To answer your question in one word: Yes.

Modular arithmetic forms the basis for number theory and many cryptosystems. A very simple, old, and well known example is the caesar cipher or shift cipher. Each letter of the alphabet is replaced with an integer from 0 to 25. A caesar cipher is then a function f(n) = (n+m) mod 26 where n is the integer representation of the letter and m is an integer representing the degree of shift. The caeser cipher is a private key cryptosystem, but public key cryptosystems are based on modular arithmetic also, a rather brilliant modern example is RSA. In RSA crypto each character is replaced with an integer and then those numbers are grouped into blocks of 4 digits. A 4 digit block of plaintext M is transformed into the the ciphertext C through the formula C = M^e mod n where n=pq. p and q are prime numbers (huge prime numbers) and e is an integer that is relatively prime to (p-1)(q-1). Then the cipher text is decrypted with the formula M = C^d mod n where d is an inverse of e mod (p-1)(q-1).

These are just a couple examples, but if you're really interested you should definitely read:
Handbook of Applied Cryptography by Alfred J. Menezes
Applied Cryptography by Bruce Schneier (aka the crypto bible)
A Course in Number Theory and Cryptography by Neal I. Koblitz

There are lots of other too, but these 3 are classics. The Handbook is fairly mathematically intensive and I don't know how mathematically inclined you are, but its the best crypto book out there IMHO and you can download the whole thing for free at http://www.cacr.math.uwaterloo.ca/hac/