Parameter generation for DSA 1. FIPS 186-4 specifies that the L and N values must be (1024, 160), (2048, 224), or (3072, 256) 2. Choose a N-bit prime q 3. Choose a L-bit prime p such that p-1 is a multiple of q 4. Choose an integer h randomly from the range [2, p-2] 5. Compute g = h^((p-1)/q) mod p
()
| 48 | // 5. Compute g = h^((p-1)/q) mod p |
| 49 | // 6. Return (p, q, g) |
| 50 | func (dsa *dsa) dsaParameterGeneration() { |
| 51 | var err error |
| 52 | p, q, bigInt := new(big.Int), new(big.Int), new(big.Int) |
| 53 | one, g, h := big.NewInt(1), big.NewInt(1), big.NewInt(2) |
| 54 | pBytes := make([]byte, L/8) |
| 55 | |
| 56 | // GPLoop is a label for the loop |
| 57 | // We use this loop to change the prime q if we don't find a prime p |
| 58 | GPLoop: |
| 59 | for { |
| 60 | // 2. Choose a N-bit prime q |
| 61 | q, err = rand.Prime(rand.Reader, N) |
| 62 | if err != nil { |
| 63 | panic(err) |
| 64 | } |
| 65 | |
| 66 | for i := 0; i < 4*L; i++ { |
| 67 | // 3. Choose a L-bit prime p such that p-1 is a multiple of q |
| 68 | // In this case we generate a random number of L bits |
| 69 | if _, err := io.ReadFull(rand.Reader, pBytes); err != nil { |
| 70 | panic(err) |
| 71 | } |
| 72 | |
| 73 | // This are the minimum conditions for p being a possible prime |
| 74 | pBytes[len(pBytes)-1] |= 1 // p is odd |
| 75 | pBytes[0] |= 0x80 // p has the highest bit set |
| 76 | p.SetBytes(pBytes) |
| 77 | |
| 78 | // Instead of using (p-1)%q == 0 |
| 79 | // We ensure that p-1 is a multiple of q and validates if p is prime |
| 80 | bigInt.Mod(p, q) |
| 81 | bigInt.Sub(bigInt, one) |
| 82 | p.Sub(p, bigInt) |
| 83 | if p.BitLen() < L || !p.ProbablyPrime(numMRTests) { // Check if p is prime and has L bits |
| 84 | continue |
| 85 | } |
| 86 | |
| 87 | dsa.P = p |
| 88 | dsa.Q = q |
| 89 | break GPLoop |
| 90 | } |
| 91 | } |
| 92 | |
| 93 | // 4. Choose an integer h randomly from the range [2, p-2]. Commonly, h = 2 |
| 94 | // 5. Compute g = h^((p-1)/q) mod p. In case g == 1, increment h until g != 1 |
| 95 | pm1 := new(big.Int).Sub(p, one) |
| 96 | |
| 97 | for g.Cmp(one) == 0 { |
| 98 | g.Exp(h, new(big.Int).Div(pm1, q), p) |
| 99 | h.Add(h, one) |
| 100 | } |
| 101 | |
| 102 | dsa.G = g |
| 103 | } |
| 104 | |
| 105 | // keyGen is key generation for DSA |
| 106 | // 1. Choose a random integer x from the range [1, q-1] |