A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
A course in computational algebraic number theory
A course in computational algebraic number theory
Handbook of Applied Cryptography
Handbook of Applied Cryptography
ACISP '97 Proceedings of the Second Australasian Conference on Information Security and Privacy
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
Practical cryptography in high dimensional tori
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Public-key cryptosystems based on cubic finite field extensions
IEEE Transactions on Information Theory
Double-Exponentiation in Factor-4 Groups and Its Applications
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Factor-4 and 6 (de)compression for values of pairings using trace maps
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Message transmission for GH-public key cryptosystem
Journal of Computational and Applied Mathematics
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XTR is one of the most efficient public-key cryptosystems that allow us to compress the communication bandwidth of their ciphertext. The compact representation can be achieved by deploying a subgroup Fq2 of extension field Fq6, so that the compression ratio of XTR cryptosystem is 1/3. On the other hand, Dijk et al. proposed an efficient public-key cryptosystem using a torus over Fq30 whose compression ratio is 4/15. It is an open problem to construct an efficient public-key cryptosystem whose compression ratio is smaller than 4/15. In this paper we propose a new variant of XTR cryptosystem over finite fields with characteristic three whose compression ratio is 1/6. The key observation is that there exists a trace map from Fq6 to Fq in the case of characteristic three. Moreover, the cost of compression and decompression algorithm requires only about 1% overhead compared with the original XTR cryptosystem. Therefore, the proposed variant of XTR cryptosystem is one of the fastest public-key cryptosystems with the smallest compression ratio.