在密码学中,最常见的一类基础运算大概就是模算术(Modular Arithmetic)了。特别地,模乘(Modular Multiplication)是其中最复杂的运算。这里记录自己对一种重要的模乘算法---蒙哥马利模乘[1]的理解。 概述 蒙哥马利模乘最主要的贡献就是提供了一种给定输入T,快速计算TR−1modN(R>N)的模约减方法。为了描述方便将该...
CRYPTOHACK学习记录 二次剩余(Quadratic Residues) 定义: 令整数a,p满足gcd(a,p)=1,若存在整数x使得 x2 ≡ a (mod p) 则称a为模p的二次剩余,否则称a为模p的二次非剩余,称x为a的平方根 题目为: 了解定义后可以编写代码解决此题: p=29 a
最终的结果是递归求解出gcd(a,b)的同时求得了x和y的值。 以下是python代码实现: defegcd(a,b):#扩展欧几里得算法ifb==0:return(a,1,0)else:gcd,x1,y1=egcd(b,a%b)x=y1 y=x1-(a//b)*y1return(gcd,x,y)print(egcd(a,b)) Top 第三题(Modular Arithmetic 1) 分析下吧,先说下同余 同余“≡...
正式叙述 正式叙述的写作思路部分参考[4],它提供了Barrett算法的Python/Java代码实现。 在实际模约减中,常常遇到的情况是0≤a<q2,q不是 power-of-2 (因为模约减之前的运算是乘法,乘法的结果不会超过q2)。 现在讨论这种情况下如何合理设置参数k和m。根据“直觉”章节的介绍,我们知道k的最小取值为⌈log2(a)...
This is a python library for some numbers functions: working with primes (generating, primality tests) common maths (gcd, lcm, n'th root) modular arithmetics (inverse, Jacobi symbol, square root, solve CRT) converting strings to numbers or binary strings ...
I'm scared that we might end up with a natural type in PLC and then we'd have to duplicate all of the arithmetic and comparison functions... Contributor effectfully Jul 29, 2024 Well mod 1 is identically zero (if you divide something by 1 then you have a remainder of 0), so it...
The reachability measure is defined as the arithmetic mean of the Reachability Index for all theoretical flange positions of the respective task pose. In detail, the six process steps are as follows: 8 A. Kluge-Wilkes et al. Fig. 3 Calculating the overlap of robot flange poses with a ...
es systematic error (in μm) x¯arithmetic mean of measured positional deviations (in μm) xtesttargeted position (in μm) Positioning repeatability, also referred to as random error, is calculated by: er = s = ∑i=1nxi-x-2n-1 er random error (in μm) s sample standard deviation ...
supporting a myriad of features like full-precision or quantized training (e.g.Q-LoRA, Q-Bottleneck Adapters, or Q-PrefixTuning),adapter merging via task arithmeticsor the composition of multiple adapters viacomposition blocks, allowing advanced research in parameter-efficient transfer learning for NL...
ArithmeticBranch[Code] Insert junk code. In this case, the junk code is composed by arithmetic computations and a branch instruction depending on the result of these computations, crafted in such a way that the branch is never taken.