8 x 8 S-boxes and Differential Cryptanalysis

Abstract

Cryptography has a twin sister called cryptanalysis. Cryptanalysis is the science and art of cracking encrypted information using mathematical methods and techniques. Cryptanalysis is derived by word Greek "kryptos ", means hidden, and "analyein ", means to untie [3] . it is used to break cryptographic security systems, regardless of whether the cryptographic key is obscure and it achieves access to the substance of encrypted messages. Although, the goal of both cryptography and cryptanalysis has been the same, but cryptanalysis have changed the techniques and methods radically during the history of cryptography. By accepting the increasing complexity of cryptography, assortment of past, by paper and pen techniques through machines like as "British Bombes" and "Colossus PCs" at "Bletchley Park" in World War II, is displayed as mathematically unrivaled mechanized plans of the present-day. Mostly the method occupies constructed problems of pure mathematics which solve carefully for breaking modern cryptosystems. Integer factorization is known best of them. In the event that some encrypted information "ciphertext", is given the motivation behind the cryptanalyst is to access the data about the first or unencrypted information ''plaintext'' as much as possible. Consider two aspects which are useful to achieving this. First is to discover how encipherment procedure function for cracking system, and second is comprehending key for encrypted group of messages or a particular message that is unique. We see historical perspectives with some examples of the cryptographer's disappointment and the cryptanalyst's prosperity. In the Battle of Midway World War II, which denoted the defining moment of the naval war in the Pacific, was won by the United States to a great extent since cryptanalysis had given Admiral Chester W. Nimitz with data about the Japanese diversionary assault on the Aleutian Islands and about the Japanese request of assault on Midway. Another renowned case of cryptanalytic achievement was the deciphering by the British amid World War I of a telegram from the German remote clergyman, Arthur Zimmermann, to the German pastor in Mexico City, Heinrich von Eckhardt, spreading out an arrangement to remunerate Mexico for entering the war as a partner of Germany. American daily papers distributed the content (without saying the British part in blocking and interpreting the telegram), and the news stories, joined with German submarine assaults on American boats, quickened a move out in the open opinion for U.S. section into the war in favor of the Allies. In 1982, amid an v open deliberation over the Falkland Islands War, an individual from Parliament, in a now-well known error, uncovered that the British were perusing Argentine political ciphers without any difficulty as Argentine code assistants. A lot of methods have been used for cryptanalysis, and some of these methods are more probably known. One of these known method is differential cryptanalysis. Differential cryptanalysis is firstly introduced by Biham and Shamir[8] for breaking DES comp1etelty. This attack is mostly used for block ciphers. Most of the cryptographers are trying to secure their ciphers or S-box againt differential attack. So, in first chapter we will deliberate the fundamentals of cryptology and algebra, with some renowened ciphers and Mini-AES shortly. In second chapter, we will discuss introduction of Mini-AES and S4AES, differential cryptanalysis on Mini-AES and S4AES and then, we apply further attack on Mini-AES. In third chapter, we will demonstrate introduction of chain ring based ciphering then find their differential probability and see either is it secure against differential attack or not? In the last of this chapter, we will discuss the attacking ways of these ciphering and also define that differential attack is possible on these ciphers or not? In fourth chapter, we will be discussed 8 x 8 S-boxes and differential cryptanalysis. We also see that which one of these S-boxes is secure against differential attack and which is not, and in the last of this chapter we will explain the comparison of differential probability of these S-boxes. The last fifth chapter is the conclusion of my thesis.