Strict key avalanche criterion

A block cipher, such as the DES cipher, is used to encrypt binary plaintext in discrete blocks of length n using a key of length m, to form ciphertext blocks of length n. A block cipher is said to satisfy the strict key avalanche criterion if a one bit change in the key causes on the average one half of the ciphertext bit positions to change. In this paper the importance of the strict key avalanche criterion for assessing the strength of a block cipher is highlighted. Statistical based methods for determining whether a block cipher satisfies the strict key avalanche criterion are given. 1. INTRODUCTION A block cipher is the process of encryption whereby a message is divided into a fixed number of characters (or blocks), and encrypted block by block. In the case of binary plaintext the message is divided into plaintext blocks of length n bits, denoted by P. A ciphertext block of n bits, denoted by C, is formed by applying an encryption function E to P under the influence of a key K of m bits where To recover P there is a decryption function D which is applied to C under the influence of a key K' where P=D(C,K'). There are two types of block ciphers namely symmetric and public key (asymmetric). In a symmetric cipher the keys K and K' are the same, or can be easily deduced from one another. The standard symmetric cipher is the DES (Data Encryption Standard) algorithm as described in [1]. In a public key cipher the keys K and K' are distinct, and cannot be easily deduced from one another. The standard public key cipher is the RSA (Rivest, Shamir and Adelman) algorithm as described in [1]. In this paper two properties from [7], namely plaintext avalanche effect and the key avalanche effect, which are commonly used to measure the strength of symmetric block ciphers, will be described. However they can equally be applied to measure the strength of public key block ciphers. Throughout the rest of this paper a block cipher will be assumed to be a symmetric cipher although in most cases the cipher could be public key as well, in relation to a particular property being examined. An important property for a secure block cipher is the plaintext avalanche effect. A block cipher satisfies the plaintext avalanche effect if for a fixed key a …