# A MULTIPLE BIRTHDAY ATTACK ON NTRU

### Raphael Overbeck

#### Abstract

In this paper we view the possibilities to lance a multiple (iterative) birthday attack on NTRU. Recently Wagner’s algorithm for the generalized birthday problem (Wagner, 2002) allowed to speed-up several combinatorial attacks. However, in the case of NTRU we can not hope to to apply Wagner’s algorithm directly, as the search space does not behave nicely. In this paper we show that we can nevertheless draw profit from a multiple birthday approach. Our approach allows us to attack ees251ep6 parameter set on a computer with only 252 Bits of memory and about 29 times faster as with Odlyzko’s combinatorial attack – this is an improvement factor about 243 in space complexity. We thus contradict the common believe, that in comparison to computational requirements, the “storage requirement is by far the larger obstacle” (Howgrave-Graham, 2007) to attack NTRU by combinatorial attacks. Further, our attack is about 27 times faster than the space-reduced variant from (Howgrave-Graham, 2007) employing the same amount of memory.

#### References

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#### Paper Citation

#### in Harvard Style

Overbeck R. (2008). **A MULTIPLE BIRTHDAY ATTACK ON NTRU** . In *Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2008)* ISBN 978-989-8111-59-3, pages 237-244. DOI: 10.5220/0001916602370244

#### in Bibtex Style

@conference{secrypt08,

author={Raphael Overbeck},

title={A MULTIPLE BIRTHDAY ATTACK ON NTRU},

booktitle={Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2008)},

year={2008},

pages={237-244},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001916602370244},

isbn={978-989-8111-59-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2008)

TI - A MULTIPLE BIRTHDAY ATTACK ON NTRU

SN - 978-989-8111-59-3

AU - Overbeck R.

PY - 2008

SP - 237

EP - 244

DO - 10.5220/0001916602370244