
{
uint64_t k,b,n,p;
int64_t c;
uint64_t r;
int i;
if (ac < 5) {
printf("usage: %s k b n c p iterations\n",av[0]);
exit(1);
}
// convert arguments
k = atoi(av[1]);
b = atoi(av[2]);
n = atoi(av[3]);
p = atoi(av[4]);
for (i=0; i< atoi(av[5]); i++); r = powmulmod(k,b,n,p);
printf("%d^%d | %d = %d\n", b,n,p,r);
printf("2^2-1 %3 = %d\n", mulmod(1,(2*2-1),3));
printf("2^3-1 %3 = %d\n", mulmod(1,(4*2-1),3));
printf("2^4-1 %3 = %d\n", mulmod(1,(8*2-1),3));
printf("2^4-2 %3 = %d\n", mulmod(1,(8*2-2),3));
printf("2^4-3 %3 = %d\n", mulmod(1,(8*2-3),3));
}
ll expmod(ll b, ll e, ll m) { //O(log b)
if (!e)
return 1;
ll q = expmod(b, e / 2, m);
q = mulmod(q, q, m);
return e % 2 ? mulmod(b, q, m) : q;
}
long long binpow(long long a, long long n) {
if (n == 0)
return 1;
long long res = binpow(a, n / 2);
res = mulmod(res, res);
if (n % 2 == 1)
return res = mulmod(res, a);
return res;
}
//(a^b)%m in log(b)
long long power(long long b, long long n, long long mod) {
long long x=1, p=b;
while(n) {
if(n&1) x = mulmod(x, p, mod);
p = mulmod(p, p, mod);
n >>= 1;
}
return x;
}
uint64 powmod(uint64 x, uint64 n, uint64 m) {
uint64 a = 1, b = x;
for (; n > 0; n >>= 1) {
if (n & 1) {
a = mulmod(a, b, m);
}
b = mulmod(b, b, m);
}
return a % m;
}
ll modulo(ll a, ll b, ll c)
{
ll x = 1, y = a%c;
while(b>0)
{
if(b&1) x = mulmod(x,y,c);
y = mulmod(y,y,c);
b = b>>1;
}
return x;
}
unsigned long long powmod(long long a, long long b, long long c){
unsigned long long result = 1;
unsigned long long base = a;
while (b){
if (b & 1){
result = mulmod(result, base , c);
}
b >>= 1;
base = mulmod(base, base , c);
}
return result;
}
unsigned long long modulo(unsigned long long a, unsigned long long b, unsigned long long P)
{
unsigned long long ans = 1;
while( b )
{
if( b & 1 )
ans = mulmod(ans, a, P);
a = mulmod(a, a, P);
b >>= 1;
}
return ans;
}
type mod_exp (type a, type n, type q)
{
type var = 1;
type mult = a;
while ( n != 0 ) {
if (n%2 == 1) {
var = mulmod(var, mult, q);
}
mult = mulmod(mult, mult, q);
n = n>>1;
}
return var;
}
/* Return a^r % n, where 0 < n. */
static uint64_t
powmod(uint64_t a, uint64_t r, uint64_t n)
{
uint64_t x = 1;
while (r != 0) {
if (r & 1)
x = mulmod(a, x, n);
a = mulmod(a, a, n);
r >>= 1;
}
return (x);
}
uint64_t modexp (uint64_t m, uint64_t e, uint64_t n)
{
uint64_t result = 1;
while (e > 0)
{
if (e & 1) {
result = mulmod (result, m, n);
}
e >>= 1;
m = mulmod (m, m, n);
}
return result;
}
unsigned long long RSA::powmod(const unsigned long long base,unsigned long long pow,const unsigned long long n)
{
unsigned long long a=base,b=pow,c=1;
while(b)
{
while(!(b&1))
{
b>>=1;
a=mulmod(a,a,n);
}
b--;
c=mulmod(a,c,n);
}
return c;
}
ull power(ull n ,ull k,ull mod)
