New Constructions of Existential Unforgeable Aggregate Signature Scheme from CSP

Abstract

In future, hundreds of years of mathematical problems that the security of public key cryptography algorithms rely on may be defeated by quantum algorithms. How can a digital signature scheme gracefully balance security and efficiency? This study uses the conjugate search problem and the left self-distributive system to combine and uses the RSA-like algorithm as the underlying structure to propose a new aggregated signature scheme. We, through the EUF game, under the random metaphor model, prove that the security of the scheme satisfies the adaptation unforgeability under selective message attack, the scheme can be finally reduced to the discrete logarithm problem or large prime number decomposition problem. In addition, we can achieve antiquantum attack and exhaustive attack by performing matrix calculations on the message, defining and changing the structure of the matrix by encoding, and setting thresholds for the matrix dimension and the length of the private key. In terms of efficiency, the message signature implementation is linear compared with the expansion rate in terms of storage and computing overhead, and the generation and verification of the final signature pair have nothing to do with the number of users. In addition, the length of the signature is fixed and the size is only the length of a single group, which effectively reduces the generation of public and private key pairs and saves a lot of storage space. The storage space and computational complexity are also effectively improved compared with other solutions.