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.Expand

This paper shows that a $390 mass-market quad-core 2.4GHz Intel Westmere (Xeon E5620) CPU can create 109000 signatures per second and verify 71000 signatures per second on an elliptic curve at a 2128… Expand

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… Expand

Abstract
We identify and fill some gaps with regard to consistency (the extent to which false positives are produced) for public-key encryption with keyword search (PEKS). We define computational and… Expand

The Diffie–Hellman scheme resulting from the group action allows for public-key validation at very little cost, runs reasonably fast in practice, and has public keys of only 64 bytes at a conjectured AES-128 security level, matching NIST’s post-quantum security category I.Expand

A high-security post-quantum stateless hash-based signature scheme that signs hundreds of messages per second on a modern 4-core 3.5GHz Intel CPU, allowing it to be a drop-in replacement for current signature schemes.Expand

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.Expand

New parameters for the McEliece and Niederreiter cryptosystems achieving standard levels of security against all known attacks are proposed, and the resulting public-key sizes are considerably smaller than previous parameter choices for the same level of security.Expand

This work identifies and fills some gaps with regard to consistency (the extent to which false positives are produced) for public-key encryption with keyword search (PEKS) and provides a transform of an anonymous IBE scheme to a secure PEKS scheme that guarantees consistency.Expand

This paper presents the first complete addition formulas for binary elliptic curves, i.e., addition formulas that work for all pairs of input points, with no exceptional cases, in the literature.Expand