Three-term Karatsuba algorithmBit-parallel multiplierTrinomialsIn this paper, we continue the study of bit-parallel multiplier using three-term Karatsuba algorithm (KA), recently introduced by Li et al. (VLSI Design 2018). The three-term KA is the simplest variation of the classic Karatsuba ...
A series of programs that enable one's investigations in the algebraic complexity theory such as matrix multiplication algorithms, primality tests, algebraic complexity, sorting algorithms etc. Each algorithm is accompanied by a comparative time complexity analysis and a class of test cases and test su...
> implementing the Karatsuba algorithm, it is implementing the > schoolbook algorithm in two steps, by splitting the longer input into > two pieces. The surprising realization here is that there are actually (var1ndigits, var2ndigits) combinations where *only* doing mul_var_karatsuba_half() r...
(N 2 ) algorithms.Inthispaper,wepresentaMontgomerymultiplier thatincorporatesthemoreefficientKaratsubaalgorithmwhichis O(N (log3/log2) ).Thissystemisparameterizabletodifferentbit- widthsandmakesexcellentuseofbothembeddedmultipliersand fine-grainedlogic.ThedesignhassignificantlylowerLUT-delay product...
10. The computer storage medium as recited in claim 1, wherein the product of the pair polynomials represents a product of a pair of large integers, and is utilized within a cryptographic algorithm. 11. A method comprising: identifying, by a computing system programmed with instructions configuri...
2) Karatsuba-Ofman algorithm Karatsuba-Ofman算法 1. The CIOS method of Montgomery algorithm is improved via the idea of Karatsuba-Ofman algorithm,: the decrease rate amounts to nearly 25%. 利用Karatsuba-Ofman算法的思想,改进了Montgomery模乘的CIOS实现算法:一方面,改进后的CIOS算法在时间效率上...
A target value is found by performing an NRHKOA(Non-Redundant Half Karatusba-Ofman Algorithm) after finding the sum. Output is found by replacing the inputted value with the target value and recursively repeating steps from the second step.LIM, JONG IN...
In this paper, we improve the Preprocess-then-NTT technique by mixing it with Karatsuba multiplication such that the time complexity is better than the original NTT algorithm asymptotically. The claim was also verified in our experiments. As a result, our new algorithm not only relaxes the ...
The proposed architecture can reduce the time x space complexity decreasing when the bit-size of multiplier is increasing.doi:10.1007/978-3-319-23207-2_22Shyan-Ming YuanChiou-Yng LeeChia-Chen FanSpringer International Publishing
In this paper, we propose a Non-Redundant Karatsuba-Ofman algorithm (NRKOA) with removing redundancy operations, and design a parallel hardware architecture based on the proposed algorithm. Comparing with existing related Karatsuba architectures with the same time complexi...