ElGamal

What

1. Alice has a secret key $x$ and a public key $X=g^x,g,p$
2. Bob has a secret key $r$ and $K=X^r=g^{xr}(\mathrm{mod}p)$, calculate the cipher $c_1=g^r$ and $c_2=m\ast K$
3. With the cipher, Alice knows $K=c_1^x=g^{rx}$ and thus can decrypt the text but Eve won’t know $K$ since Eve don’t know both $x$ and $r$

Note that $m=c_2\ast K^{-1}(\mathrm{mod}p)$(egcd)

How

Why

• A two way Diffie Hellman

Links

• ElGamal encryption - Wikipedia
• Asymmetric Cryptography