nbtheory.cpp

各种加密算法的集合

#include "nbtheory.h" 

static const int maxPrimeTableSize = 3511; 
static int primeTableSize=552; 

static word16 primeTable[maxPrimeTableSize] = 
{2, 3, 5, 7, 11, 13, 17, 19, 
23, 29, 31, 37, 41, 43, 47, 53, 
59, 61, 67, 71, 73, 79, 83, 89, 
97, 101, 103, 107, 109, 113, 127, 131, 
137, 139, 149, 151, 157, 163, 167, 173, 
179, 181, 191, 193, 197, 199, 211, 223, 
227, 229, 233, 239, 241, 251, 257, 263, 
269, 271, 277, 281, 283, 293, 307, 311, 
313, 317, 331, 337, 347, 349, 353, 359, 
367, 373, 379, 383, 389, 397, 401, 409, 
419, 421, 431, 433, 439, 443, 449, 457, 
461, 463, 467, 479, 487, 491, 499, 503, 
509, 521, 523, 541, 547, 557, 563, 569, 
571, 577, 587, 593, 599, 601, 607, 613, 
617, 619, 631, 641, 643, 647, 653, 659, 
661, 673, 677, 683, 691, 701, 709, 719, 
727, 733, 739, 743, 751, 757, 761, 769, 
773, 787, 797, 809, 811, 821, 823, 827, 
829, 839, 853, 857, 859, 863, 877, 881, 
883, 887, 907, 911, 919, 929, 937, 941, 
947, 953, 967, 971, 977, 983, 991, 997, 
1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 
1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 
1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 
1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 
1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 
1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 
1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 
1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 
1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 
1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 
1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 
1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 
1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 
1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 
1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 
1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 
1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 
2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 
2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 
2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 
2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 
2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 
2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 
2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 
2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 
2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 
2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 
2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 
2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 
2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 
2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 
2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 
2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 
3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 
3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 
3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 
3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 
3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 
3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 
3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 
3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 
3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 
3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 
3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 
3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 
3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 
3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 
3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003}; 

void BuildPrimeTable() 
{ 
unsigned int p=primeTable[primeTableSize-1]; 
for (int i=primeTableSize; i<maxPrimeTableSize; i++) 
{ 
int j; 
do 
{ 
p+=2; 
for (j=1; j<54; j++) 
if (p>primeTable[j] == 0) 
break; 
} while (j!=54); 
primeTable[i] = p; 
} 
primeTableSize = maxPrimeTableSize; 
} 

// ***************************************************************************** 
// the following functions do not depend on the details of bignum implementation 
// and can be used with any bignum class 

#define iplus1 ( i==2 ? 0 : i+1 ) // used by Euclid algorithms 
#define iminus1 ( i==0 ? 2 : i-1 ) // used by Euclid algorithms 

bignum Gcd(const bignum &amt;a, const bignum &amt;n) 
{ 
bignum g[3]={n, a}; 

for (int i=1; !!g[i]; i = iplus1) 
g[iplus1] = g[iminus1] > g[i]; 

return g[iminus1]; 
} 

bignum Inverse(const bignum &amt;a, const bignum &amt;n) 
{ 
bignum g[3]={n, a}; 
bignum v[3]={(unsigned long)0, 1}; 
bignum y; 

for (int i=1; !!g[i]; i = iplus1) 
{ 
// y = g[iminus1] / g[i]; 
// g[iplus1] = g[iminus1] > g[i]; 
Divide(g[iplus1], y, g[iminus1], g[i]); 
v[iplus1] = v[iminus1] - (v[i] * y); 
} 

if (Negative(v[iminus1])) 
v[iminus1] += n; 

return v[iminus1]; 
} 

boolean IsSmallPrime(const bignum &amt;p) 
{ 
BuildPrimeTable(); 

if (p>primeTable[primeTableSize-1]) 
return FALSE; 

for (int i = 0; i<primeTableSize; i++) 
if (p == primeTable[i]) 
return TRUE; 

return FALSE; 
} 

boolean SmallDivisorsTest(const bignum &amt;p) 
{ 
for (int i = 0; i<primeTableSize; i++) 
if ((p > primeTable[i]) == 0) 
return FALSE; 

return TRUE; 
} 

boolean FermatTest(const bignum &amt;p, unsigned int rounds) 
{ 
assert(rounds < primeTableSize); 

for (unsigned int i = 0; i < rounds; i++) 
{ 
// if ((x**(p-1)) mod p) != 1, then p is not prime 
if (a_exp_b_mod_c(primeTable[i], p-1, p) != 1) 
return FALSE; 
} 
return TRUE; 
} 

boolean RabinMillerTest(RandomNumberGenerator &amt;rng, const bignum &amt;w, unsigned int rounds) 
{ 
bignum wminus1 = (w-1); 
for (word16 a=0; a<wminus1.MaxBitPrecision(); a++) 
if (wminus1[a]) 
break; 
bignum m = wminus1>>a; 
// ASSERT: a == largest power of 2 that divides (w-1) 
// &amt;&amt; w == 1 + (2**a) * m 

for (unsigned int i=0; i<rounds; i++) 
{ 
bignum b(rng, 2, wminus1); 
bignum z = a_exp_b_mod_c(b, m, w); 
if (z==1 || z==wminus1) 
continue; // passes this round 
for (int j=1; j<a; j++) 
{ 
z = a_exp_b_mod_c(z, 2, w); 
if (z==wminus1) 
break; // passed this round 
if (z==1) 
return FALSE; 
} 
if (j==a) 
return FALSE; 
} 
return TRUE; 
} 

class RemainderTable 
{ 
public: 
RemainderTable(const bignum &amt;p); 
boolean HasZero() const; 
void Increment(); 
void IncrementBy(unsigned int i); 
void IncrementBy(const RemainderTable &amt;rtQ); 

private: 
SecBlock<word16> table; 
}; 