{
ull temp = 1,ans=1;
while(k>0)
{
if(k&temp)
{
ans = mulmod(ans,n,mod);
k-=temp;
}
temp <<=1;
n = mulmod(n,n,mod);
}
return ans%mod;
}
bool passesMiLLerRabin(unsigned long long N)
{
if(N < 2) return false;
if( N % 2 == 0) return N == 2;
if( N % 3 == 0) return N == 3;
if( N % 5 == 0) return N == 5;
if( N % 7 == 0) return N == 7;
int d = 0;
long long odd = N - 1;
while( (odd & 1) == 0)
{
d++;
odd>>= 1;
}
for(int i = 0; i < maxIter; i++)
{
long long a = rand() % ( N - 1) + 1; // a is random number from 1 to N -1
long long mod = modulo( a, odd, N);
bool passes = ( mod == 1 || mod == N -1 );
for(int r = 1; r < d && !passes; r ++)
{
mod = mulmod( mod, mod, N);
passes = passes || mod == N - 1;
}
if(!passes)
return false;
}
return true;
}
ll rho(ll n) {
if ((n & 1) == 0)
return 2;
ll x = 2, y = 2, d = 1;
ll c = rand() % n + 1;
while (d == 1) {
x = (mulmod(x, x, n) + c) % n;
y = (mulmod(y, y, n) + c) % n;
y = (mulmod(y, y, n) + c) % n;
if (x - y >= 0)
d = gcd(x - y, n);
else
d = gcd(y - x, n);
}
return d == n ? rho(n) : d;
}
/*
* Miller-Rabin primality test, iteration signifies the accuracy
*/
bool EulerUtility::isPrime(ll p, int iteration)
{
if ((p < 2) || (p != 2 && p % 2 == 0))
return false;
ll s = p - 1;
while (s % 2 == 0)
s /= 2;
for (int i = 0; i < iteration; i++)
{
ll a = rand() % (p - 1) + 1, temp = s;
ll mod = modulo(a, temp, p);
while (temp != p - 1 && mod != 1 && mod != p - 1)
{
mod = mulmod(mod, mod, p);
temp *= 2;
}
if (mod != p - 1 && temp % 2 == 0)
return false;
}
return true;
}
bool is_prime_fast(long long n) {
static const int np = 9, p[] = {2, 3, 5, 7, 11, 13, 17, 19, 23};
for (int i = 0; i < np; i++) {
if (n % p[i] == 0) {
return n == p[i];
}
}
if (n < p[np - 1]) {
return false;
}
uint64 t;
int s = 0;
for (t = n - 1; !(t & 1); t >>= 1) {
s++;
}
for (int i = 0; i < np; i++) {
uint64 r = powmod(p[i], t, n);
if (r == 1) {
continue;
}
bool ok = false;
for (int j = 0; j < s && !ok; j++) {
ok |= (r == (uint64)n - 1);
r = mulmod(r, r, n);
}
if (!ok) {
return false;
}
}
return true;
}
static int sqrmod(void *a, void *b, void *c)
{
LTC_ARGCHK(a != NULL);
LTC_ARGCHK(b != NULL);
LTC_ARGCHK(c != NULL);
return mulmod(a, a, b, c);
}
int isPrime (long p,int iteration){ // Miller-Rabin Primality Test
long mulmod(long a, long b, long c);
int modulo(int a,int b,int c);
if(p<2){
return 0;
}
if(p!=2 && p%2==0){
return 0;
}
long long s=p-1;
while(s%2==0){
s/=2;
}
for(int i = 0; i < iteration;i++){
long a = rand()%(p-1)+1,temp=s;
long mod = modulo (a,temp,p);
while (temp !=p-1 && mod != 1 && mod != p-1){
mod=mulmod(mod,mod,p);
temp *= 2;
}
if(mod != p-1 && temp %2 ==0){
return 0;
}
}
return 1;
}
long long modulo(long long a,long long b,long long c){
