Cryptology ePrint Archive: Report 2009/330

NTRU, quaternion algebra, public key cryptography

Ehsan Malekian and Ali Zakerolhosseini and Atefeh

Abstract: We propose QTRU, a probabilistic and multi-dimensional public key cryptosystem based on the NTRU public key cryptosystem using quaternion algebra. QTRU encrypts four data vectors in each encryption session and the only other major difference between NTRU and QTRU is that the underlying algebraic structure has been changed to a non-commutative algebraic structure. As a result, QTRU inherits the strength of NTRU and its positive points. In addition, the non-commutativity of the underlying structure of QTRU makes it much more resistant to some lattice-based attacks. After a brief description of NRTU, we begin by describing the algebraic structure used in QTRU. Further, we present the details of the key generation, encryption and decryption algorithms of QTRU and discuss the issues regarding key security, message security, and probability of successful decryption. Last but not least, QTRUís resistance against lattice-based attacks is investigated.

Category / Keywords: NTRU, quaternion algebra, public key cryptography

Date: received 4 Jul 2009, last revised 8 Jul 2009, withdrawn 3 Aug 2009

Contact author: a-zaker at sbu ac ir

Available format(s): (-- withdrawn --)

Note: Some text formats have been changed

Version: 20090804:025320 (All versions of this report)

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