This an example in my notes...
Encipering transformation: f(x) = 9x + 3(mod 100)
Finding the deciphering transformation:
Alice now wishes to find a number t such that 9t = 1 mod 100. She finds that 9 x 89 = 1 mod 100. She finds by trial and error (until she improves her arithmetic!) that 9 x 89 = 1 mod 100.
I was just wondering is there another quicker way that alice can find this t, rather than trial and error?
Thanks in advance!