Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstra's
ECM factorization algorithm. Since then, his curves and the algorithms associated with them …

The rapid developments in the Internet of Medical Things (IoMT) help the smart healthcare
systems to deliver more sophisticated real-time services. At the same time, IoMT also raises …

An argument system for NP is a proof system that allows efficient verification of NP
statements, given proofs produced by an untrusted yet computationally-bounded prover …

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

The theory of elliptic curves is distinguished by its long history and by the diversity of the
methods that have been used in its study. This book treats the arithmetic theory of elliptic …

The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

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 …

VI Preface methods from information theory. Unconditionally secure schemes are now
addressed in an extra chapter, Chapter 10.• Unconditional security is not achievable without …

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 …

The Montgomery ladder is a remarkably simple method of computing scalar multiples of
points on a broad class of elliptic curves. This article surveys a wide range of topics related …