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Asked: 2026-05-12T21:40:20+00:00

I know that an affine cipher substitutes BD with SG. I need to find

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I know that an affine cipher substitutes BD with SG. I need to find the encryption formula, in the form y = a x + b, where a and b are coefficients.
From the information above I end up having to equations:
a+b=18 and
3a+b=6
So I am working like this:

a+b=18 and 3a + b = 6-> 3a+18-a=6->  2a= 6-18 -> 2a=14 (as it is mod 26)

b=18-a 

2a=? 

So, O want to multiply by the multiplicative inverse of 2 mod 26

I can’t find a multiplicative inverse of number 2 with 26 (y = ax + b mod 26)

Can anyone please help me find a and b?

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1 Answer

  1. Editorial Team

    That’s because 2 doesn’t have a multiplicative inverse mod 26: since 13*2=0, there does not exist K such that K * a = 1. Your modulus must be prime. Try looking up the Chinese Remainder Theorem for more information.

    To be more specific, integers mod 26 is not a field (a mathematical set where every element, except 0, has a multiplicative inverse). Any ring in which a * b = 0, for some a!=0 and b!=0, is not a field.

    In fact, a field will always have p^n elements, where p is a prime number and n is a positive integer. The simplest fields are just integers mod a prime number, but for prime powers you need to construct a more elaborate system. So, in short, use a different modulus like 29.

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