Large integer modular multiplication and exponentiation are arithmetic primitives required by the public-key cryptosystems. In this paper, an efficient technique to determine the quotient for modular multiplication which is independent of the length of modulus and a 4bits-serial systolic array implementation for high speed modular multiplication are proposed. RSA cryptosystem is used as an example of the application, and the architecture is very suitable for high speed VLSI implementation. Moreover the proposed low-cost implementation (using single processing element (PE)) is feasible in restricted computing environments.

In this paper, the structure of a 16-by-16 unsigned hybrid (serial-parallel) multiplier has been proposed. Parallel multipliers, in comparison with serial multipliers, have higher speed and higher power consumption. In hybrid structures, to reduce power and increase speed, both serial and parallel techniques are used. The proposed structure improves propagation delay and reduces power consumption using pipeline and retime techniques. Simulation results show that it has 5. 7 ns propagation delay and 2. 65 mW power consumption. The figure of merit for energy consumption is 15. 2 PJ. The proposed multiplier has been designed using 0. 18 μ m TSMC process at 1. 8 V supply and simulated using Cadence tools. The layout of the multiplier occupies 52414 μ m 2.

In this paper, we introduce the notion of multiplier in BL-algebra and study relationships between multipliers and some special mappings, likeness closure operators, homomorphisms and (ʘ, Ú)-derivations in BL-algebras. We introduce the concept of idempotent multipliers in BL-algebra and weak congruence and obtain an interconnection between idempotent multipliers and weak congruences. Also, we introduce the special multiplier ap and study some properties. Finally, we show that if A is a boolean algebra, then the set of all multipliers of A is a BL-algebra under some conditions.

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In this note we obtain a reverse version of the Haagerup Theorem. In particular, if $ A \in \mathbb{M}_{n}$ has a $ 2\times2- $ principal submatrix as $ \left[ \begin{array}{cc}1& \alpha \\\beta & 1\\\end{array}\right]$ with $ \beta \neq \bar{\alpha}, $ then $ \Vert S_{A} \Vert > 1$ where the operator $ S_{A}:\mathbb{M}_{n}\longrightarrow \mathbb{M}_{n} $ is defined by $S_{A}(B) := A \circ B $ where $ "\circ " $ stands for Schur product.