A Stream Cipher Based on Chaotic Permutations

Authors
1 Kharazmi University
2 Sharif University of Technology
Abstract
In this paper we introduce a word-based stream cipher consisting of a chaotic part operating as a chaotic permutation and a linear part, both of which designed on a finite field. We will show that this system can operate in both synchronized and self-synchronized modes. More specifically, we show that in the self-synchronized mode the stream cipher has a receiver operating as an unknown input observer. In addition, we evaluate the statistical uniformity of the output and also show that the system in the self-synchronized mode is much faster and lighter for implementation compared to similar self-synchronized systems with equal key size.
Keywords

1. آزادی یزدی آذین، بررسی امنیت سیستم رمزنگاری دنباله‌ای بر مبنای جابجایی آشوبی، پایان‌نامۀ کارشناسی ارشد، دانشگاه صنعتی شریف (‎1389). 2. اقبالی حمیدرضا، بررسی و مقایسۀ سامانۀ رمزنگاری دنباله‌ای سوئیچینگ، پایان‌نامۀ کارشناسی ارشد، دانشگاه صنعتی شریف (‎1391‎). 3. Addabbo T‎. ‎, Alioto M‎. ‎, Fort‎ A‎. ‎, "A ‎‎variability-‎t‎‎olerant ‎f‎‎eedback ‎t‎‎echnique for throughput. ‎maximization of TRBGs with ‎p‎‎‎redefined ‎E‎ntropy"‎, ‎J‎. ‎of Circuits‎, ‎Systems and Computers 19 (4) (2010) 1-17.‎‎ 4. Addabbo T‎. ‎‎, ‎Fort ‎A‎.‎, ‎ ‎Rocchi S‎., ‎Vignoli V‎., "Digitized chaos for pseudo-random number generation in cryptography", Studies in Computational Intelligence, Vol 354‎, ‎(2011) ‎67-97.‎‎‎ 5. Amigo‎ J‎., ‎ ‎Kocarev L‎.‎, ‎ ‎Szczepanski‎ J‎., "Theory and ‎p‎ractice of chaotic cryptography", Physic letters A‎, ‎366 (2007) ‎211-216.‎ 6. ‎Baptista M‎.‎S‎. ‎, "Cryptography with ‎c‎‎haos", ‎Physics Letters A‎, ‎240‎ (‎1998) ‎50-54‎.‎ 7. ‎Blum L‎., ‎Blum M‎.‎, ‎ ‎Shub M‎., "A simple unpredictable psuedorandom number generator", ‎SIAM J‎. ‎on Computing a5(2) ‎(1986) ‎364-383‎. 8. ‎Daemen J‎.,"Cipher and ‎h‎ash ‎f‎unction ‎d‎esign ‎s‎trategies ‎b‎ased on ‎l‎inear and differential, ‎c‎ryptanalysis‎"‎‎, ‎PhD thesis‎, ‎Katholieke Universiteit Leuven‎, ‎Belgique ‎(1995).‎ 9. ‎Daemen J‎., Govartz R., Vanderwalle J.‎, "On ‎the‎ design of ‎h‎igh speed self-synchronizing stream ciphers"‎, ‎ICCS/ISITA ‎(1992).‎ 10. ‎Daemen J‎., ‎Kitsos P‎., "The self-synchronizing stream cipher Mosquito‎: ‎eSTREAM documentation‎, ‎ version 2" (2005).‎ 11. ‎Daemen J‎., ‎Kitos P‎. ‎, "The Self-synchronizing ‎s‎tream cipher Moustique", New stream ‎c‎ipher, ‎d‎esigns‎, ‎LNCS 4986‎ ‎(2007) ‎‎‎210-223‎.‎ 12. ‎Daemen J‎. ‎, ‎Lano‎J‎., ‎Preneel B‎.‎, "Chosen ‎c‎iphertext ‎a‎ttack on SSS", Submission to ECRYPT (2005).‎ 13. ‎Devaney R.L‎.‎, "An Introduction to ‎c‎haotic ‎d‎ynamical ‎‎s‎ystems‎,‎ 2nd Ed."‎, ‎Westview‎ Press ‎(2003‎).‎ 14. ‎Gürkaynak‎ F‎.‎K‎., ‎et ‎al‎. "Hardware ‎e‎valuation of eSTREAM ‎c‎andidates‎: Achterbahn‎, ‎Grain‎, ‎MICKEY‎, ‎MOSQUITO‎, ‎SFINKS‎, ‎Trivium‎, ‎VEST‎, ‎ZK-Crypt", ‎Submission to ECRYPT (2006).