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Algebraic Analysis of a Rabin-Like Cryptosystem and Its Countermeasures

Affiliations

  • Al-Kindi Cryptography Research Laboratory, Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, Malaysia
  • Mathematics Department, Faculty of Science, Universiti Putra Malaysia, Malaysia

Abstract


Objective: In this paper, we present two algebraic analyses upon a new Rabin-like public key cryptosystem namely the Rabin-p cryptosystem. Methods/Analysis: We show that by using the continued fraction’s method and the Coppersmith’s theorems, there exists inappropriate parameter’s size that can affect the security of Rabin-p cryptosystem. Findings: The first analysis proved that the prime factors of its public key can be found amongst the list of the continued fraction expansion of the ciphertext c and the modulus in polynomial time. For the second analysis, by using the Coppersmith’s theorems we showed that the message m can be retrieved in polynomial time provided some condition on the message length. We also propose a countermeasure to avoid both analyses. Novelty/Improvement: The purpose of this work is to offer suggestions for a countermeasure for the aforementioned analysis upon implementing the Rabin-p cryptosystem. Hence, all the parameters should be chosen carefully.

Keywords

Algebraic Analysis, Continued Fraction, Coppersmith’s Theorems, Rabin-p Cryptosystem.

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