long long x=1,y=a;
while(b>0){
if(b%2==1){
x=mulmod(x,y,c);
}
y=mulmod(y,y,c);
b/=2;
}
return x%c;
}
T chineseremainder(const std::vector<T>& remainders, const std::vector<T>& moduli) {
T N = 1;
for (auto& v : moduli) N *= v;
T x = 0;
for (auto ai = remainders.begin(), ni = moduli.begin(); ai != remainders.end() && ni != moduli.end(); ai++, ni++)
{
if (*ai > 0) {
T Nni = N / (*ni);
T term = mulmod(*ai, Nni, N);
term = mulmod(term, inverse(Nni, *ni), N);
x += term;
}
}
return x % N;
}
__int64 powmod(__int64 b, __int64 p, __int64 n)
{
__int64 val;
if(!n) return -1;
p = p % n;
if(p==0) return 1;
if(p<0) p += n-1;
val = 1;
while(p)
{
if(p&1) val = mulmod(val,b,n);
p = p>>1;
b = mulmod(b,b,n);
}
return val;
}
/* Naive znorder. Works well if limit is small. Note arguments. */
static UV order(UV r, UV n, UV limit) {
UV j;
UV t = 1;
for (j = 1; j <= limit; j++) {
t = mulmod(t, n, r);
if (t == 1)
break;
}
return j;
}
/**
* Generate a keypair for the U-LP cryptosystem.
* @param size_t n - security parameter
* @param size_t l - message length
* @param uint64_t sk - error bound for key generation
* @param uint64_t se - error bound for encryption
* @param uint64_t q - modulus, must be less than 2^63 due to possible overflow problems
* @param ulp_public_key** pub_key_p - pointer to a public key pointer (will be generated)
* @param ulp_private_key** priv_key_p - pointer to a private key pointer (will be generated)
* @return int - 0 on success, a negative value otherwise
*/
int ulp_generate_key_pair(size_t n, size_t l, uint64_t sk, uint64_t se, uint64_t q, ulp_public_key** pub_key_p, ulp_private_key** priv_key_p) {
if(n == 0 || l == 0 || sk == 0 || se == 0 || q == 0 || pub_key_p == NULL || priv_key_p == NULL || q >= 0x8000000000000000)
return -2;
// allocate memory for keys
ulp_public_key* pub_key = ulp_alloc_public_key(n, l);
ulp_private_key* priv_key = ulp_alloc_private_key(n, l);
uint64_t* SA = calloc(l*n, sizeof(q));
if(pub_key == NULL || priv_key == NULL || SA == NULL)
goto fail;
// store parameters in key structs
pub_key->se = se;
pub_key->q = q;
priv_key->q = q;
// sample random data
int err = 0;
err += get_random_numbers(pub_key->A, n*n, q);
err += get_random_numbers(pub_key->P, l*n, sk);
err += get_random_numbers(priv_key->S, l*n, sk);
if(err != 0)
goto fail;
// S*A
for(size_t i = 0; i < l; i++) {
for(size_t j = 0; j < n; j++) {
for(size_t k = 0; k < n; k++) {
SA[i*n+j] = (SA[i*n+j] + mulmod(priv_key->S[i*n+k], pub_key->A[k*n+j], q)) % q;
}
}
}
// P = E - S*A
for(size_t i = 0; i < l*n; i++) {
pub_key->P[i] = (pub_key->P[i] + q - SA[i]) % q;
}
// exit properly
free(SA);
*pub_key_p = pub_key;
*priv_key_p = priv_key;
return 0;
