Paper 2017/522
On the Hardness of the Mersenne Low Hamming Ratio Assumption
Marc Beunardeau, Aisling Connolly, 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.
Note: Minor update on the probability estimate.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Contact author(s)
- remi geraud @ ens fr
- History
- 2017-06-20: last of 3 revisions
- 2017-06-05: received
- See all versions
- Short URL
- https://ia.cr/2017/522
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2017/522,
author = {Marc Beunardeau and Aisling Connolly and Rémi Géraud and David Naccache},
title = {On the Hardness of the Mersenne Low Hamming Ratio Assumption},
howpublished = {Cryptology {ePrint} Archive, Paper 2017/522},
year = {2017},
url = {https://eprint.iacr.org/2017/522}
}
