Table 2.

Attack-resistance evaluation of the proposed RSA–Hilbert model.

Attack Type	Vulnerability in Classical RSA	Resistance in Proposed Framework
Chosen-Plaintext (CPA)	Possible through multiple plaintext–ciphertext pairs	Each block encrypted with dynamic Hilbert key; random nonce prevents repetition.
Chosen-Ciphertext (CCA)	Decryption oracle may reveal partial plaintext	Secret-sharing layer prevents oracle reconstruction; ciphertext must be recombined before decryption.
Replay Attack	Identical ciphertext retransmission undetected	Session-based random in Eq. (3.8) ensures uniqueness of every encryption.
Side-Channel / Timing Attack	Correlation between timing and key bits	Random padding and uniform modular exponentiation time reduce leakage.
Brute-Force Attack	Complexity limited to RSA key size	Combined RSA and Hilbert key space () makes exhaustive search infeasible.
Statistical / Differential Attack	Ciphertext correlations may leak patterns	Hilbert diffusion creates high avalanche effect; adjacent pixel correlation .