logmod

Version 1.4.0.0 (22.6 KB) by Steven Gregory
Computes y such that mod(a^y, p^N) == x
5.0
(2)
644 Downloads
Updated 23 Apr 2009

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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

Cite As

Steven Gregory (2026). logmod (https://se.mathworks.com/matlabcentral/fileexchange/23803-logmod), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2006a
Compatible with any release
Platform Compatibility
Windows macOS Linux
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Acknowledgements

Inspired by: nextperm, modinv(x, N)

Inspired: modinv(x, N), nextperm, egcd.m

Version Published Release Notes
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