The time complexity of Karatsuba algorithm for fast multiplication is O(nlog 3).ExampleIn the complete implementation of Karatsuba Algorithm, we are trying to multiply two higher-valued numbers. Here, since the long data type accepts decimals upto 18 places, we take the inputs as long values....
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
Specifically, we found that related Mastrovito matrix is very simple for equally spaced trinomial (EST) combined with classic Karatsuba algorithm (KA), which leads to a highly efficient Karatsuba multiplier. In this paper, we consider a new special class of irreducible trinomial, namely, xm+xm/...
> 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...
any explicit multiplication, implementing the entire algorithm using solely addition. They require O(N) additions, each with bit-width of N. Thus, they have at least O(N 2 ) complexity where N is the bit-width of the computation. Such systems ...
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...
We construct a bit-parallel multiplier for AOP based on a generalized Karatsuba algorithm.We examine the influence about multiplier efficiency with respect to decomposition of polynomial degree.The lower bound of the space complexity is m2/2+O(m{3/2})+O(m).The time complexity nearly matches ...
The research results presented in this paper prove that it is also possible to achieve high performance over binary fields by combing the algorithm with sub-quadratic complexity. Furthermore, we suggest constant time KBC method. Block-Comb method does not provide constant time, and look-up table...
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 complexity, the proposed architecture ...
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 ...