a study of digital signature and variants

Abstract

Achieving security is the most important goal for any digital signature scheme. These schemes newlineare based on various public key cryptosystems like RSA and Elgamal. The security of RSA, the newlinemost widely used digital signature is based on the difficulty of factoring of large integers. newlineAccording to the current technology, for RSA digital signature the minimum size of modulus newlinerequired for secure communications is at least 1024 bits which needs to be increased with the newlinedevelopment of new technologies. However, with the increase in size the required time and newlinestorage to implement the RSA signature scheme will be a big hurdle which needs to overcome. newlineSeveral variants have been proposed to increase the efficiency of the implementation of RSA newlinescheme through various approaches. Recently, many signature schemes based on multiple newlinehardness and non-abelian groups are being designed so that they can resist quantum computer newlineattacks. This work introduces Modified Euler s function, the most essential component of RSA newlinepublic key cryptosystem, using matrices. Proposed function is used in the design of Matrix newlinemodified RSA public key cryptosystem and its variants using different modulus of the form prq newlineand prqs along with the analysis of existing schemes by Takagi. Matrices discrete logarithm newlineproblem (MDLP) a new one-way (trapdoor) function based on non-abelian groups is identified newlinewhich is more complex and provides the same security as discrete logarithm problem (DLP). newlineNovel and efficient digital signature scheme and its variants proxy and blind signatures are newlinedeveloped using new modified Euler s function and new trapdoor function MDLP. As schemes newlinebased on multiple hardness are more secure than those based on single hard problems new newlinesignature schemes are designed using the concept of Tribonacci and multinacci matrices along newlinewith factoring and MDLP with their security analysis. Finally, implementation of improved newlinesignature schemes for authentication of medical images is explained with an example. newline