1. Algorithm: 多项式乘法 Polynomial Multiplication: 快速傅里叶变换 FFT / 快速数论变换 NTT(1526) 2. Solution & Method: 洛谷 P1001 A+B Problem(Python 3 基本输入输出方法及代码简化)(894) 3. Solution: 题解 USACO2020JAN-Silver Loan Repayment(668) 4. Basic Thought / Data Structure: 前缀和...
polynomial multiplicationsystems for symbolic manipulationtime complexity of X+Y sortingExploiting the structure of the 2-dimensional sorting problem associated with the polynomial product has been the strategy in t...
All the basic arithmetic operations (addition, subtraction, multiplication, division, and comparison) can be done in polynomial time. Maximum matchingsingraphscan be found in polynomial time. Complexity classes[edit] The concept of polynomial time leads to several complexity classes in computational comp...
(13) and (14) are essentially the same as in MPPK/DS in6 except for the multiplication by the values \(\alpha , \beta\), and every term is associated with a noise variable. The private key of the optimized MPPK/DS consists of \(f(x_0)\) and \(h(x_0)\) \(R_0, R_n,...
addition, subtraction, multiplication, division, and comparison, instead of the number of steps of a Turing machine. In the arithmetic model, the encoding length of a problem instance is simply the number of input numbers, not the encoding length of these numbers. The running time of an ...
(α1,...,αn)∈V (α1,...,αn)∈V Thus the set of eigenvalues of the linear transformation corresponding to multiplication by g in the ring R is precisely the set {g(α1, . . . , αn) | (α1, . . . , αn) ∈ V}. This means that the characteristic polynomial of g(...
This reduction of XOR gates can also reduce the complexity of multipliers for large fields (such as those used in Elliptic Curve Cryptography) if composite fields GF((2n)k), with m=n·k, are considered [21], where the reduction of the multiplication complexity over the ground field GF(2n...
(For the computational complexity of the "di-rect" problems such as polynomial multiplication or determination of g.c.d.'s see [1, 16] and also [9].) It should be remarked that as a result a hierarchical re-lationship between the computational problems of polynomial algebra, from the ...
Finite Field multiplication operation is one of the most important operations in the finite field arithmetic. Recently, Fan and Dai introduced a Shifted Polynomial Basis(SPB) and construct a non-pipeline bit-parallel multiplier for . In this paper, we propose a new bit-parallel shifted polynomial...