On Security Enhancement of Lightweight Encryption Employing Error Correction Coding and Simulators of Channels with Synchronization Errors Miodrag MIHALJEVIC Mathematical Institute, Serbian Academy of Sciences and Arts Belgrade, Serbia - COST CRYPTACUS Workshop - 16-18 November 2017, Nijmegen - Netherlands 1 1 1 1
Roadmap • Introduction • A Framework for Security Enhanced Encryption Based on Channels with Synchronization Errors • Particular Instantiation • Information-Theoretic Security Evaluation • Computational-Complexity Security Evaluation • Concluding Notes 2
1. Introduction Noisy Channels and Security Enhancement of Encryption 3 3 3 3
Security of Encryption and Implementation Complexity • Mainly based on • Security heuristic assumptions enhancement appers as an interesting • Particularly when the approach ... encryption is based • Asymmetric on employment of finite state machines implementation complexity of • Lightweight encryption and encryption implies decryption also additional challenges appears as an ... interesting issue 4
Claude Shannon (1916-2001) 5
Two Key Papers • Information Thory • Cryptology • C. E. Shannon, “ A • C. E. Shannon mathematical theory " Communication of communication ”. Theory of Secrecy Bell System Technical Systems ". Bell Journal, vol. 27, pp. System Technical 379 – 423 and 623 – Journal, vol. 28 (4), pp. 656 – 715, 1949. 656, July and October 1948.
Noisy Channels Channels with Channels with Additive Synchronization Noise Noise • Channels with insertion • Erasure Channel • Channels with deletions • Binary Symmetric • Channels with Insertion, Channel deletion and additive • Gaussian Channel noise • ... • ... 7
Binary Channel with Random Erasures Initial vector with bits subject to erasure Erasure of bits is RANDOM – Positions of erased bits are KNOWN 8
Binary Channel with Random Bit Complementation (BSC Channel) Initial vector with bits subject to complementation Complementation of bits is RANDOM – Positions of deleted bits are UNKNOWN 9
Binary Channel with Random Bit Insetion Initial vector with bits subject to bit insertion Expanded vector after the chanel with random bits insertion Insertion of bits is RANDOM – Positions of insereted bits are UNKNOWN 10
Binary Channel with Random Bit Deletion Initial vector with bits subject to deletion Shrinked vector after the chanel with random bits deletion Deletion of bits is RANDOM – Positions of deleted bits are UNKNOWN 11
2. A Framework for Security Enhancement Based on the Channels with Synchronization Errors 12
Paradigm I Homophonic Binary & Encryption Symmetric Error Correction Channel Encoding Paradigm II Error Correction Coding & Simmulation of a Encryption Channel with Synchronization Errors 13
Desired Model of Encryption an Attacker Should Face 14
Encryption at Party I Encryption at Party II Keystream Generator Keystream Generator + + Binary Channel Binary Channel with with Insertion Errors Deletion Errors 15 Attacker Side
A Framework for Encryption Based on Simulated Channels with Synchronization Errors stream-ciphering error correction + decoding Lightweight Party-I Keystream Generator error correction simulated channel + encoding with sync. errors stream-ciphering error correction + decoding Lightweight Party-II Keystream Generator error correction simulated channel + encoding with sync. errors 16
A Framework for Encryption with Asymmetric Implementation Complexity stream-ciphering error correction + decoding (after channel with erasures) Lightweight Party-I Keystream Generator random bits + embedding stream-ciphering + decimation Lightweight Party-II Keystream Generator error correction decimation + encoding 17 (for channel with erasures)
control of the simulator encoding for simulator binary of a block cipher erasure binary encryption channel erasure channel control of decoding decoding of the binary block cipher erasure error decryption correction code
A Linear Binary Block Code Encoding Paradigm binary vector Generator Matrix of Linear Block Code codeword channel with bit erasures degraded codeword x x x with erased bits 19
3. Particular Instantiation Under Security Evaluation
A Framework for Encryption and Decryption with Asymmetric Implementation Complexity encryption deterministic mapping Lightweight G’ Keystream Generator G C M Y X random bits + embedding Transmitting Entity simulator of a binary channel source of with insertions randomness decryption deterministic mapping Lightweight G’ Keystream Generator G C M X Y + decimation Receiving Entity
4. Information-Theoretic Security Evaluation
Preliminaries
Illustrative Numerical Example 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
5. Computational Complexity Security Evaluation
Y. Liron and M. Langberg, “A Characterization of the Number of Subsequences Obtained via the Deletion Channel”, IEEE Transactions on Information Theory , vol. 61, no. 5, pp. 2300-2312, May 2015.
Y. Liron and M. Langberg, “A Characterization of the Number of Subsequences Obtained via the Deletion Channel”, IEEE Transactions on Information Theory , vol. 61, no. 5, pp. 2300-2312, May 2015.
Concluding Notes
Main Messages • A paradigm for the • Evaluation of the security enhancement security enhancement based on results has been discussed regarding channels from the information- with synchronization theoretic and errors has been computational proposed complexity points of view 40
Thank You Very Much for the Attention, and QUESTIONS Please! 41
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