Design of Non-linear Component of Block Cipher based on MEC using Modular Exponentiation

Abstract

The standards for accessibility, security, and privacy have expanded throughout time, but they haven’t altered. Data should be encrypted both while transmission to and from other computers as well as during storage on a computer. The study of methods for protecting communication from outside parties, or adversaries, is known as cryptology. The two branches of this study are called cryptography and cryptoanalysis. Cryptography is the study of how to decrypt data and recover encrypted data without having the key; it is similar to cracking cryptographic systems. On the other hand, cryptoanalysis concentrates on putting the technology required to develop secure communication protocols into practice. It is clear that these two fields cannot exist without each other, underscoring the importance of their relationship. Historically, this discipline was seen only from a privacy standpoint, and names like ”encryption” and ”cryptography” were considered synonymous. Symmetric cryptography, the original purpose of encryption, was to allow two parties to share a key in a secure manner. But when computers became more widespread, modern cryptology took off and now includes a wide range of protocols, including public-key cryptography, authentication techniques, zero-knowledge methods of identifying, and more. Concerns over the security of private data have grown over the past few decades, drawing a lot of attention to cryptography. Scholars have put out a number of recommendations for data security techniques, each with its own mathematical foundation. The goal of these methods is to protect confidential data by rendering it unintelligible and therefore preventing unauthorized access. The majority of conventional symmetric cryptosystems, including the Data Encryp tion Standard (DES), Advanced Encryption Standard (AES), and International Data Encryption Algorithm (IDEA), rely extensively on the utilization of substi tution boxes (S-boxes) to generate a degree of confusion in the input data. The cryptographic characteristics of these systems’ S-boxes are crucial to their efficacy, making the S-box an essential part in boosting encryption’s resilience. Elliptic curves, or ECs, are becoming more and more popular in the cryptography world and are being used in some of the safest cryptosystems. Some cryptographers have created techniques that use ECs to build S-boxes.Using an elliptic curve over an ordered isomorphic elliptic curve and standard orderings on a class of Mordell elliptic curves over a finite field, they have constructed 8x8 S-boxes. It’s crucial to remember that none of these elliptic curve-based methods can produce more than one S-box in either x or y coordinates for a given elliptic curve. The framework of this thesis is created in such a way that the definitions and beginning concepts offered in Chapter 1 are critical to understanding the overall thesis argument. The second chapter digs into the examination of S-box gener ation utilizing Mordell elliptic curves over Modular Exponentiation. A model approach for constructing S-boxes via elliptic curves over Modular Exponentiation is explained in Chapter 3. Finally, Chapter 4 compares the newly developed S-boxes to different existing schemes and conducts a detailed security study of their architecture