Cryptanalysis Of Modern Cryptograph Algorithm

Algebraic properties of AES and the security of CAC are researched, the security of signature algorithm such as ElGamal is also cryptanalyzed.We obtain the main results as follows:(1) A proof of the equivalence is presented among the q -polynomials, matrices of order n and linear functions over finite fields. And then based on the observation that one linear function will have distinct matrix forms under different basis, a generic scheme is extended to determine the relationship between the linear functions and matrices of order n over finite field quickly. As another important contribution, a new scheme is also designed to determine their linear relation, with advantage of full generality over available schemes. Finally the essential reason why the algebraic expression of Rijndael s -box is so simple is proposed.(2) An improved AES is proposed, which can significantly increase the complexity with an algebraic expression involving 255 items. At the same time, it also gives good characters of Boolean function in balance and strict avalanche criterion, ie. A cryptanalysis on its security is also made, which shows that the proposed scheme is capable of resisting against the powerful known differential and linear cryptanalysis.(3) The order of AES S-box is researched and it is found that the S-box continue state transfer is a Markov chain. The whole 256 states are classed into 5 rebound closed classes, and their periods are 59,87,81,27,2.(4) We replace the constants in Rijndael, including the replacement of the affine transformation in the Rijndael S box and the coefficients of the MixColumn operation. We show that the replacements of the affine transformation in the Rijndael S box can create the new S box with the same truth table which encryption and decryption share, and we present all such affine transformations in the Rijndael S box. We also describe that it exists the coefficients matrix of the MixColumn operation in Rijndael which satisfy that the encryption and decryption can share the same operation. This method can make it a very low-complexity architecture, especially in saving the hardware resource in implementing the AES (Inv)SubBytes module and(Inv)Mixcolumns module,etc. The proposed AES S box is suited for hardware-critical applications, such as smart card, PDA, and mobile phone, etc.(5) We show that the new CAC(Cellular Automata Cryptosystem) is insecure. It can be broken by a chosen-plaintext attack. The attack is very efficient, requiring only two chosen plaintexts and a small computation amount with time complexity of two encryptions. Although the designer has omitted many design parts, this paper restores the omitted parts clearly by deriving the rotating number d of plaintext byte and the procedure of Major CA.The clock circle â–³ of Major CA and the key S_n are also found. So the research shows that CAC is insecurity to protect the sense information and should be intensified.(6) It is proved that the ElGamal signature scheme is insecure against the chosen ciphertext. It can not only determine the secret key, but also forge the signature substituting the right signature. The attack action does not depend on the computation of discrete logarithm. Finally a new ElGamal-based signature scheme is presented which can avoid the forged signature, and its security is based on the difficulty of decomposing large number. (7)Bent function plays an important role in cryptography, error-correcting code and design. It is found that all the Walsh values of even n=4 dimension balanced Boolean functions are divided exactly by 4, and the maximum absolute value is also presented. The upper-bound counts and the lower-bound counts of Bent functions are proposed by researching the Hadamard matrix, which decrease the searching space of Bent functions.