Encryption Algorithms

The development of encryption technologies has come about over a long period of time, an appendix at the back provides an interesting timeline for the development of cryptology. Until fairly recently almost all encryption algorithms were based on fairly simple principles, they were secure because the computational power was not available to break them. Computers (specifically to break algorithms such as the Engima cipher during World War II) have enabled algorithms to become progressively more complex and mathematical and the increase in computing power to perform the encryption and decryption goes hand in hand with the computing power needed to break ciphers.

All the most commonly used cryptographic algorithms are 20 or less years old, in many cases the mathematical principles which underlie their operation are similarly young.

Modern ciphers break into two groups - the private key (or symmetric) algorithms and the public key (or asymmetric) ciphers. We will take a look at the operation of these ciphers and the differences between them, we will not be analysing how they work in detail since it is a highly mathematical process. We will however, look at comparisons between them and how their working principles affect their usage.

We use the following notation when talking about cryptosystems. We say that a cryptographic algorithm maps a plaintext (P) and a key (K) to a ciphertext (C). This is usually written as:

C ¬ K[P]

There is an inverse operation that maps a ciphertext and key K-1 to the original plaintext:

P ® K-1[C]

In a symmetric key system the K = K-1 while in a public key system K ¹ K-1 . The attackers goal is to recover the keys (or just the private key K-1 in the case of a public key system). For any good algorithm it should be impossible to recover them by any means other than trying all the possible values (brute force). This should hold true no matter how much ciphertext and plaintext the attacker has captured.

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