# THE POLYNOMIAL MULTICOMPOSITION PROBLEM IN (Z/nZ)

### Neculai Daniel Stoleru, Victor Valeriu Patriciu

#### 2007

#### Abstract

Generally, the public-key cryptographic schemes base their security on the difficulty of solving hard mathematical problems. The number of such problems currently known is relative reduced. Therefore the further investigation of mathematical problems with applications in cryptography is of central interest. This paper explores a new problem based on polynomial composition. We analyze the connections between the proposed problem and the RSA problem. Adjacent, we derive from it a zero – knowledge identification protocol. We show that the method allows the definition of a commutative class of polynomials. Based on this class, a “Diffie – Hellman like” key exchange protocol can be devised..

#### References

- M. Bellare and P. Rogaway, 1993, Random Oracles are Practical: A Paradigm for Designing Efficient Protocols. In Proceedings of the 1st ACM-CCS, pages 62-73. ACM Press, New York.
- W. Diffie and M. Hellman, 1976, New Directions in Cryptography, IEEE Trans. Info. Theory 22(6), pages 644-654.
- Marc Joye, David Naccache, and Stéphanie Porte, 2004, The Polynomial Composition Problem in (Z/nZ)[X], Article retrieved April 3, 2007 from http://citeseer.ist.psu.edu/joye04polynomial.html.
- Alfred J. Menezes, Paul C. van Oorschot, and Scott A. Vanderstone, 1997, Handbook of Applied Cryptography, CRC Press.
- RSA report “Recent Results on OAEP Security, study retrieved May 27, 2007 from ”http://www.rsa.com/rsalabs/node.asp?id=2147.

#### Paper Citation

#### in Harvard Style

Daniel Stoleru N. and Valeriu Patriciu V. (2007). **THE POLYNOMIAL MULTICOMPOSITION PROBLEM IN (Z/nZ)** . In *Proceedings of the Second International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2007)* ISBN 978-989-8111-12-8, pages 269-272. DOI: 10.5220/0002123402690272

#### in Bibtex Style

@conference{secrypt07,

author={Neculai Daniel Stoleru and Victor Valeriu Patriciu},

title={THE POLYNOMIAL MULTICOMPOSITION PROBLEM IN (Z/nZ)},

booktitle={Proceedings of the Second International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2007)},

year={2007},

pages={269-272},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002123402690272},

isbn={978-989-8111-12-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Second International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2007)

TI - THE POLYNOMIAL MULTICOMPOSITION PROBLEM IN (Z/nZ)

SN - 978-989-8111-12-8

AU - Daniel Stoleru N.

AU - Valeriu Patriciu V.

PY - 2007

SP - 269

EP - 272

DO - 10.5220/0002123402690272