Muhammad Asyraf Asbullah

New attacks on RSA with modulus N = p2q using continued fractions

In this paper, we propose two new attacks on RSA with modulus N = p2q using continued fractions. Our first attack is based on the RSA key equation ed – (N)k = 1 where (N) = p(p – 1)(q – 1). Assuming that and , we show that can be recovered among the convergents of the continued fraction expansion of . Our second attack is based on the equation eX – (N – (ap2 + bq2)) Y = Z where a,b are positive integers satisfying gcd(a,b) = 1, |ap2 – bq2| < N1/2 and ap2 + bq2 = N2/3+α with 0 < α < 1/3. Given the conditions , we show that one can factor N = p2q in polynomial time.

Provably secure Rabin-p cryptosystem in hybrid setting

In this work, we design an efficient and provably secure hybrid cryptosystem depicted by a combination of the Rabin-p cryptosystem with an appropriate symmetric encryption scheme. We set up a hybrid structure which is proven secure in the sense of indistinguishable against the chosen-ciphertext attack. We presume that the integer factorization problem is hard and the hash function that modeled as a random function.

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.