Hashing

Distinct from the concept of encryption (and present in many mechanisms used in cryptography, such as cryptographic signatures and authentication) is hashing, which refers to a deterministic algorithm used to map data to a fixed-size string. Aside from determinism, cryptographic hashing algorithms must exhibit several other characteristics, which will be covered in this section.

As we'll see in the following section, a hash function must be difficult to reverse. Most readers who got through high school algebra will remember being tormented with factoring. Multiplication is an operation that is easy to complete, but difficult to reverse—it takes substantially more effort to find the common factors of a large number as opposed to creating that number as a product of multiplication. This simple example actually enjoys practical application. Suitably large numbers that are the product of the multiplication of two prime numbers—called semiprimes or (less often) biprimes—are employed in RSA, a widely used public-key cryptography algorithm.

RSA is the gold standard in public key cryptography, enabling things such as SSH, SSL, and systems for encrypting email such as PGP. Building on operations such as this — easy to do one way and very hard to do in the other—is what makes cryptography so robust.