# MULTI-COLLISIONS ATTACK IN RING HASH STRUCTURE

### Nasour Bagheri, Babak Sadeghiyan, Majid Naderi

#### Abstract

Ring hash structure is a new hash structure which has been introduced by Joux to strengthen the current hash structures against multi-collision attacks. In this paper, we present a cryptanalysis on Ring hash structure. We show that finding multi-collisions, i.e. 2k-way collision, for a Ring hash structure is not much harder than finding such multi-collisions for ordinary MD hash structure. The complexity of our attack is approximately log (n) times harder than the complexity of attacks against MD structures. We employ these multi-collisions to find a D-way pre-image for this structure. We show the complexity of finding 2K-way multi-collision and 2k-way preimage are O((k+1)x(n / 2)x2n/2 ) and O(kx n / 2x2n/2+2x2n ) respectively. We also show that Ring structure should not be used to create a hash function of 2n-bit length, by concatenatingmthis structure to any other hash structure of n-bit output length. We show that the time complexity of finding a collision for this concatenated structure is O((k+1)x(n / 2)x 2n /2 )that is much smaller than Ω(2n ), which is expected for a generic-birthday attack.

#### References

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#### Paper Citation

#### in Harvard Style

Bagheri N., Sadeghiyan B. and Naderi M. (2008). **MULTI-COLLISIONS ATTACK IN RING HASH STRUCTURE** . In *Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2008)* ISBN 978-989-8111-59-3, pages 278-284. DOI: 10.5220/0001917102780284

#### in Bibtex Style

@conference{secrypt08,

author={Nasour Bagheri and Babak Sadeghiyan and Majid Naderi},

title={MULTI-COLLISIONS ATTACK IN RING HASH STRUCTURE},

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

year={2008},

pages={278-284},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001917102780284},

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 - MULTI-COLLISIONS ATTACK IN RING HASH STRUCTURE

SN - 978-989-8111-59-3

AU - Bagheri N.

AU - Sadeghiyan B.

AU - Naderi M.

PY - 2008

SP - 278

EP - 284

DO - 10.5220/0001917102780284