A Security Enhanced Encryption Scheme and Evaluation of Its Cryptographic Security

Abstract

An approach for security enhancement of a class of encryption schemes is pointed out and its security is analyzed. The approach is based on certain results of coding and information theory regarding communication channels with erasures and deletion errors. In the security enhanced encryption scheme, the wiretapper faces a problem of cryptanalysis after a communication channel with bits deletion and a legitimate party faces a problem of decryption after a channel with bit erasures. This paper proposes the encryption-decryption paradigm for the security enhancement of lightweight block ciphers based on dedicated error-correction coding and a simulator of the deletion channel controlled by the secret key. The security enhancement is analyzed in terms of the related probabilities, equivocation, mutual information and channel capacity. The cryptographic evaluation of the enhanced encryption includes employment of certain recent results regarding the upper-bounds on the capacity of channels with deletion errors. It is shown that the probability of correct classification which determines the cryptographic security depends on the deletion channel capacity, i.e., the equivocation after this channel, and number of codewords in employed error-correction coding scheme. Consequently, assuming that the basic encryption scheme has certain security level, it is shown that the security enhancement factor is a function of the deletion rate and dimension of the vectors subject to error-correction encoding, i.e., dimension of the encryption block.

Security Enhanced Symmetric Key Encryption Employing an Integer Code for the Erasure Channel

“…One of the encryption approaches is based on the use of a cryptographic key to control error correction coding algorithms, and it is reported, for example, in [4][5][6][7][8][9][10][11][12][13][14][15]. The other approach is the use of error correction coding and noisy channels for the cryptographic security enhancement of a given encryption scheme: this approach has been reported, for example, in [1,[16][17][18][19][20][21][22][23][24]. These security enhancements are based on paradigms of the additive noisy channel or channels with synchronization errors.…”

“…In the following, we discuss the following two paradigms for the security enhancement: (i) encode → encrypt → degrade paradigm employed for stream ciphers enhancement in [17,19,21,23,24]; (ii) encrypt → encode → degrade paradigm reported in [1,18,20,22].…”

“…Additionally, the required number of plaintext-ciphertext pairs for mounting a known plaintext attack, in the presence of noise in the ciphertexts, as well as the trade-off between security enhancement and performance degradation, were considered. In [1,18,20], schemes are proposed for a security-enhanced encryption scheme based on simulators of certain channels with synchronization errors and LDPC or polar error correction coding. An approach for the security enhancement employing a simulated noisy channel with bits insertion was proposed in [18] and the enhancement was evaluated by an informationtheoretic approach.…”

“…An approach for the security enhancement employing a simulated noisy channel with bits insertion was proposed in [18] and the enhancement was evaluated by an informationtheoretic approach. Two approaches for the security enhancement of encryption algorithms employing simulated noisy binary channels that consisted of the erasure channels for the legitimate receivers and as the binary deletion channels for an attacker were proposed in [1,20]. The security enhancement was considered by employing a traditional game-based evaluation approach to show the reduction of the attacker advantage.…”

“…The ST for the(25,20) integer 4-erasure correcting code when p =(1,2,3,4). Suppose that b = 5 and p =(2,4,3,2).…”