Cryptanalysis on Polynomial Congruence-Based Public Key with Chinese Remainder Theorem

Public key cryptography is an asymmetric cryptographic scheme that consists of two key pairs: a public key, which is publicly known, and a private key, which is kept secret. Public keys are typically constructed based on the properties of number theory, and one example is polynomial congruence. Karyadi’s public key algorithm is an example of a public key algorithm based on polynomial congruence. Cryptanalysis is the method of analyzing a cryptographic system by attempting to attack it, including public key cryptosystems. Cryptanalysis of public key systems can focus on obtaining the encrypted message or the secret private key through various attack methods. In this paper, cryptanalysis of Karyadi’s public key algorithm and Rabin Cryptosystem are conducted with the aim of obtaining the original message from the encrypted message without knowing the trapdoor information. The cryptanalysis results demonstrate that it is possible to easily recover the original plaintext of the encrypted message in Karyadi’s public key algorithm, Rabin Cryptosystem, and other polynomial congruence-like cryptosystems under specific conditions without requiring the trapdoor information. Furthermore, a general method is presented for cryptanalysis to obtain the plaintext without knowing the trapdoor information in public key systems based on polynomial congruence using the Chinese Remainder Theorem. Additionally, measures to avoid the impact of this cryptanalysis method on polynomial congruence-like cryptosystems are provided.