Known-Plaintext Attack to Two Cryptosystems Based on the BB Equation
Gonzalo Álvarez, Luis Hernández Encinas, J. Muñoz Masqué · IEEE Transactions on Circuits & Systems II Express Briefs · 2008
Recently, Rama Murthy and Swamy proposed a symmetric cryptosystem based on the Brahmagupta-Bhaskara (BB) equation. The BB equation is the quadratic Diophantine equationnx2+k=y2, wherekis an integer andnis a positive integer such that radic(n)is irrational. For the particular casek=1, the equation is called the Pell equation. The proposed cryptosystem was modified later by the same authors in order to avoid the cryptanalysis given by Youssef. Below, a known-plaintext attack to both cryptosystems is presented.