The Diffie---Hellman problem and generalization of Verheul's theorem
Designs, Codes and Cryptography
The critical groups of a family of graphs and elliptic curves over finite fields
Journal of Algebraic Combinatorics: An International Journal
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
FPGA and ASIC implementations of the ηT pairing in characteristic three
Computers and Electrical Engineering
On the number of distinct elliptic curves in some families
Designs, Codes and Cryptography
Division polynomials for Jacobi quartic curves
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Fault attack to the elliptic curve digital signature algorithm with multiple bit faults
Proceedings of the 4th international conference on Security of information and networks
Efficient pairing computation on ordinary elliptic curves of embedding degree 1 and 2
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Fast tate pairing computation on twisted Jacobi intersections curves
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
An identity based encryption using elliptic curve cryptography for secure M2M communication
Proceedings of the First International Conference on Security of Internet of Things
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Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves. New to the Second Edition Chapters on isogenies and hyperelliptic curves A discussion of alternative coordinate systems, such as projective, Jacobian, and Edwards coordinates, along with related computational issues A more complete treatment of the Weil and TateLichtenbaum pairings Douds analytic method for computing torsion on elliptic curves over Q An explanation of how to perform calculations with elliptic curves in several popular computer algebra systems Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introd uces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermats Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices.