We study the complexity of multiplication in noncommutative group algebras which is closely related to the complexity of matrix multiplication. We characterize such semisimple group algebras of the minimal bilinear complexity and show nontrivial lower bounds for the rest of the group algebras. These lower bounds are built on the top of Bläser’s results for semisimple algebras and algebras with ...

In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach ...

We show how to obtain all nonassociative Moufang loops of order less than 64 and 4262 nonassociative Moufang loops of order 64 in a unified way. We conjecture that there are no other nonassociative Moufang loops of order 64. The main idea of the computer search is to modify precisely one quarter of the multiplication table in a certain way, previously applied to small

We present a new 2-ary elliptic curve point multiplication method with resistance against side-channel attacks. This method provides two advantages compared with previous similar side-channel attack countermeasures: It avoids a fixed table, thus reducing potential information leakage available to adversaries; and it is easily parallelizable on two-processor systems, where it provides much impro...

Table-based scalar multiplication provides practical security for ECDSA signature generation. However, a novel key recovery attack against this form of generation that exploits the collisions between entries was recently proposed at CHES 2021. This is possible even if table are unknown, such as with random permutated entry ordering. In paper, we enhance efficiency secure based on fixed-base com...

We present a new combinatorial algorithm for Boolean matrix multiplication that runs in O(n(log log n)/ log n) time. This improves the previous combinatorial algorithm by Bansal and Williams [FOCS’09] that runs in O(n(log log n)/ log n) time. Whereas Bansal and Williams’ algorithm uses regularity lemmas for graphs, the new algorithm is simple and uses entirely elementary techniques: table looku...

Many large arithmetic computations rely on tables of all primes less than n. For example, the fastest algorithms for computing n! takes time O(M(n logn) + P(n)), where M(n) is the time to multiply two n-bit numbers, and P(n) is the time to compute a prime table up to n. The fastest algorithm to compute ( n n/2 ) also uses a prime table. We show that it takes time O(M(n) + P(n)). In various mode...

A vector space is a group of objects that closed under finite addition and scalar multiplication. This paper discusses multiplication binomial coefficients defined in combinatorial geometric series. The series with derived from the multiple summations idea can enable scientific researchers to solve real world problems.

This paper proposes a fast elliptic curve multiplication algorithm applicable for any types of curves over finite fields Fp (p a prime), based on [Mon87], together with criteria which make our algorithm resistant against the side channel attacks (SCA). The algorithm improves both on an addition chain and an addition formula in the scalar multiplication. Our addition chain requires no table look...