2
$\begingroup$

I know that – within the elgamal cryptosystem – the values of $a$ and $b$ are public. But which values are used to create public keys?

$\endgroup$
0
5
$\begingroup$

Let $p$ be a prime such that the Discrete Logarithm problem in $({\mathbb Z_p}^*,.)$ is infeasible, and let $\alpha \in {\mathbb Z_p}^*$ be a primitive element.

$$\beta =\alpha^a \bmod p$$

The values $p,\alpha , \beta$ are the public key, and $a$ is a private key. For a secret random number $k$ encryption and decryption are as follow:

  • $\operatorname{Enc}(x,k)=(\alpha^k \bmod p,x\beta^k \bmod p)$

  • $\operatorname{Dec}(y_1,y_2)=y_2\cdot{({y_1}^a)}^{-1}\bmod p$

$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.