Being new to Cryptography, I'm having a hard time understanding the basic concepts.

a busy cat

I understand all parts except why 4 power -1 has become to 7.

Can anyone explain why this is?

  • $\begingroup$ Lookup modular multiplicative inverse. Its basically what division becomes on modular rings. $\endgroup$ Aug 7 '17 at 6:32

First note the $\pmod{27}$ at the end, which tells us that all these equations are to be taken modulo $27$.

Also note that $4^{-1}$ literally means "the number $x$ such that $x\cdot4=1\pmod{27}$" (much like with the real numbers where $4^{-1}=\frac14$ with $4^{-1}\cdot 4=\frac14\cdot 4=1$).

Finally observe that $7\cdot 4=28\bmod 27=1$ and it follows that $7=4^{-1}\pmod{27}$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.