Elliptic curves in cryptography
Elliptic curves in cryptography
Improving the parallelized Pollard lambda search on anomalous binary curves
Mathematics of Computation
Faster Attacks on Elliptic Curve Cryptosystems
SAC '98 Proceedings of the Selected Areas in Cryptography
Algorithms for Multi-exponentiation
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Integer Decomposition for Fast Scalar Multiplication on Elliptic Curves
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
An Alternate Decomposition of an Integer for Faster Point Multiplication on Certain Elliptic Curves
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Faster Multi-exponentiation through Caching: Accelerating (EC)DSA Signature Verification
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
Skew-Frobenius Maps on Hyperelliptic Curves
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Journal of Symbolic Computation
Improved techniques for fast exponentiation
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
Affine precomputation with sole inversion in elliptic curve cryptography
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Faster addition and doubling on elliptic curves
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Fractional windows revisited: improved signed-digit representations for efficient exponentiation
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Curve25519: new diffie-hellman speed records
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Accelerated verification of ECDSA signatures
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
On Modular Decomposition of Integers
AFRICACRYPT '09 Proceedings of the 2nd International Conference on Cryptology in Africa: Progress in Cryptology
Jacobi Quartic Curves Revisited
ACISP '09 Proceedings of the 14th Australasian Conference on Information Security and Privacy
On the Security of Pairing-Friendly Abelian Varieties over Non-prime Fields
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
Fast Hashing to G2 on Pairing-Friendly Curves
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
An Improvement to the Gaudry-Schost Algorithm for Multidimensional Discrete Logarithm Problems
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Efficient 3-dimensional GLV method for faster point multiplication on some GLS elliptic curves
Information Processing Letters
Efficient techniques for high-speed elliptic curve cryptography
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Constructing tower extensions of finite fields for implementation of pairing-based cryptography
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
A family of implementation-friendly BN elliptic curves
Journal of Systems and Software
High-speed high-security signatures
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Using equivalence classes to accelerate solving the discrete logarithm problem in a short interval
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Implementing the 4-dimensional GLV method on GLS elliptic curves with j-invariant 0
Designs, Codes and Cryptography
Fast elliptic curve cryptography in OpenSSL
FC'11 Proceedings of the 2011 international conference on Financial Cryptography and Data Security
Efficient java implementation of elliptic curve cryptography for J2ME-Enabled mobile devices
WISTP'12 Proceedings of the 6th IFIP WG 11.2 international conference on Information Security Theory and Practice: security, privacy and trust in computing systems and ambient intelligent ecosystems
Faster implementation of scalar multiplication on koblitz curves
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
Four-Dimensional gallant-lambert-vanstone scalar multiplication
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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Efficiently computable homomorphisms allow elliptic curve point multiplication to be accelerated using the Gallant-Lambert- Vanstone (GLV) method. We extend results of Iijima, Matsuo, Chao and Tsujii which give such homomorphisms for a large class of elliptic curves by working over ${\mathbb F}_{p^2}$ and demonstrate that these results can be applied to the GLV method. In general we expect our method to require about 0.75 the time of previous best methods (except for subfield curves, for which Frobenius expansions can be used). We give detailed implementation results which show that the method runs in between 0.70 and 0.84 the time of the previous best methods for elliptic curve point multiplication on general curves.