Abstract
Learning Parity with Noise (LPN) is an attractive post-quantum cryptosystem for low-resource devices due to its simplicity. Communicating parties only require the use of AND and XOR gates to generate or verify LPN cryptogram samples exchanged between the parties. However, the LPN setup is complicated by different parameter choices including key length, noise rate, sample size, and verification window which can determine the usability and security of the implementation. To address advances in LPN cryptanalysis, recommendations for ever increasing key lengths have made LPN no longer feasible for low-resource devices. In this paper, we use a series of experiments to simulate and cryptanalyze LPN authentication under different parameter values to arrive at recommended values suitable for low-resource devices. We also examine the impact of limiting the key lifespan of the LPN secret vector as a means to balance security while keeping key lengths relatively short.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In the case of LPN, the key is also referred to as the secret vector. For this paper, we will use key and secret vector interchangeably for readability purposes.
- 2.
Including 3M, EM Microelectronic, Fujitsu, NXP and Rockwell Automation.
References
2013, I...: Information technology-radio frequency identification for item management-part 6: Parameters for air interface communications at 860 MHz to 960 MHz general (2013)
Belaïd, S., Coron, J.-S., Fouque, P.-A., Gérard, B., Kammerer, J.-G., Prouff, E.: Improved side-channel analysis of finite-field multiplication. In: Güneysu, T., Handschuh, H. (eds.) CHES 2015. LNCS, vol. 9293, pp. 395–415. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48324-4_20
Bernstein, D.J., Lange, T.: Never trust a bunny. In: Hoepman, J.-H., Verbauwhede, I. (eds.) RFIDSec 2012. LNCS, vol. 7739, pp. 137–148. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36140-1_10
Blum, A., Furst, M., Kearns, M., Lipton, R.J.: Cryptographic primitives based on hard learning problems. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 278–291. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48329-2_24
Blum, A., Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. J. ACM (JACM) 50(4), 506–519 (2003)
Bogos, S., Tramer, F., Vaudenay, S.: On solving LPN using BKW and variants. Cryptogr. Commun. 8(3), 331–369 (2016)
Brakerski, Z., Lyubashevsky, V., Vaikuntanathan, V., Wichs, D.: Worst-case hardness for LPN and cryptographic hashing via code smoothing. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11478, pp. 619–635. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17659-4_21
Bringer, J., Chabanne, H., Dottax, E.: HB\(^{++}\): a lightweight authentication protocol secure against some attacks. In: Second international Workshop on Security, Privacy and Trust in Pervasive and Ubiquitous Computing (SecPerU 2006), pp. 28–33. IEEE (2006)
Esser, A., Kübler, R., May, A.: LPN decoded. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 486–514. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63715-0_17
Gad, A.F.: PyGAD: An Intuitive Genetic Algorithm Python Library (2021)
Geurts, P., Ernst, D., Wehenkel, L.: Extremely randomized trees. Mach. Learn. 63(1), 3–42 (2006)
Gilbert, H., Robshaw, M.J.B., Seurin, Y.: HB#: increasing the security and efficiency of HB\(^+\). In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 361–378. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_21
Grilo, A.B., Kerenidis, I., Zijlstra, T.: Learning-with-errors problem is easy with quantum samples. Phys. Rev. A 99(3), 032314 (2019)
Guo, Q., Johansson, T., Löndahl, C.: Solving LPN using covering codes. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 1–20. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45611-8_1
Heyse, S., Kiltz, E., Lyubashevsky, V., Paar, C., Pietrzak, K.: Lapin: an efficient authentication protocol based on ring-LPN. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 346–365. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34047-5_20
Holland, J.H.: Genetic algorithms. Sci. Am. 267(1), 66–73 (1992)
Hopper, N.J., Blum, M.: Secure human identification protocols. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 52–66. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45682-1_4
Juels, A., Weis, S.A.: Authenticating pervasive devices with human protocols. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 293–308. Springer, Heidelberg (2005). https://doi.org/10.1007/11535218_18
Kearns, M.: Efficient noise-tolerant learning from statistical queries. J. ACM (JACM) 45(6), 983–1006 (1998)
Kiltz, E., Pietrzak, K., Venturi, D., Cash, D., Jain, A.: Efficient authentication from hard learning problems. J. Cryptol. 30(4), 1238–1275 (2017)
Kübler, R.: Where Machine Learning meets Cryptography (2020). https://towardsdatascience.com/where-machine-learning-meets-cryptography-b4a23ef54c9e. Accessed Mar 2022
Kübler, R.J.: Time-memory trade-offs for the learning parity with noise problem. Ph.D. thesis, Ruhr University Bochum, Germany (2018)
Lenstra, A.K., Verheul, E.R.: Selecting cryptographic key sizes. J. Cryptol. 14(4), 255–293 (2001)
Levieil, É., Fouque, P.-A.: An improved LPN algorithm. In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 348–359. Springer, Heidelberg (2006). https://doi.org/10.1007/11832072_24
Lyubashevsky, V., Masny, D.: Man-in-the-middle secure authentication schemes from LPN and weak PRFs. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 308–325. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_18
Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48285-7_33
NIST: Post-Quantum Cryptography: Round 3 Submissions (2019). https://csrc.nist.gov/projects/post-quantum-cryptography/round-3-submissions. Accessed Mar 2022
Wiggers, T., Samardjiska, S.: Practically solving LPN. In: 2021 IEEE International Symposium on Information Theory (ISIT), pp. 2399–2404. IEEE (2021)
Acknowledgement
This project is supported by the Ministry of Education, Singapore, under its MOE AcRF Tier 2 grant (MOE2018-T2-1-111). The computational work for this article was partially performed on resources of the National Supercomputing Centre, Singapore (https://www.nscc.sg).
The work is also supported by A*STAR under its RIE2020 Advanced Manufacturing and Engineering (AME) Industry Alignment Fund - Pre Positioning (IAF-PP) Award A19D6a0053. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of A*STAR.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
A Algorithm Pseudocode
A Algorithm Pseudocode
We assume the existence of a function Random(n, p) that returns a binary matrix/vector of size n where each element has a probability p to be 1. The secret key s is randomly generated.
We performed a sub-experiment to measure the efficacy of the fitness function by varying the number of erroneous bits in \(s^{\prime }\) and noise rate to find any advantage that adversaries may be able to uncover.
Return values for simulated fitness function for \(k=64,\delta =0.5\)
Figure 8 shows the graph which plots the return values of the fitness function for error bits in \(s^{\prime }\) from 0 to \(\frac{k}{2}\) in increments of 1 and for noise rate \(\tau \) = {0.05, 0.125, 0.25, 0.4}. For clarity purposes, we have fixed \(k=64,\delta =0.5,n=500\). It clearly shows that the fitness function is unable to tell the difference in the number of error bits for partial solutions since the fitness values become close to zero once there is at least one error bit in \(s^{\prime }\).
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this paper
Cite this paper
Tan, T.G., Soh, D.W., Zhou, J. (2022). Calibrating Learning Parity with Noise Authentication for Low-Resource Devices. In: Alcaraz, C., Chen, L., Li, S., Samarati, P. (eds) Information and Communications Security. ICICS 2022. Lecture Notes in Computer Science, vol 13407. Springer, Cham. https://doi.org/10.1007/978-3-031-15777-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-031-15777-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-15776-9
Online ISBN: 978-3-031-15777-6
eBook Packages: Computer ScienceComputer Science (R0)