Description: DigitalSignature Algorithm (DSA) is a variation of the Signature Algorithm of Schnorr and ElGamal, which is used by the NIST as the DSS(DigitalSignature Standard). The following parameters are applied in the algorithm:
P: L bits long prime. L is a multiple of 64, the range is 512 to 1024;
Q: 160bits of prime factor of p-1;
G: g = h ^ ((p - 1)/q) mod p, h meet h & lt; P - 1, h ^ ((1) p/q) mod p & gt; 1;
X: x & lt; Q, x is the private key;
Y: y = g ^ mod p, x (p, q, g, y) as the public key;
H (x) : one-way Hash function. The Secure Hash Algorithm is selected in DSS.
P, q, g can be Shared by a group of users, but in practice, the use of public modulus may pose a threat. Signature and verification protocol is as follows:
1. The random number k, k < Q;
2. Calculate r = P mod q ^ k mod P (g)
S = (k ^ (1) (H (m) + xr)) mod q
The signature result is (m, r, s).
3. Verify the calculation w = s ^ (1) the mod q
U1 = (H (m) * w) mod q
U2 = (r * w) mod q
V = ((g * y ^ ^ u1, u2) mod p) mod q
If v = r, the signature is considered valid.
DSA is based on integer finite domain discrete logarithm problem, and its security is similar to RSA. DSA is an important feature of two prime Numbers, so when using p and q of others, even if they don't know the private key, you can confirm whether they are random, or the hands and feet. The RSA algorithm does not.
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