Analysis on the Rabin-p cryptosystem

This paper presents an analysis toward estimating the algorithm running time on the Rabin-p cryptosystem. Next, we evaluate the memory cost for system parameters and accumulators for the Rabin-p encryption and decryption procedure, respectively. We then conduct a comparative analysis between three Rabin-like cryptosystems, namely the Rabin-p, the Rabin-Takagi and the HIME(R) cryptosystem. In summation, we conclude that Rabin-p cryptosystem performs faster and used less storage in comparison to the other two Rabin-like cryptosystems in consideration

The Rabin cryptosystem revisited

The Rabin public-key cryptosystem is revisited with a focus on the problem of identifying the encrypted message unambiguously for any pair of primes. In particular, a deterministic scheme using quartic reciprocity is described that works for primes congruent 5 modulo 8, a case that was still open. Both theoretical and practical solutions are presented. The Rabin signature is also reconsidered and a deterministic padding mechanism is proposed.Comment: minor review + introduction of a deterministic scheme using quartic reciprocity that works for primes congruent 5 modulo

Design of Rabin-like cryptosystem without decryption failure

In this work, we design a new, efficient and practical Rabin-like cryptosystem without using the Jacobi symbol, redundancy in the message and avoiding the demands of extra information for finding the correct plaintext. Decryption outputs a unique plaintext without any decryption failure. In addition, decryption only requires a single prime. Furthermore, the decryption procedure only computes a single modular exponentiation instead of two modular exponentiation executed by other Rabin variants. As a result, this reduces the computational effort during the decryption process. Moreover the Novak’s side channel attack is impractical over the proposed Rabin-like cryptosystem. In parallel, we prove that the Rabin-p cryptosystem is indeed as intractable as the integer factorization problem

Efficient methods to overcome Rabin cryptosystem decryption failure

Rabin cryptosystem is an efficient factoring-based scheme, however, its decryption produces 4-to-1 output, which leads to decryption failure. In this work, in order to overcome the 4-to-1 decryption problem for the Rabin cryptosystem, we propose two distinct methods using the modulus of the type N=p2q coupled with the restriction on the plaintext space M. In the first method, the plaintext space is limited to M ∈ Zpq. For the second method, we restrict the plaintext in the range of M ∈ (0,22n−2). Importantly, we prove that the decryption output of the proposed methods is unique and without decryption failure. The results in this work indicate that the decryption problem of Rabin cryptosystem is overcome

Rabin-RZ: a new efficient method to overcome Rabin cryptosystem decryption failure problem

We propose a new efficient method to overcome the 4 to 1 decryption failure for the Rabin cryptosystem by reducing the phase space of plaintext from M ε ℤ to M ε 22n-2, 22n-1 ⊂ ℤpq, where pq is a product of 2 strong primes and pq ε 22n, 22n+2. Instead of utilizing the pubic modulus N = pq, we use N = p2q. Upon decrypting by using the private modulus d = pq via the Chinese Remainder Theorem, we prove that there exist only one plaintext from the 4 roots obtained that will reside within the interval 22n, 22n+2. As a result, the decryption failure is overcome and this technique also enhances the decryption process for the Rabin cryptosystem. Furthermore, we make analytical comparison with other methods designed in previous literature to overcome the Rabin cryptosystem problem

Civitas: Implementation of a Threshold Cryptosystem

This paper describes the implementation of a threshold cryptosystem for Civitas, a secure electronic voting system. The cryptosystem improves the availability of Civitas by enabling tabulation to complete despite the failure of some agents. The implementation includes a sophisticated distributed key generation protocol, which was designed by Gennaro, Jarecki, Krawczyk, and Rabin. The cryptosystem is implemented in Jif, a security-typed language