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I am facing difficulty in grasping square and square roots modulo a prime and a non-prime. I am using An Introduction to Mathematical Cryptography but the content is not very clear. Can someone please refer a text that explains the concept clearly.

TheNoob
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  • Any decent Number Theory Book...and some hundreds of thousands of sites in the web. You can search by "quadratic residues" – DonAntonio Oct 03 '13 at 18:35
  • Yeah i did that too. I also used "An introduction to Number Theory" by Niven et. al. I guess I will try and find a good text online itself. Thanks – TheNoob Oct 03 '13 at 18:53

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It's very simple:

  • The square of a number $x$ modulo $n$ is $x^2 \mod n$ (duh).
  • If $x^2 \equiv y \pmod n$, then $x$ is a square root of $y \mod n$.

These definitions don't depend on whether $n$ is prime or composite.

TonyK
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  • Thanks a lot for this. But I want to study it in a little more detail like quadratic reciprocity etc. Thanks for your time though. – TheNoob Oct 04 '13 at 14:46