A course in computational algebraic number theory
A course in computational algebraic number theory
Algorithmic number theory
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Software Implementation of the NIST Elliptic Curves Over Prime Fields
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Unbelievable Security. Matching AES Security Using Public Key Systems
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application 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
Optimal Extension Fields for XTR
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
Hidden Number Problem with the Trace and Bit Security of XTR and LUC
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Unbelievable Security. Matching AES Security Using Public Key Systems
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On Montgomery-Like Representationsfor Elliptic Curves over GF(2k)
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Efficient Subgroup Exponentiation in Quadratic and Sixth Degree Extensions
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
On the Computational Efficiency of XTR+
Information Security and Cryptology
On Cryptographic Schemes Based on Discrete Logarithms and Factoring
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Double-Exponentiation in Factor-4 Groups and Its Applications
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
On XTR and side-channel analysis
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Fast irreducibility testing for XTR using a gaussian normal basis of low complexity
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Improved zero value attack on XTR
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Collision attack on XTR and a countermeasure with a fixed pattern
EUC'05 Proceedings of the 2005 international conference on Embedded and Ubiquitous Computing
High security pairing-based cryptography revisited
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Further security analysis of XTR
ISPEC'06 Proceedings of the Second international conference on Information Security Practice and Experience
Practical cryptography in high dimensional tori
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Faster squaring in the cyclotomic subgroup of sixth degree extensions
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Curve25519: new diffie-hellman speed records
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Message transmission for GH-public key cryptosystem
Journal of Computational and Applied Mathematics
An overview of trace based public key cryptography over finite fields
Journal of Computational and Applied Mathematics
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This paper describes several speedups and simplifications for XTR. The most important results are new XTR double and single exponentiation methods where the latter requires a cheap precomputation. Both methods are on average more than 60% faster than the old methods, thus more than doubling the speed of the already fast XTR signature applications. An additional advantage of the new double exponentiation method is that it no longer requires matrices, thereby making XTR easier to implement. Another XTR single exponentiation method is presented that does not require precomputation and that is on average more than 35% faster than the old method. Existing applications of similar methods to LUC and elliptic curve cryptosystems are reviewed.