// on failure, do cleanup
fail:
ulp_free_public_key(pub_key);
ulp_free_private_key(priv_key);
free(SA);
return -1;
}
ll pollard_rho(ll n) {
int i = 0, k = 2;
ll x = 3, y = 3; // random seed = 3, other values possible
while (1) {
i++;
x = (mulmod(x, x, n) + n - 1) % n; // generating function
ll d = gcd(abs_val(y - x), n); // the key insight
if (d != 1 && d != n) return d; // found one non-trivial factor
if (i == k) y = x, k *= 2;
}
}
T AP_pow(T x, T y, T p) {
T z;
assert(x);
assert(y);
assert(y->sign == 1);
assert( (!p) || (p->sign==1 && !iszero(p) && !isone(p)));
if (iszero(x))
return AP_new(0);
if (iszero(y))
return AP_new(1);
if (isone(x))
return AP_new((((y)->digits[0]&1) == 0) ? 1 : x->sign);
if (p)
if (isone(y))
z = AP_mod(x, p);
else {
T y2 = AP_rshift(y, 1), t = AP_pow(x, y2, p);
z = mulmod(t, t, p);
AP_free(&y2);
AP_free(&t);
if (!(((y)->digits[0]&1) == 0)) {
z = mulmod(y2 = AP_mod(x, p), t = z, p);
AP_free(&y2);
AP_free(&t);
}
}
else if (isone(y))
z = AP_addi(x, 0);
else {
T y2 = AP_rshift(y, 1), t = AP_pow(x, y2, NULL);
z = AP_mul(t, t);
AP_free(&y2);
AP_free(&t);
if (!(((y)->digits[0]&1) == 0)) {
z = AP_mul(x, t = z);
AP_free(&t);
}
}
return z;
}
//Ps: 这里选取伪随机数方程为 F(x)= x*x+c 并默认 c = 12323。注意最大只能分解 2^62-1。
//分解失败(返回 n)就尝试变换 c,c 不得取 0 或-2。若还失败,尝试变换 X0
//PB 函数调用前先 MR 判素数,每次可以分解出一个因数(不一定是素数),需配合 MR 算法。
ll PB(ll n,int c=12323,int x0=2){
if(~n&1) return 2;
ll x,y,d=1,k=0,i=1;
x=y=x0;
while(1){
x=(mulmod(x,x,n)+c)%n;
//f(x)=x*x+c,c 可换 24251 或其他素数
d=gcd(n+x-y,n);
if(d!=1 && d<n) return d; //如莫名其妙一直 TLE 可尝试 d<n 改成 d<=n,目前没碰到过
if(y==x) return n;
if(++k == i) y=x,i<<=1;
}
}
bool rabin_miller(long long p) {
if (p < 2) return false;
if (p != 2 && p % 2 == 0) return false;
if (p < 8) return true;
long long s = p-1, val = p-1, a, m, temp;
while (s % 2 == 0) s >>= 1;
for (int i = 0; i < 3; ++i) {
a = 1ll*rand()%val + 1ll;
temp = s;
m = power(a, temp, p);
while (temp != (p-1) && m != 1 && m != (p-1)) {
m = mulmod(m, m, p);
temp <<= 1;
}
if (m != (p-1) && temp % 2 == 0) return false;
}
return true;
}
int Miller(long long p,int iteration){
if(p<2)return 0;
if(p!=2 && p%2==0)return 0;
long long s=p-1,i;
while(s%2==0)s/=2;
for(i=0;i<iteration;i++){
long long a=rand()%(p-1)+1,temp=s;
long long mod=powmod(a,temp,p);
while(temp!=p-1 && mod!=1 && mod!=p-1){
mod=mulmod(mod,mod,p);
temp *= 2;
}
if(mod!=p-1 && temp%2==0){
return 0;
}
}
return 1;
}
bool es_primo_prob(ll n, int a) {
if (n == a)
return true;
ll s = 0, d = n - 1;
while (d % 2 == 0)
s++, d /= 2;
ll x = expmod(a, d, n);
if ((x == 1) || (x + 1 == n))
return true;
for (int i = 0; i < s-1; ++i) {
x = mulmod(x, x, n);
if (x == 1)
return false;
if (x + 1 == n)
return true;
}
return false;
}
