Book ChapterDOI
Twisted Edwards curves
Daniel J. Bernstein,Peter Birkner,Marc Joye,Tanja Lange,Christiane Peters +4 more
- pp 389-405
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This paper introduces "twisted Edwards curves," a generalization of the recently introduced Edwards curves, and shows that twisted Edwards curves include more curves over finite fields, and in particular every elliptic curve in Montgomery form.Abstract:
This paper introduces "twisted Edwards curves," a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over finite fields, and in particular every elliptic curve in Montgomery form; shows how to cover even more curves via isogenies; presents fast explicit formulas for twisted Edwards curves in projective and inverted coordinates; and shows that twisted Edwards curves save time for many curves that were already expressible as Edwards curves.read more
Citations
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Book ChapterDOI
Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies
David Jao,Luca De Feo +1 more
TL;DR: In this article, the authors proposed a quantum-resistant public-key cryptosystem based on the conjectured difficulty of finding isogenies between supersingular elliptic curves, which allows the two parties to arrive at a common shared key despite the noncommutativity of the endomorphism ring.
Journal ArticleDOI
High-speed high-security signatures
TL;DR: In this paper, the authors show that a $390 mass-market quad-core 2.4GHz Intel Westmere (Xeon E5620) CPU can create 109000 signatures per second and verify 71000 signature per second on an elliptic curve at a 2128 security level.
Book ChapterDOI
Faster addition and doubling on elliptic curves
Daniel J. Bernstein,Tanja Lange +1 more
TL;DR: An extensive comparison of different forms of elliptic curves and different coordinate systems for the basic group operations (doubling, mixed addition, non-mixed addition, and unified addition) as well as higher-level operations such as multi-scalar multiplication.
Journal ArticleDOI
Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies
TL;DR: A new zero-knowledge identification scheme and detailed security proofs for the protocols, and a new, asymptotically faster, algorithm for key generation, a thorough study of its optimization, and new experimental data are presented.
Book ChapterDOI
Twisted Edwards Curves Revisited
TL;DR: In this article, the authors introduced fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography forward in a wide range of applications.
References
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Book
The Arithmetic of Elliptic Curves
TL;DR: It is shown here how Elliptic Curves over Finite Fields, Local Fields, and Global Fields affect the geometry of the elliptic curves.
Book
Elliptic Curves in Cryptography
TL;DR: In the past few years elliptic curve cryptography has moved from a fringe activity to a major challenger to the dominant RSA/DSA systems as mentioned in this paper, and it has become all pervasive.
Journal ArticleDOI
Speeding the Pollard and elliptic curve methods of factorization
TL;DR: In this paper, a parametrization of elliptic curves is proposed to speed up the p 1 and Monte Carlo methods. But the parametrized elliptic curve method requires n/2 + o(n) multiplications.
BookDOI
Handbook of elliptic and hyperelliptic curve cryptography
Henri Cohen,Gerhard Frey,Roberto Avanzi,Christophe Doche,Tanja Lange,Kim Nguyen,Frederik Vercauteren +6 more
TL;DR: The introduction to Public-Key Cryptography explains the development of algorithms for computing Discrete Logarithms and their applications in Pairing-Based Cryptography and its applications in Fast Arithmetic Hardware Smart Cards.
Book ChapterDOI
Curve25519: new diffie-hellman speed records
TL;DR: This paper explains the design and implementation of a high-security elliptic-curve-Diffie-Hellman function achieving record-setting speeds: e.g., 832457 Pentium III cycles more than twice as fast as other authors' results at the same conjectured security level.