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Efficient Adaptation of the Karatsuba Algorithm for Implementing on FPGA Very Large Scale Multipliers for Cryptographic Algorithms [PDF]

International Journal of Reconfigurable and Embedded Systems (IJRES), 2020
<span lang="EN-US">Here, we present a modified version of the Karatsuba algorithm to facilitate the FPGA-based implementation of three signed multipliers: 32-bit × 32-bit, 128-bit x 128-bit, and 512-bit × 512-bit. We also implement the conventional 32-bit × 32-bit multiplier for comparative purposes.
Andre, Walder, Walder Andre
exaly   +5 more sources

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On Karatsuba Multiplication Algorithm

The First International Symposium on Data, Privacy, and E-Commerce (ISDPE 2007), 2007
Xianjin Fang
exaly   +2 more sources

High-Speed RLWE-Oriented Polynomial Multiplier Utilizing Karatsuba Algorithm

IEEE Transactions on Circuits and Systems II: Express Briefs, 2021
Lattice-based cryptography (LBC) is one of the promising post-quantum candidates which offers good security and performance. The most time consuming operations in LBC is the polynomial multiplication, which can be performed through widely explored algorithms like schoolbook polynomial multiplication algorithm (SPMA) and Number Theoretic Transform (NTT).
Denis C -K Wong, Zheng Yan Wong, Kai-Ming Mok   +2 more
exaly   +2 more sources

A Non-Redundant and Efficient Architecture for Karatsuba-Ofman Algorithm

Lecture Notes in Computer Science, 2005
The divide-and-conquer method is efficiently used in parallel multiplier over finite field GF(2n). Leone proposed optimal stop condition for iteration of Karatsuba-Ofman algorithm (KOA). Multi-segment Karatsuba method (MSK) is proposed by Ernst et al. In this paper, we propose a Non-Redundant Karatsuba-Ofman algorithm (NRKOA) with removing redundancy ...
Young-Ho Park, Jongin Lim, Chang Han Kim
exaly   +3 more sources

Exploration of Karatsuba Algorithm for Efficient Barrett Modular Multiplication

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Mingzhe Zhang, Bo Zhang, Shoumeng Yan
exaly   +3 more sources

A Karatsuba-Based Algorithm for Polynomial Multiplication in Chebyshev Form

IEEE Transactions on Computers, 2010
In this paper, we present a new method for multiplying polynomials in Chebyshev form. Our approach has two steps. First, the well-known Karatsuba's algorithm is applied to polynomials constructed by using Chebyshev coefficients. Then, from the obtained result, extra arithmetic operations are used to write the final result in Chebyshev form.
Juliano B. Lima, Daniel Panario, Qiang Wang 0012   +2 more
openaire   +2 more sources

Some Improvements of the Parallel Karatsuba Algorithm: Student paper

2020 19th International Symposium INFOTEH-JAHORINA (INFOTEH), 2020
Multiplying long integers is one of the basic mathematical operations used mostly in cryptography. The topic of this paper is experimental testing of different implementations of the Karatsuba algorithm for multiplying long integers using shared memory parallel programming.
Mirza Delibasic, Amra Habibovic, Naida Hanjalic, Envera Husagic   +3 more
openaire   +1 more source

A Karatsuba Algorithm Based Accelerator for Pairing Computation

2019 IEEE International Conference on Electron Devices and Solid-State Circuits (EDSSC), 2019
Elliptic curve cryptosystem costs smaller calculation complexity compared with RSA. Identity Based Cryptography is a state-of-art scheme in all the elliptic curve cryptosystems. Bilinear pairing calculation over elliptic curves is the most time-consuming part which is also the pivotal to build IBC schemes.
Yi Wu, GuoQiang Bai, XingJun Wu
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A reconfigurable recursive and efficient hardware for Karatsuba-Ofman's multiplication algorithm

Proceedings of 2003 IEEE Conference on Control Applications, 2003. CCA 2003., 2004
Multiplication of long integers is a cornerstone primitive in most public-key cryptosystems. Multiplication for big numbers can be performed best using Karatsuba-Ofman's divide-and-conquer approach. We propose a recursive and efficient hardware for Karatsuba-Ofman's multiplication algorithm.
Nadia Nedjah, Luiza de Macedo Mourelle
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Karatsuba-ZOT Multiplication Algorithm and its Application in Cryptography

Applied Mechanics and Materials, 2012
The number theory based cryptography algorithms are the most commonly used public-key cryptosystems. One of the fundamental arithmetic operations for such systems is the large integer multiplication. The efficiency of these cryptosystems is directly related to the efficiency of this large integer multiplication operation.
Shahram Jahani, Azman Samsudin
openaire   +1 more source