A practical attack to Bouftass's cryptosystem

In public key cryptography, the security of traditional methods is based on number theoretic problems, and suffers from high computational cost due to problems such as dealing with large numbers. Each user in a public key system has a pair of cryptographic keys, consisting a public key and a private key. These are related through a hard mathematical inversion problem, so that the private key cannot be feasibly derived from the public key. A standard implementation of public key cryptography is based on the Diffie-Hellman key agreement protocol[1]. This protocol allows two users, Alice and Bob, to exchange a secret key over an insecure communication channel. It can be described as following: 1. Alice and Bob openly agree upon a large prime p and g ∈ Zp. 2. Alice randomly chooses the secret integer a ∈ [1, p − 1]. 3. Alice computes A = g mod p, and publishes A.