相关论文: Efficient FPGA-based multipliers for F_{3^97} and …
Elliptic Curve Cryptography (ECC) is widely accepted for ensuring secure data exchange between resource-limited IoT devices. The National Institute of Standards and Technology (NIST) recommended implementation, such as B-163, is…
Efficient computation of the Tate pairing is an important part of pairing-based cryptography. Recently with the introduction of the Duursma-Lee method special attention has been given to the fields of characteristic 3. Especially…
Finite field multiplier is mainly used in error-correcting codes and signal processing. Finite field multiplier is regarded as the bottleneck arithmetic unit for such applications and it is the most complicated operation over finite field…
Securing communication channels is especially needed in wireless environments. But applying cipher mechanisms in software is limited by the calculation and energy resources of the mobile devices. If hardware is applied to realize…
While the Karatsuba algorithm reduces the complexity of large integer multiplication, the extra additions required minimize its benefits for smaller integers of more commonly-used bitwidths. In this work, we propose the extension of the…
We introduce a new class of irreducible pentanomials over $\mathbb{F}_2$ of the form $f(x) = x^{2b+c} + x^{b+c} + x^b + x^c + 1$. Let $m=2b+c$ and use $f$ to define the finite field extension of degree $m$. We give the exact number of…
Floating point multiplication is a crucial operation in high power computing applications such as image processing, signal processing etc. And also multiplication is the most time and power consuming operation. This paper proposes an…
We set new speed records for multiplying long polynomials over finite fields of characteristic two. Our multiplication algorithm is based on an additive FFT (Fast Fourier Transform) by Lin, Chung, and Huang in 2014 comparing to previously…
We improve the space complexity of Karatsuba multiplication on a quantum computer from $O(n^{1.427})$ to $O(n)$ while maintaining $O(n^{\lg 3})$ gate complexity. We achieve this by ensuring recursive calls can add their outputs directly…
Integer arithmetic is the underpinning of many quantum algorithms, with applications ranging from Shor's algorithm over HHL for matrix inversion to Hamiltonian simulation algorithms. A basic objective is to keep the required resources to…
In this paper, two approximate 3*3 multipliers are proposed and the synthesis results of the ASAP-7nm process library justify that they can reduce the area by 31.38% and 36.17%, and the power consumption by 36.73% and 35.66% compared with…
Multipliers are widely-used arithmetic operators in digital signal processing and machine learning circuits. Due to their relatively high complexity, they can have high latency and be a significant source of power consumption. One strategy…
The rapid updates in error-resilient applications along with their quest for high throughput have motivated designing fast approximate functional units for Field-Programmable Gate Arrays (FPGAs). Studies that proposed imprecise functional…
A representation of finite fields that has proved useful when implementing finite field arithmetic in hardware is based on an isomorphism between subrings and fields. In this paper, we present an unified formulation for multiplication in…
Various post-quantum cryptography algorithms have been recently proposed. Supersingluar isogeny Diffie-Hellman key exchange (SIKE) is one of the most promising candidates due to its small key size. However, the SIKE scheme requires numerous…
In todays world, high-power computing applications such as image processing, digital signal processing, graphics, and robotics require enormous computing power. These applications use matrix operations, especially matrix multiplication.…
The finite field multiplier is mainly used in many of today's state of the art digital systems and its hardware implementation for bit parallel operation may require millions of logic gates. Natural causes or soft errors in digital design…
We propose a Recursive Polynomial Generic Construction (RPGC) of multiplication algorithms in any finite field $\mathbb{F}_{q^n}$ based on the method of D.V. and G.V. Chudnovsky specialized on the projective line. They are usual polynomial…
In this paper, we present an energy-efficient, yet high-speed approximate maximally redundant signed digit (MRSD) multiplier (called AMR-MUL) based on a parallel structure. For the reduction stage, we suggest several approximate Full-Adder…
In this paper, we propose an architecture/methodology for making FPGAs suitable for integer as well as variable precision floating point multiplication. The proposed work will of great importance in applications which requires variable…