Suppose A chooses DSA signature scheme with p = 797 = 4q + 1, q = 199, a = 2 and

Question

Suppose A chooses DSA signature scheme with p = 797 = 4q + 1, q = 199, a = 2 and a = 17 What is the public key ? What is the private key ? Sign the message x = 123 for A using as a random number k = 30. Suppose B receives the signed message (x; gamma, delta) = (30; 66, 113) as it is from A. Verify for him if this signature is valid. Suppose A chooses DSA signature scheme with p = 53 = 4q + 1, q = 13, alpha = 16 and a = 5. What is the public key ? What is the private key ? Sign the message x = 85 for A using as a random number k = 8 Suppose B receives the signed message (x; gamma, delta) = (20; 3; 6) as it is from A. Verify for him if this signature is valid.

Explanation / Answer

Here for the first question the given data is p=797 ,q=199

a=5

By using RSA algorithm

Public key (n)=(p-1)(q-1)=796*198=157608

. Choose e, 1 < e < (n) s.t. gcd(e, (n)) = 1

Private key,d=e^(-1) mod (n)

here n=pq

Say we want to sign the message m=85, we compute s=m^d mod n which is s=85^(d) mod n

The message and signature get sent to the other party (m,s)=(85,s). Who takes the signature and raises it to the e modulo n, . Then makes sure that this value is equal to the message that was received, which it is, so the message is valid.

Similary we can find public key and private key for second example.

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