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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 2 k 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.

On the Insecurity of Generalized (Rivest-Shamir-Adleman) - Advance and Adaptable Cryptosystem