Implement A Digital Signature Batch Screening For Elgamal

ElGamal

The ElGamal Encryption Scheme is an asymmetric key encryption algorithm for public key cryptography algorithm for public key cryptography and it is based on Diffie Helman key exchange.

Key generation

Randomly choose a secret key x with 1 < x < p − 1.

Compute y = g^x mod p.

The public key is (p, g, y).

The secret key is x.

These steps are performed once by the signer.

Signature generation

To sign a message m the signer performs the following steps.

Choose a random k such that 1 < k < p − 1 and gcd(k, p − 1) = 1.

Compute $r \, \equiv \, g^k \pmod p$ .

Compute $s \, \equiv \, (H(m)-x r)k^{-1} \pmod{p-1}$ .

If $s=0$ start over again.

Then the pair (r,s) is the digital signature of m. The signer repeats these steps for every signature.

Verification

A signature (r,s) of a message m is verified as follows.

$0<r<p$ and $0<s<p-1$ .

$g^{H(m)} \equiv y^r r^s \pmod p.$

The verifier accepts a signature if all conditions are satisfied and rejects it otherwise.

Batch verification approach

In modified version of ElGamal Batch verification approach, multiplication of

is computed for a batch of r and s. Then get the summation of collision-resistant hash value for every message and checks for the equality of both values of summation of hash and the multiplication of

A signature (r,s) of a message m is verified as follows.

and .

The verification scheme accepts a signatures if all conditions are satisfied and rejects if there exists at least one forged signature.

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