An Information-Theoretic Security Evaluation of a Class of Randomized Encryption Schemes

• Published in: IEEE transactions on information forensics and security Vol. 9; no. 2; pp. 158 - 168
• Main Authors: Oggier, Frederique, Mihaljevic, Miodrag J.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2014; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Channel coding; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Cryptography; Encryption; error-correction coding; Exact sciences and technology; Generators; homophonic coding; Information, signal and communications theory; information-theoretic security evaluation; Memory and file management (including protection and security); Memory organisation. Data processing; Randomized encryption; Signal and communications theory; Software; Telecommunications and information theory; Vectors; wire-tap channel coding; Corruption; Error probability; Pseudorandom number; Encryption; Modeling; error-correction coding; Eavesdropping; Randomization; Security of data; Cryptography; Ciphertext attack; Computer security; Binary channel; information-theoretic security evaluation; wire-tap channel coding; Transmission channel; Homophonic coding; Randomized encryption; Random distribution; Confidentiality; Noisy channel; Cryptanalysis; Secret key; Error correction; Information theory
• ISSN: 1556-6013; 1556-6021
• DOI: 10.1109/TIFS.2013.2294763

Randomized encryption techniques, where randomness is used for security enhancement, are considered. We focus on the case where the encrypted data experiences noise, e.g., is transmitted over a noisy channel, within the encoding-encryption paradigm, where the data is first encoded for error correction, before being encrypted for security. We assume that the ciphertext is subject to a corruption equivalent to its transmission through a binary symmetric channel with known probability of error. The enhanced security is based on a dedicated wire-tap channel coding that introduces extra randomness, combined with that of the communication channel noise. The encryption is based on a block-by-block modulo 2 addition between an encoded message vector and a pseudorandom vector. The goal is to enhance the protection of the secret key employed in the encryption algorithm. Security evaluations of the model are performed employing an information-theoretic approach. Assuming both a passive and an active attacker, we show that there is a threshold before which the wire-tap encoder guarantees an information-theoretic security (during which the equivocation of the secret key is increased), and after which the uncertainty reduces, entering a regime in which a computational security analysis is needed for estimating the complexity resistance against the secret key recovery.