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Volume 58 >>> № 2 MARCH — APRIL 2021

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UDC 519.2

A.N. Alekseychuk¹, A.A. Matiyko²

¹ National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine

alex-dtn@ukr

² National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine

alexm1710@ukr.net.

DISTINGUISHING ATTACK ON THE NTRUCIPHER ENCRYPTION SCHEME

Abstract. A distinguishing attack on the NTRUCipher symmetric encryption scheme, defined over the residue ring modulo a cyclotomic polynomial over a finite field of simple order, is proposed. The attack is based on the existence of a homomorphism from this ring into the specified field and can be quite effective under sufficiently general conditions.

Keywords: lattice-based cryptography, symmetric encryption scheme, distinguishing attack, cyclotomic polynomial, NTRUCipher.

FULL TEXT

REFERENCES

Valluri M.R. NTRUCipher-lattice based secret key encryption. arXiv:1710.01928V2.6/10/2017.

Hoffstein J., Pipher J., Silverman J.H. NTRU: a new high speed public key cryptosystem. Algorithmic Number Theory (ANTS III). LNCS. 1998, Vol. 1423. P. 267–288.

Matiyko A.A. Comparative analysis of NTRUEncrypt and NTRUCipher encryption algorithms. Matematychne ta komp’yuterne modelyuvannya. Ser.: Technical Sciences. 2019, Iss. 19. P. 81–87.

Matiyko A.A. BKW attack on NTRUCIPHER and NTRUCIPHER + encryption systems. Information Technology and Security. 2020. Vol. 8, N 2. P. 164–176.

Albrecht M.R., Curtis B.R., Deo A., Davidson A., Player R., Postlethwaite E.W., Virdia F., Wunderer T. Estimate all the {LWE, NTRU} schemes!. Cryptology ePrint Archive, Report 2018/331. URL: http://eprint.iacr.org/2018/331.

Diop S., SanБ B.O., Seck M., Diarra N. NTRU-LPR IND-CPA: a new ideal lattice-based scheme. Cryptology ePrint Archive, Report 2018/109. URL: http://eprint.iacr.org/2018/109.

Lidl R., Niederreiter G. Finite fields: In 2 vols. [Russian translation] Moscow: Mir, 1988. 818 p.

Lybashevsky V., Peikert C., Regev O. On ideal lattices and learning with errors over rings. Advanced in Cryptology – EUROCRYPT 2010. LNCS 6110. Springer-Verlag, 2010. P. 1–23.

Katz J., Lindell Y. Introduction to modern cryptography. CRC Press, 2015. 598 p.

Hoeffding W. Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 1963. Vol. 58, N 301. P. 13–30.

Cheremushkin A.V. Lectures on arithmetic algorithms in cryptography [in Russian]. Moscow: MCNMO, 2002. 104 p.