Cryptology ePrint Archive: Report 2017/522

On the Hardness of the Mersenne Low Hamming Ratio Assumption

Marc Beunardeau and Aisling Connolly and Rémi Géraud and David Naccache

Abstract: In a recent paper, Aggarwal, Joux, Prakash, and Santha (AJPS) describe an ingenious public-key cryptosystem mimicking NTRU over the integers. This algorithm relies on the properties of Mersenne primes instead of polynomial rings. The security of the AJPS cryptosystem relies on the conjectured hardness of the Mersenne Low Hamming Ratio Assumption, defined in [AJPS].

This work shows that AJPS' security estimates are too optimistic and describes an algorithm allowing to recover the secret key from the public key much faster than foreseen in [AJPS].

In particular, our algorithm is \emph{experimentally practical} (within the reach of the computational capabilities of a large organization), at least for the parameter choice $\{n=1279,h=17\}$ conjectured in [AJPS] as corresponding to a $2^{120}$ security level. The algorithm is fully parallelizable.

Category / Keywords: public-key cryptography /

Date: received 3 Jun 2017, last revised 20 Jun 2017

Contact author: remi geraud at ens fr

Available format(s): PDF | BibTeX Citation

Note: Minor update on the probability estimate.

Version: 20170620:100229 (All versions of this report)

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