Curve based cryptography are preferred for embedded hardware since they require shorter operand size than RSA to attain the same security level. So ECC and HECC are more suitable in constrained environment such as smart cards if we can select suitable curves and efficient scalar multiplication technique to speed up arithmetic on the curve. With this in view, this paper explores in details the m...

Matrix multiplication is a fundamental mathematical operation that has numerous applications across most scientific fields. Cannon’s distributed algorithm to multiply two n-by-n matrices on a two dimensional square mesh array with n cells takes exactly 3n−2 communication steps to complete. We show that it is possible to perform matrix multiplication in just 1.5n − 1 communication steps on a two...

We explicitly identify infinitely many curves which are quotients of Fermat curves. We show that some of these have simple Jacobians with complex multiplication by a non-cyclotomic field. For a particular case we determine the local zeta functions with two independent methods. The first uses Jacobi sums and the second applies the general theory of complex multiplication, we verify that both met...

A new matrix multiplication algorithm is proposed for massively parallel supercomputers with 2D/3D, all-port torus interconnection networks. The proposed algorithm is based on the traditional row-by-column multiplication matrix product model and employs a special routing pattern for better scalability. It compares favorably to the variants of Cannon’s and DNS algorithms since it allows matrices...

Recall that in a commutative ring 〈R, 0, 1, +,×〉, • 〈R, 0,+〉 is an abelian group, • 〈R− {0}, 1,×〉 is an abelian semigroup, and • multiplication distributes over addition. The same structure is a field if, in the second clause, 〈R − {0}, 1,×〉, is a group; in other words, every nonzero element has an inverse. A vector space V over a field F is an abelian group 〈V, 0, +〉 with an operation of “scal...

Despite encryption, you can extract a fair amount of information from VoIP traffic based on variable bit rates. Previous research shows that the language and specific phrases can be identified in this manner. DiOrio’s research looks at detecting different accents based on the encoding bit rate. Preliminary results show that the average accuracy of differentiating accent pairs is 73%, with the b...

In this paper, the relationship between the thermodynamic and historical arrows of time is studied. In the context of a simple combinatorial model, their definitions are made more precise and in particular strong versions (which are not compatible with time symmetric microscopic laws) and weak versions (which can be compatible with time symmetric microscopic laws) are given. This is part of a l...

Let f(z) = ∑∞ n=1 λf (n)e 2πinz ∈ S k (Γ0(N)) be a newform of even weight k ≥ 2 on Γ0(N) without complex multiplication. Let P denote the set of all primes. We prove that the sequence {λf (p)}p∈P does not satisfy Benford’s Law in any base b ≥ 2. However, given a base b ≥ 2 and a string of digits S in base b, the set Aλf (b, S) := {p prime : the first digits of λf (p) in base b are given by S} h...

We propose a neuromorphic architecture for real-time processing of acoustic transients in analog VLSI. We show how judicious normalization of a time-frequency signal allows an elegant and robust implementation of a correlation algorithm. The algorithm uses binary multiplexing instead of analog-analog multiplication. This removes the need for analog storage and analog-multiplication. Simulations...