Handbook of Applied Cryptography
Handbook of Applied Cryptography
A Chosen-Ciphertext Attack against NTRU
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Dimension Reduction Methods for Convolution Modular Lattices
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Achieving NTRU with Montgomery Multiplication
IEEE Transactions on Computers
Sliding Window Method for NTRU
ACNS '07 Proceedings of the 5th international conference on Applied Cryptography and Network Security
An Introduction to Mathematical Cryptography
An Introduction to Mathematical Cryptography
Low-dimensional lattice basis reduction revisited
ACM Transactions on Algorithms (TALG)
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
NTRU over rings beyond $${\mathbb{Z}}$$
Designs, Codes and Cryptography
MaTRU: a new NTRU-Based cryptosystem
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Public key cryptography in sensor networks—revisited
ESAS'04 Proceedings of the First European conference on Security in Ad-hoc and Sensor Networks
Symplectic lattice reduction and NTRU
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
CT-RSA'10 Proceedings of the 2010 international conference on Topics in Cryptology
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In this paper we will prove that a lattice-based public key cryptosystem based on non-associative algebra is not only feasible but also arguably more secure than the existing lattice based cryptosystems such as NTRU, because its lattice does not fully fit within circular and convolutional modular lattice (CCML). The underlying algebraic structure of the proposed non-associative cryptosystem is the power-associative and alternative octonions algebra which can be defined over any Dedekind domain such as convolution polynomial ring. Besides the detailed specification of the proposed cryptosystem, we have proved that the security of the proposed scheme relies on the difficulty of the finding shortest vector in a certain kind of lattice. Since there is no isomorphic matrix representation for octonions, the only method for attacking the proposed cryptosystem and finding a spurious key for decryption is to form a lattice of dimension 16.N which is eight times larger than the NTRU lattice. By reducing the dimension of the underlying convolution polynomial ring (N) and using optimization techniques, we can increase the encryption and decryption speed, to a level equal to NTRU. Mathematics Subject Classification (2000): 94A60, 11T71 Copyright © 2011 John Wiley & Sons, Ltd. (The simulation codes (in Maple and Java) are available from the authors upon request.)