std::string IDEA::decrypt(const std::string & DATA){
if (!keyset){
throw std::runtime_error("Error: Key has not been set.");
}
if (DATA.size() != 8){
throw std::runtime_error("Error: Data must be 64 bits in length.");
}
keys.clear();
std::vector <uint16_t> t;
for(uint8_t x = 0; x < 8; x++){
k.push_back(invmod(static_cast <int> (65537), static_cast <int> (k[48 - 6 * x])));
k.push_back(two_comp(k[50 - 6 * x]));
k.push_back(two_comp(k[49 - 6 * x]));
k.push_back(invmod(static_cast <int> (65537), static_cast <int> (k[51 - 6 * x])));
k.push_back(k[46 - 6 * x]);
k.push_back(k[47 - 6 * x]);
}
k.push_back(invmod(static_cast <int> (65537), static_cast <int> (k[0])));
k.push_back(two_comp(k[1]));
k.push_back(two_comp(k[2]));
k.push_back(invmod(static_cast <int> (65537), static_cast <int> (k[3])));
k.erase(k.begin(), k.begin() + 52);
for(uint8_t x = 0; x < 8; x++){
for(uint8_t y = 0; y < 6; y++){
t.push_back(k[6 * x + y]);
}
keys.push_back(t);
t.clear();
}
for(uint8_t x = 48; x < 52; x++){
t.push_back(k[x]);
}
keys.push_back(t);
t.clear();
std::swap(keys[0][1], keys[0][2]);
return run(DATA);
}
int main(void){
inv[1] = 1;
for(i = 2; i < 1000000; i++)
inv[i] = (inv[i-1]*invmod(i,1300031))%MMM;
scanf("%d",&t);
while(t--){
scanf("%d%d",&n,&c);
int p = ((c < n-1) ? c : n-1);
for(k = c+n-1, r = i = 1; i <= p; i++,k--)
r = (r*k)%MMM;
printf("%lld\n",((r%MMM)*(inv[p]%MMM))%MMM);
}
return 0;
}
int main (int argc, char *argv[])
{
uint64_t p, q, e, n, phi, d, s;
char *m;
puts ("\n RSA example");
if (argc != 2) {
printf ("\n usage: rsa <message>\n");
return 0;
}
m=argv[1];
// generate 2 RN-bit primes
printf ("\n Generating p...");
p=safe_prime(RN);
printf ("%llu", p);
printf ("\n Generating q...");
q=safe_prime(RN);
printf ("%llu\n", q);
// compute modulus, n = pq
n=multiply (p, q);
printf ("\n modulus : %llu [%0llX]", n, n);
printf ("\n message : \"%s\"", m);
// (p-1) * (q-1)
// phi=totient (n);
phi=multiply (p-1, q-1);
// find e
e=65537;
while (gcd (e, phi) != 1)
e++;
printf ("\n encryption key : %llu [%0llX]", e, e);
// d = (e ^ -1) % phi
d=invmod (e, phi);
printf ("\n decryption key : %llu [%0llX]", d, d);
s=sign (m, e, n);
printf ("\n signature : %llu [%0llX] (%s)\n", s, s,
verify (m, s, d, n) ? "good" : "bad");
return 0;
}
int main() {
freopen("puncte.in", "r", stdin);
freopen("puncte.out", "w", stdout);
int N, P;
long long M;
scanf("%d%lld%d", &N, &M, &P);
int R = N - M % N;
long long max_cnt = M / N;
comb[0] = 1;
int i;
for (i = 1; i <= N; ++i)
comb[i] = 1LL * comb[i - 1] * (N - i + 1) % Mod * invmod(i) % Mod;
for (i = 0; i <= N; ++i) {
csaved[i] = comb[i];
comb[i] = LPow(comb[i], max_cnt);
}
dp[0][0] = 1;
int u;
for (i = 1, u = 1; i <= N; ++i, u ^= 1) {
int K = min(i * N, P), j;
memset(dp[u], 0, sizeof dp[u]);
for (j = 0; j <= K; ++j) {
int k;
for (k = 0; k <= N && j - k >= 0; ++k) {
dp[u][j] = (dp[u][j] + 1LL * dp[u ^ 1][j - k] * comb[k]) % Mod;
}
}
if (i == R) {
for (j = 0; j <= N; ++j)
comb[j] = 1LL * comb[j] * csaved[j] % Mod;
}
}
printf("%d\n", dp[N & 1][P]);
}
/* Modular Binomial Coefficients {{{ */
long long cmod(long long n, long long k, long long m) {
long long ret = 1;
for(long long i = n; i > max(n-k, k); i--) ret = (ret*i)%m;
for(long long i = min(n-k, k); i > 1; i--) ret = (ret*invmod(i, m))%m;
return ret;
}
int main (int argc, char *argv[])
{
uint64_t p, q, g, t, x, y, k, r, s=0, kinv, xr, H;
uint64_t v, w, u1, u2;
char *m;
puts ("\n Digital Signature Algorithm example");
if (argc != 2) {
printf ("\n usage: dsa <message>\n");
return 0;
}
m=argv[1];
printf ("\n Generating p...");
p=safe_prime(RP);
printf ("%llX\n Generating g...", p);
// find g
q=(p-1)/2;
for (g=1; g == 1;) {
// g = t ^ (p-1)/q % p
t=rand_range (q); // normally, t would be a hash of q bits
g=powmod (t, (p-1)/q, p);
}
printf ("%llX\n", g);
/**
generated by modified openssl gen_params
p=hex2bin("5E6DDA8BC9B2B5A9");
q=hex2bin("D549");
g=hex2bin("22729DB49EE21F4B");
powmod
invmod
*/
printf ("\np=%llX\nq=%llX\ng=%llX", p, q, g);
// generate random x in range of q
x=rand_range(q);
// y = g ^ x % p
y=powmod (g, x, p);
y = 0x7632D; x = 0x628A5;
printf ("\n\npublic key = %llX\nPrivate key = %llX", y, x);
H=hex2bin(m);
// sign message
do {
// generate k in range of q
k=rand_range(q);
// k ^ -1 % q
kinv=invmod (k, q);
// r = (g ^ k % p) % q
r=modulo (powmod (g, k, p), q);
if (r == 0)
continue;
// s = (kinv * (H + x*r)) % q
xr=multiply (x, r);
s=add (xr, H);
s=mulmod (s, kinv, q);
} while (s == 0);
printf ("\n\n(k=%llX, r=%llX, s=%llX)", k, r, s);
// now verify
// w = s invmod q
w=invmod (s, q);
// u1 = (H * w) % q
u1=mulmod(H, w, q);
// u2 = (r * w) % q
u2=mulmod(r, w, q);
// v = ((g^u1 * y^u2) % p) % q
u1=powmod (g, u1, p);
u2=powmod (y, u2, p);
v=mulmod(u1, u2, p);
v=modulo(v, q);
printf ("\nv = %llX", v);
printf ("\n signature is %s", v==r ? "valid" : "invalid");
return 0;
}
