The Meet-in-The-Middle Attack on The Matrix NTRU Cryptosystem

The Matrix NTRU cryptosystem, based on matrix rings and modular arithmetic, is a variant of the NTRU cryptosystem introduced in 1996. In the Matrix NTRU cryptosystem, messages are encrypted into ciphertext using a public key generated by the receiver, and decryption using the corresponding private key. The confidentiality of the private key is crucial for maintaining the cryptosystem's security. This paper is dedicated to analyzing the protection of the private key in the Matrix NTRU cryptosystem using meet-in-the-middle attacks. It means the attackers found the private key by searching two matrices that, when combined, produce a result with specific characteristics. By scrutinizing the public key and employing a meet-in-the-middle strategy, the attacker can recover the private key. This paper comprehensively outlines the steps involved in the meet-in-the-middle attack and discusses the conditions the candidate's private key must satisfy. The security analysis helps assess the vulnerability of the Matrix NTRU cryptosystem and highlights the importance of protecting the private key to ensure the cryptosystem's security. Through this research, we contribute to the ongoing efforts in advancing cryptographic techniques and data protection measures.