Cohen's cryptosystem

In Cohen's cryptosystem, a 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. 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==