Hilyati Hanina, Zazali (2012) A new cryptographic algorithm based on decomposition problem in elliptic curve cryptography / Hilyati Hanina Zazali. Masters thesis, University of Malaya.
Abstract
This study describes three algorithms for efficient implementations in Elliptic Curve Cryptography (ECC). The first algorithm determines an approach of performing key exchanges between two subgroups for Decomposition Problem and three subgroups for Triple Decomposition Problem. The algorithms work by arranging parameters using finite field group in elliptic curve E. It is a new approach which performs core operation using multiplication of points based in ECC. The algorithm explores computational advantages of computing cofactor number of points on E and it is computationally infeasible to obtain if the cofactor are large enough. This approach presents better platform in finite field E as compared to the original works using the braid groups. The second algorithm deals with the use of Decomposition Problem in encryption scheme for ECC. We introduce two concepts of splitting messages using the scheme in El-Gamal and Massey-Omura algorithms. The messages can be split either before or after the user sends the messages to the receiver. The third algorithm describes the application of Decomposition Problem to the signing and verifying digital messages in ECC. Since subexponential-time algorithm is known for ordinary discrete logarithm problem and integer factorization problem and not for elliptic curve discrete logarithm problem, the algorithm presented for the digital signature in this study has substantially greater strength per key bit than in other digital signature algorithm
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