Cohen's cryptosystem

Cohen's cryptosystem^[1] is a public-key cryptosystem proposed in 1998 by Bram Cohen.

Key generation

In Cohen's cryptosystem, private key is a positive integer $p$ .

The algorithm uses $k$ public-keys $w_{0},\ldots ,w_{{k-1}}$ defined as follows:

Generate $k$ random integers $u_{0},\ldots ,u_{{k-1}}$ chosen randomly and uniformly between $-B$ and $B$ . Where $B$ is some bound.

Let $A=\lfloor {\frac {p}{2k}}\rfloor$ and generate $k$ random integers $v_{0},\ldots ,v_{{k-1}}$ chosen randomly and uniformly between $0$ and $A$ .

Define $w_{i}=(u_{i}p+v_{i})$ .

Encrypting a bit

To encrypt a bit $m$ Alice randomly adds ${\frac {k}{2}}$ public keys and multiplies the result by either 1 (if she wishes to send a 0) or by −1 (if she wishes to send a 1) to obtain the ciphertext $c=(-1)^{{m}}\sum w_{i}$ .

De-cryption

To de-crypt, Bob computes $h=c\mod p=(-1)^{{m}}\sum v_{i}$

It is easy to see that if $m=0$ then $0<h<p/2$ . However, if $m=1$ then $p>h>p/2$ . Hence Bob can read the bit sent by Alice on the most significant bit of h.

References

↑ Bram Cohen. "Simple Public Key Encryption". Archived from the original on October 7, 2011.

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[1] Bram Cohen. "Simple Public Key Encryption". Archived from the original on October 7, 2011.