On the Extension of the Domain of Rabin Cryptosystem

The Rabin cryptosystem is an asymmetric cryptographic algorithm. Its security is based on the problem of integer factorization. Rabin cryptosystem has the advantage that the problem on which its security depends is proved to be as hard as factorization. The Rabin cryptosystem works in the domain of the odd primes which satisfy the criteria that 𝑝≡3 (𝑚𝑜𝑑 4), where 𝑝 is any odd prime. The decryption process is very difficult when we take the odd primes which satisfy 𝑝≡1 (𝑚𝑜𝑑 4). Rabin cryptosystem will be more applicable and flexible if we include a wide range of primes. We have extended the domain of primes in Rabin cryptosystem to a subset of the primes satisfying 𝑝≡5 (𝑚𝑜𝑑 8). The primes satisfying 𝑝≡5 (𝑚𝑜𝑑 8) forms a subset of the primes satisfying 𝑝≡1 (𝑚𝑜𝑑 4) without compromising on the security of the Rabin cryptosystem. Our proposed method covers a larger range of primes for the Rabin cryptosystem as compared to original method. Our method is especially useful for resource constrained Networks such as Mobile Ad Hoc Networks (MANET).