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Garner's Formula to find a and b given 2 mod equations equal the same variable

ec flag

I'm working on a Chinese Remainder Theorem Garner's Formula problem in my Cryptography module and was hoping for some help.


Question:
Given the data below use Garner’s formula to find T,U and s

$$ N = pq = 6815731 $$ $$ s \% p = 1 $$ $$ s \% q = 62537 $$

$ s = a \% p $

$ s = b \% q $

$ T = p-1 mod q $

$ U = (b-a)T mod q $

$ s = a+Up $

(p = the smaller prime)

I've figured out $p = 13, q = 524287 $, and $ T = 362968$ and have tried using modular inverses and this python program to figure out a and b with no avail.
There seems to be little information or examples on Garner's Theorem online.
I'm stumped on how to find a and b and would appreciate any help

kelalaka avatar
in flag
It is better to write this solution as an answer and close accept your answer.
hjds avatar
ec flag
No solution for it yet, am hoping on some help to solve it
I sit in a Tesla and translated this thread with Ai:

mangohost

Post an answer

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