Substantial number of cryptographic keys and its application to encryption designs

Abstract

A new concept of the substantial number of cryptographic keys (SNK) in key spaces is proposed and is applied to encryption designs. SNK is defined as the number of keys which is far from each other. It must be greater than 256, for instance, to have essentially the same number of keys in DES. This SNK condition restricts design parameters of encryption systems. In this paper, SNK is strictly defined in key spaces, followed by illustrations of SNK’s in fundamental encryption algorithms and product ciphers. Then SNK is applied to the design of encryption systems to decide the design parameters. It is useful for designing product cipher in particular. SNK should be considered as one of the criteria of encipherment strength.