Known-Plaintext Attack to Two Cryptosystems Based on the BB Equation

@article{lvarez2008KnownPlaintextAT,
title={Known-Plaintext Attack to Two Cryptosystems Based on the BB Equation},
author={Gonzalo {\'A}lvarez and Luis Hern{\'a}ndez Encinas and Jaime Mu{\~n}oz Masqu{\'e}},
journal={IEEE Transactions on Circuits and Systems II: Express Briefs},
year={2008},
volume={55},
pages={423-426}
}

Recently, Rama Murthy and Swamy proposed a symmetric cryptosystem based on the Brahmagupta-Bhaskara (BB) equation. The BB equation is the quadratic Diophantine equation <i>nx</i> <sup>2</sup> + <i>k</i> = <i>y</i> <sup>2</sup>, where <i>k</i> is an integer and <i>n</i> is a positive integer such that radic(<i>n)</i> is irrational. For the particular case <i>k</i>=1, the equation is called the Pell equation. The proposed cryptosystem was modified later by the same authors in order to avoid the… CONTINUE READING