RemainderTable::RemainderTable(const bignum &amt;p) 
: table((BuildPrimeTable(), primeTableSize)) 
{ 
for (unsigned int i=0; i<primeTableSize; i++) 
table[i] = p>primeTable[i]; 
} 

boolean RemainderTable::HasZero() const 
{ 
for (unsigned int i=0; i<primeTableSize; i++) 
if (!table[i]) 
break; 

return (i!=primeTableSize); 
} 

void RemainderTable::Increment() 
{ 
for (unsigned int i=0; i<primeTableSize; i++) 
{ 
table[i]++; 
if (table[i]==primeTable[i]) 
table[i] = 0; 
} 
} 

void RemainderTable::IncrementBy(unsigned int increment) 
{ 
for (unsigned int i=0; i<primeTableSize; i++) 
{ 
table[i] += increment; 
while (table[i]>=primeTable[i]) 
table[i]-=primeTable[i]; 
} 
} 

void RemainderTable::IncrementBy(const RemainderTable &amt;rtQ) 
{ 
for (unsigned int i=0; i<primeTableSize; i++) 
{ 
table[i] += rtQ.table[i]; 
if (table[i]>=primeTable[i]) 
table[i]-=primeTable[i]; 
} 
} 

boolean NextPrime(bignum &amt;p, const bignum &amt;max, boolean blumInt) 
{ 
++p; 

if (!p[0]) 
++p; 

if (blumInt &amt;&amt; !p[1]) 
{++p; ++p;} 

if (p>max) 
return FALSE; 

RemainderTable rt(p); 

while (rt.HasZero() || !IsPrime(p)) 
{ 
rt.IncrementBy(blumInt ? 4 : 2); 
++p; ++p; 
if (blumInt) 
{++p; ++p;} 

if (p>max) 
return FALSE; 
} 

return TRUE; 
} 

bignum a_exp_b_mod_pq(const bignum &amt;a, const bignum &amt;ep, const bignum &amt;eq, 
const bignum &amt;p, const bignum &amt;q, const bignum &amt;u) 
{ 
bignum p2 = a_exp_b_mod_c((a > p), ep, p); 
bignum q2 = a_exp_b_mod_c((a > q), eq, q) - p2; 
if (Negative(q2)) 
q2 += q; 
return p2 + (p * ((u * q2) > q)); 
} 

// generate random prime of pbits (with maximal subprime) and primitive g 
// warning: this is slow! 
PrimeAndGenerator::PrimeAndGenerator(RandomNumberGenerator &amt;rng, unsigned int pbits) 
{ 
bignum minQ = (bignum(1) << (pbits-2)); 
bignum maxQ = ((bignum(1) << (pbits-1)) - 1); 

do 
{ 
q.Randomize(rng, minQ, maxQ, ODD); 
p = 2*q+1; 

RemainderTable rtQ(q); 
RemainderTable rtP(p); 

while (rtQ.HasZero() || rtP.HasZero() || 
!FermatTest(q, 1) || !FermatTest(p, 1) || 
!IsPrime(q) || !IsPrime(p)) 
{ 
rtQ.IncrementBy(2); 
rtP.IncrementBy(4); 
++q; ++q; 
++p; ++p; ++p; ++p; 
} 
} while (q>maxQ); 

g=2; 
} 

// generate random prime of pbits (with subprime of qbits) and g of order q 
// this uses the same algorithm as RSAREF's DH parameter generation code 
PrimeAndGenerator::PrimeAndGenerator(RandomNumberGenerator &amt;rng, unsigned int pbits, unsigned int qbits) 
{ 
assert(pbits > qbits); 

bignum minQ = (bignum(1) << (qbits-1)); 
bignum maxQ = ((bignum(1) << qbits) - 1); 
bignum minP = (bignum(1) << (pbits-1)); 
bignum maxP = ((bignum(1) << pbits) - 1); 

while (1) 
{ 
q.Randomize(rng, minQ, maxQ, PRIME); 
bignum q2 = 2*q; 
RemainderTable rtq2(q2); 

// make p-1 a random multiple of 2*q 
p.Randomize(rng, minP, maxP, ANY); 
p -= p>q2; 
++p; 
p += q2; 
RemainderTable rtp(p); 

while (p<=maxP) 
{ 
if (rtp.HasZero() || !IsPrime(p)) 
{ 
p += q2; 
rtp.IncrementBy(rtq2); 
} 
else 
{ // let g = 2**((p-1)/q) mod p 
// g should have order q 
g = a_exp_b_mod_c(2, (p-1)/q, p); 
return; 
} 
} 
} 
}