‎ 15. ‎Jakimoski G‎., ‎Klapper‎‎A‎., "Analysis of some recently proposed chaos-based‎ ‎encryption algorithms"‎, ‎Physics Letters A‎, ‎291 (2001) ‎381-384. 16. ‎Jakimoski G‎., ‎ ‎Klapper A‎., "Differential and ‎l‎inear ‎p‎robabilities of a‎ ‎b‎lock-‎e‎ncryption Cipher", ‎IEEE Trans‎. ‎on circuits and systems-I‎: ‎Fundumental Theory and Applications‎, ‎Vol‎. ‎50‎, ‎No‎. ‎1‎ ‎(2003).‎ 17. ‎Joux A‎.‎, ‎Muller‎F‎.‎, "Loosening the KNOT", FSE 2003, ‎LNCS 2887 ‎(2003) ‎87-99‎.‎ 18. ‎Joux A‎.‎, ‎Muller‎F‎.‎, "Chosen-Ciphertext ‎a‎ttacks ‎a‎gainst MOSQUITO", FSE 2006‎, ‎LNCS 4047 ‎(2006) ‎‎‎390-‎404.‎ 19. ‎Kocarev L‎.‎, ‎ ‎Jakimoski G‎., "Logistic map as a block encryption algorithm"‎,‎Physics Letters A,‎ 289 ‎(2001) 199-206‎. 20. ‎Kocarev L‎.‎, ‎‎‎Lian‎‎S‎‎.‎, "Chaos-Based ‎‎‎Cryptography;‎‎‎ Theory, Algorithms and Applications"‎, Springer‎ (2011).‎‎‎‎‎‎‎ 21. ‎Kocarev L‎., "A ‎c‎haos-‎b‎ased approach to the design of secure substitutions", ‎Physics Letters A‎, ‎343‎ ‎(2005).‎ 22. ‎Kocarev L‎., ‎ Szczepanski J‎., "‎Discrete Chaos I‎: ‎t‎‎‎heory"‎, ‎IEEE Trans. on Circuits and Systems-I‎: ‎Regular papers, Vol‎. ‎53‎, ‎No‎. ‎6 ‎(2006).‎ 23. ‎Maurer‎ U‎.‎m‎., "New ‎a‎pproaches to the ‎d‎esign of ‎s‎elf-‎s‎ynchronizing ‎s‎tream ‎c‎iphers"‎‎, EUROCRYPT'91,‎ ‎458-471‎, ‎(1992).‎ 24. ‎Menezes A‎.‎, ‎‎van Oorschot P‎.‎, ‎‎Vanstone S‎.‎, "Handbook of applied cryptography", ‎CRC Press‎, ‎(2006).‎ 25. Millerioux G‎.‎, "A ‎c‎onnection ‎b‎etween ‎c‎haotic and ‎c‎onventional ‎c‎ryptography", ‎in IEEE Trans. On circuits and systems‎, ‎Vol‎. ‎55 No‎. ‎6‎, ‎1695-1703‎, ‎(2008)‎. 26. ‎Millerioux G‎.‎, ‎Amigo‎ J.M‎., ‎Daafouz J‎.‎, "A connection between chaotic message-embedding and conventional‎ ‎self-synchronizing stream ciphers", NOLTA 2006‎, ‎Bologna‎, ‎Italy ‎(2006).‎ 27. NIST Special Publication 800-22 Rev.1a‎, "‎A statistical test suite for random and ‎psu‎edorandom number generators for cryptographic applications" ‎(2010).‎ 28. ‎Papadimitriou‎ S‎., ‎Bezerianos A‎., ‎Bountis T‎., ‎Palvlides G‎.‎, "Secure communication protocols with discrete chaotic map"‎, ‎Jour. Of systems Architecture 47‎ ‎(2001) ‎61-72‎.‎ 29. Rose G‎. ‎‎, ‎ ‎Hawkes P‎. ‎, ‎Paddon‎ M‎., ‎Wiggers de Vries‎ M‎., "Primitive ‎s‎pecification for SSS"‎, ‎Submitted eStream Project, ‎(2005).‎ 30. ‎Tan P‎.‎V‎.‎, ‎ ‎Millerioux G‎., ‎Daafouz J‎. ‎, "A ‎compariss‎on between the message embedded cryptosystem‎ ‎and the self-synchronous stream cipher Mosquito", 18th Euro‎. ‎Conf‎. ‎on Circuit Theory and Design‎, ‎ECCTD'2007‎, ‎Séville‎, ‎Spain (2007).‎ 31. ‎Tan P‎.‎V‎.‎, ‎Millerioux‎ G‎., ‎Daafouz J‎.‎, "Left invertibility‎, ‎flatness and identifiability of‎ ‎switched linear dynamical systems‎: ‎a framework for cryptographic applications", Intl‎. J. ‎of Control 83‎, ‎1 (2010) 145-153.‎