On the insecurity of generalized (Rivest-Shamir-Adleman) - advance and adaptable cryptosystem

• Main Authors: Isa, M.A.M., Rahmany, N.N.A., Asbullah, M.A., Sathar, M.H.A., Rasedee, A.F.N.
• Format: Article
• Language: English
• Published: IOP Publishing 2019
• Online Access: http://psasir.upm.edu.my/id/eprint/106322/1/Isa_2019_J._Phys.__Conf._Ser._1366_012021.pdf; http://psasir.upm.edu.my/id/eprint/106322/; https://iopscience.iop.org/article/10.1088/1742-6596/1366/1/012021

This paper explores the security claims of the Generalized (Rivest-Shamir-Adleman) - Advance and Adaptable Cryptosystem, in short the GRSA-AA cryptosystem. In the GRSA-AA design proposal, the public key n is defined as the multiplication of two large prime numbers, while the values of encryption key E and decryption key D are relying on the result of multiplying 2k large prime numbers called N where n divides N. The GRSA-AA claimed that the brute force is necessary to break the cryptosystem even if the integer n was factored. Nevertheless, this paper aims to show that this scheme is insecure once n is factored. The mathematical proof is presented to show that it is easy to generate an alternative value to the private key D without brute-forcing, yet successfully break the system.