Malaysian Journal of Mathematical Sciences, August 2013, Vol. 7(S)
Special Issue: The 3rd International Conference on Cryptology & Computer Security 2012 (CRYPTOLOGY2012)
On the Hastad's Attack to LUC$_{4,6}$ Cryptosystem and Compared with Other RSA-Type Cryptosystem
Wong Tze Jin, Hailiza Kamarulhaili and Mohd. Rushdan Md Said
Corresponding Email: sherlock.wong.tj@gmail.com
Received date: -
Accepted date: -
Abstract:
The LUC$_{4,6}$ cryptosystem is a system analogy to RSA cryptosystem and extended from LUC and LUC$_{3}$ cryptosystems. Therefore, the security problem of the LUC$_{4,6}$ cryptosystem is based on integer factorization which is similar to RSA, LUC and LUC$_{3}$ cryptosystems. The Hastad's attack is one of the polynomial attack which relied on the polynomial structure of RSA-type cryptosystem. In this paper, Hastad's Theorem will be used to solve a system of multivariate modular equations and Coppersmith Theorem will be used to find a root of a modular equation. Thus, the number of plaintexts which are required to succeed the attack can be found.
Keywords: Hastad's Theorem, Coppersmith Theorem, Lucas Sequence, Dickson Polynomial
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