This study analyzes the application of the concatenated fractional representation in high-precision numerical computation, and concentrates on its role in cryptanalysis for deciphering, such as deciphering the Okamoto regime, deciphering the Throwfan Tou public key regime, and deciphering the RSA regime with a short decryption index. On this basis, an attack algorithm based on the Legendre’s theorem of continuous fractional approximation is proposed. The experimental platform is built for simulation and analysis, and it is found that the attack result of this RSA attack algorithm is consistent with the set 512bit key, which realizes the successful attack on the key of RSA algorithm. Moreover, the concatenated score RSA attack algorithm has good time computation efficiency and small communication cost, and its total time consumed for preprocessing, authentication, and server for 1GB file is within 51%, 64%, and 51% of the comparison methods, respectively, and the average value of communication cost is within 88% of the comparison methods. The results show that the proposed concatenated fractional attack algorithm is effective for RSA, which makes the complexity of the RSA attack greatly reduced and improves the execution efficiency of RSA deciphering.
