Data security based on homographic function

• Published in: Pattern recognition letters 2020-01, Vol.129, p.240-246
• Main Authors: ALI-PACHA, Hana, HADJ-SAID, Naima, ALI-PACHA, Adda
• Format: Article
• Language: English
• Subjects: Chaos-based cryptography; Cryptography; Data security; Digital imaging; Homographic function; Hénon map; Lightweight encryption algorithm; Pixels; Quotients; Substitution cipher; Switching
• ISSN: 0167-8655; 1872-7344
• DOI: 10.1016/j.patrec.2019.10.032

•The first main idea and it is not used before, is to use homographic function.•The second original idea is to work in finite field Z/257Z, 257 is prime number.•Our cryptosystem based on homographic function is a kind of substitution cipher. In this paper, we adapt a homographic function to encrypt digital images, which takes into account the value of the pixel as well as its position in the image. The homographic function is a function represented as a quotient of two affine functions in a switching field K; it is represented by four different coefficients of zeros, which must verify certain conditions. One take the field K equal Z/257Z switching field (257 is a prime number), (all its non-zero elements are invertible, we take into account the following condition if we have 0 as the pixel value we put 256), 256 is the inverse of 256 in Z/257Z. We will show that this a homophonic substitution, which can represent the confusion part in a modern cryptographic system. We strengthened this proposal by a diffusion method and, we have used the Hénon attractor of is 2-dimensional; each pixel will be permuted to another position of the encrypted image. We managed to build a cryptosystem who passed all the statistic tests, and that has a secret key of 253 bits in length.