Many papers have proposed elliptic curves which are faster and easier to implement than
the NIST prime-order curves. Most of these curves have had fields of size around $2^ 256 …

In this paper, we introduce the generalized Mersenne sequence and we deal with, in detail,
two special cases, namely, Mersenne and Mersenne-Lucas sequences. We present Binet's …

We prove that n-bit integers may be multiplied in O (n log n 4 log∗ n) bit operations. This
complexity bound had been achieved previously by several authors, assuming various …

Post-quantum cryptosystems are the subject of a significant research effort, witnessed by
various international standardization competitions. Among them, the NTRU Key …

Montgomery Arithmetic from a Software Perspective* Page 1 Montgomery Arithmetic from a
Software Perspective* Joppe W. Bos1 and Peter L. Montgomery2 1NXP Semiconductors 2Self …

In this paper, we introduce the generalized p-Mersenne sequence and deal with, in detail,
two special cases, namely, p-Mersenne and p-Mersenne-Lucas-sequences. We present …

It is aimed to describe generalized Bigollo sequences and to examine Bigollo and Bigollo-
Lucas sequences in this article. For this purpose, we give Binet's formulas, Simson formulas …

In this paper we present a new multiplication algorithm for residues modulo the Mersenne
prime 2^ 521-1. Using this approach, on an Intel Haswell Core i7-4770, constant-time …

There are a variety of ways of applying the Karatsuba idea to multi-digit multiplication. These
apply particularly well in the context where digits do not use the full word-length of the …

Generating and standardizing elliptic curves to use them in a cryptographic context is a hard
task. In this note, we don't make an explicit proposal for an elliptic curve, but we deal with the …