the content of this book is a little odd: it seems narrowly oriented towards getting enough number theory to understand RSA, Diffie-Hellman, and elliptic curve cryptography.

i very much enjoy a book with the same title but by burton:

http://www.mcgraw-hill.co.uk/html/0071244255.html

it contains a lot more of number theory and a little cryptography too.

"...in the context of cryptography, computation, and deep open research problems."

There must be dozens of books named "elementary number theory", is this one somehow special?

It's free?