On the Hardness of the Mersenne Low Hamming Ratio Assumption

Attacks on the AJPS Mersenne-Based Cryptosystem

“…Our analysis requires several minor heuristics, which we have confirmed experimentally. Secondly, we formally analyze the attack of Beunardeau et al [6]. Our analysis suggest that the attack is slightly less efficient, asymptotically, than suggested in [6].…”

“…Secondly, we formally analyze the attack of Beunardeau et al [6]. Our analysis suggest that the attack is slightly less efficient, asymptotically, than suggested in [6]. However, this small difference in complexity makes little difference in practice.…”

“…Although Beunardeau et al [6] provide experimental evidence for the efficiency of their attack, they leave open the task of providing a theoretical analysis to support the correctness of their approach. This leaves some uncertainty for a concrete security estimate of the cryptosystem of Aggarwal et al We attempt to fill this gap with a more in-depth analysis of their attack.…”

“…Second, they argue that their variation makes an adaptation of known lattice attacks against NTRU ineffective. The latter claim was rapidly challenged, when a faster experimental attack using LLL reduction was found by Beunardeau et al [6]. This attack exploits the low weight of f and g, and is able to find f, g using partition-search in the integer interval {0, .…”

“…The authors argue that their attack reduces the bit security to about λ ≈ 2w. Beunardeau et al [6] warn that their attack is only practically feasible, and might not work with, for example, increasing parameters. They further expect that slightly changing the cryptosystem protects against this attack [6,Sect.…”