Fast Implementation of RNC-based Authentication Codes

Authentication codes (A-codes) are a widely utilized technique for verifying the integrity and authenticity of messages in various information systems. A-codes based on rational normal curves (RNC) are a family of perfect authentication systems. A notable feature of them is the high selectivity of their encoding rules, which allows for a wide variety of application scenarios. However, implementing them to authenticate a source state necessitates the encrypted transmission of a nonsingular matrix. Over 2-dimensional projective spaces over the finite fields with prime number elements, this paper constructs a set of encoding rules for compressible transmission. Additionally, we present the inverse matrices of the set of encoding rules, allowing the receiver to complete message authentication without decompression. Experimental results demonstrate that the methods described in this paper achieve a compression ratio ranging from 20% to 33.33% for encoding rules, and significantly reduce computation overhead. This contributes to an enhanced the authentication efficiency of RNC-based A-codes.