Abstract
Counter mode encryption uses a blockcipher to generate a key stream, which is subsequently used to encrypt data. The mode is known to achieve security up to the birthday bound. In this work we consider two approaches in literature to improve it to beyond birthday bound security: CENC by Iwata (FSE 2006) and its generalization NEMO by Lefranc et al. (SAC 2007). Whereas recent discoveries on CENC argued optimal security, the state of the art of NEMO is still sub-optimal. We draw connections among various instantiations of CENC and NEMO, and particularly prove that the improved optimal security bound on the CENC family carries over to a large class of variants of NEMO. We further conjecture that it also applies to the remaining variants, and discuss bottlenecks in proving so.
Keywords
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
This follows from looking at the modes at a pseudorandom function level, i.e., isolating the pseudorandom function \(F_k(N) = E_k(N\Vert 0)\oplus E_k(N\Vert 1)\) from the mode.
- 2.
In this work we are only concerned with binary linear codes.
References
Bellare, M., Desai, A., Jokipii, E., Rogaway, P.: A concrete security treatment of symmetric encryption. In: 38th Annual Symposium on Foundations of Computer Science, FOCS 1997, Miami Beach, Florida, USA, 19–22 October 1997, pp. 394–403. IEEE Computer Society (1997). https://doi.org/10.1109/SFCS.1997.646128
Bellare, M., Impagliazzo, R.: A tool for obtaining tighter security analyses of pseudorandom function based constructions, with applications to PRP to PRF conversion. Cryptology ePrint Archive, Report 1999/024 (1999). http://eprint.iacr.org/1999/024
Bellare, M., Krovetz, T., Rogaway, P.: Luby-Rackoff backwards: increasing security by making block ciphers non-invertible. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 266–280. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0054132
Bhattacharya, S., Nandi, M.: Revisiting variable output length XOR pseudorandom function. IACR Trans. Symmetric Cryptol. 2018(1), 314–335 (2018). https://doi.org/10.13154/tosc.v2018.i1.314-335
Dai, W., Hoang, V.T., Tessaro, S.: Information-theoretic indistinguishability via the Chi-squared method. In: Katz and Shacham [8], pp. 497–523. https://doi.org/10.1007/978-3-319-63697-9_17
Iwata, T.: New blockcipher modes of operation with beyond the birthday bound security. In: Robshaw, M. (ed.) FSE 2006. LNCS, vol. 4047, pp. 310–327. Springer, Heidelberg (2006). https://doi.org/10.1007/11799313_20
Iwata, T., Mennink, B., Vizár, D.: CENC is optimally secure. Cryptology ePrint Archive, Report 2016/1087 (2016). http://eprint.iacr.org/2016/1087
Katz, J., Shacham, H. (eds.): CRYPTO 2017. LNCS, vol. 10403. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63697-9
Lefranc, D., Painchault, P., Rouat, V., Mayer, E.: A generic method to design modes of operation beyond the birthday bound. In: Adams, C., Miri, A., Wiener, M. (eds.) SAC 2007. LNCS, vol. 4876, pp. 328–343. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-77360-3_21
Lucks, S.: The sum of PRPs is a secure PRF. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 470–484. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45539-6_34
Mennink, B., Neves, S.: Encrypted Davies-Meyer and its dual: towards optimal security using mirror theory. In: Katz and Shacham [8], pp. 556–583. https://doi.org/10.1007/978-3-319-63697-9_19
Nachef, V., Patarin, J., Volte, E.: Feistel Ciphers - Security Proofs and Cryptanalysis. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-49530-9
Patarin, J.: On linear systems of equations with distinct variables and small block size. In: Won, D.H., Kim, S. (eds.) ICISC 2005. LNCS, vol. 3935, pp. 299–321. Springer, Heidelberg (2006). https://doi.org/10.1007/11734727_25
Patarin, J.: A proof of security in O(2n) for the Xor of two random permutations. In: Safavi-Naini, R. (ed.) ICITS 2008. LNCS, vol. 5155, pp. 232–248. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85093-9_22
Patarin, J.: Introduction to mirror theory: analysis of systems of linear equalities and linear non equalities for cryptography. Cryptology ePrint Archive, Report 2010/287 (2010). http://eprint.iacr.org/2010/287
Singleton, R.C.: Maximum distance q-nary codes. IEEE Trans. Inf. Theory 10(2), 116–118 (1964). https://doi.org/10.1109/TIT.1964.1053661
Vermani, L.R.: Elements of Algebraic Coding Theory. CRC Press, Boca Raton (1996)
Acknowledgments
Bart Mennink is supported by a postdoctoral fellowship from the Netherlands Organisation for Scientific Research (NWO) under Veni grant 016.Veni.173.017.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Mennink, B. (2018). The Relation Between CENC and NEMO. In: Camenisch, J., Papadimitratos, P. (eds) Cryptology and Network Security. CANS 2018. Lecture Notes in Computer Science(), vol 11124. Springer, Cham. https://doi.org/10.1007/978-3-030-00434-7_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-00434-7_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-00433-0
Online ISBN: 978-3-030-00434-7
eBook Packages: Computer ScienceComputer Science (R0)