ABSTRACT This paper describes a parallelized radix-4 scalable Montgomery multiplier implementation. The design does not require hardware multipliers, and uses parallelized multiplication to shorten the critical path. By left-shifting the sources rather than right-shifting the result, the latency between processing elements is shortened from two cycles to nearly one. The new design can perform 1...

Distributed Arithmetic, along with Modulo Arithmetic, are computation algorithms that perform multiplication with look-up table based schemes. Both stirred some interest over two decades ago but have languished ever since. Indeed, DA specifically targets the sum of products (sometimes referred to as the vector dot product) computation that covers many of the important DSP filtering and frequenc...

We introduce a relaxation of the notion of tensor rank, called s-rank, and show that upper bounds on the s-rank of the matrix multiplication tensor imply upper bounds on the ordinary rank. In particular, if the “s-rank exponent of matrix multiplication” equals 2, then ω = 2. This connection between the s-rank exponent and the ordinary exponent enables us to significantly generalize the group-th...

Binary field multiplication is the most fundamental building block of binary field Elliptic Curve Cryptography (ECC) and Galois/Counter Mode (GCM). Both bit-wise scanning and Look-Up Table (LUT) based methods are commonly used for binary field multiplication. In terms of Side Channel Attack (SCA), bit-wise scanning exploits insecure branch operations which leaks information in a form of timing ...

This paper introduces “hyper-and-elliptic-curve cryptography”, in which a single high-security group supports fast genus-2-hyperelliptic-curve formulas for variable-base-point single-scalar multiplication (e.g., Diffie–Hellman shared-secret computation) and at the same time supports fast elliptic-curve formulas for fixed-base-point scalar multiplication (e.g., key generation) and multi-scalar m...

In the late 1990s, R. Coleman and Greenberg (independently) asked for a global property characterizing those $p$-ordinary cuspidal eigenforms whose associated Galois representation becomes decomposable upon restriction to decomposition group at $p$. It is expected that such are precisely with complex multiplication. this paper, we study Coleman–Greenberg’s question using deformation theory. par...

The recent discovery that the exponent of matrix multiplication is determined by the rank of the symmetrized matrix multiplication tensor has invigorated interest in better understanding symmetrized matrix multiplication. I present an explicit rank 18 Waring decomposition of $sM_{\langle 3\rangle}$ and describe its symmetry group.

Problem statement: In this study we propose a group re-keying protocol based on modular polynomial arithmetic over Galois Field GF(2). Common secure group communications requires encryption/decryption for group re-keying process, especially when a group member is leaving the group. Approach: This study proposes secret keys multiplication protocol based on modular polynomial arithmetic (SKMP), w...

The objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a Fibonacci Hypercube structure. Most of the popular algorithms for parallel matrix multiplication can not run on Fibonacci Hypercube structure, therefore giving a method that can be run on all structures especially Fibonacci Hypercube structure is necessary for parallel matr...