logmod

版本 1.4.0.0 (22.6 KB) 作者: Steven Gregory
Computes y such that mod(a^y, p^N) == x
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643.0 次下载
更新时间 2009/4/23

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Suppose
p is an odd prime,
ord(a) = p-1
GCD(x, p) = 1
N is an integer >= 2

Then
y = logmod(x, a, p, N)

Returns y such that a^y = x (mod p^N)

Example
Let x= vpi(154), a = vpi(7), p = vpi(17), N = vpi(37)
y = logmod(x, a, p, N)
returns
y = 2088349219044680767324467844670001776975183904

引用格式

Steven Gregory (2024). logmod (https://www.mathworks.com/matlabcentral/fileexchange/23803-logmod), MATLAB Central File Exchange. 检索来源 .

MATLAB 版本兼容性
创建方式 R2006a
兼容任何版本
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在 Help Center 和 MATLAB Answers 中查找有关 Number Theory 的更多信息
致谢

参考作品: nextperm, modinv(x, N)

启发作品: modinv(x, N), nextperm, egcd.m

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版本 已发布 发行说明
1.4.0.0

Brought the description up to date. This routine no longer needs the m-file modinv.m.
1.3.0.0

Modified to correct logic errors and to exploit the latest version of the vpi software. A Microsoft word file has been included that describes and proves the algorithm used.
1.2.0.0

Rewrote the description.
1.0.0.0