Skip to main content
SpringerLink
Log in

One-Hot Conversion: Towards Faster Table-Based A2B Conversion

  • Conference paper
  • First Online:
Advances in Cryptology – EUROCRYPT 2023 (EUROCRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14007))

Abstract

Arithmetic to Boolean masking (A2B) conversion is a crucial technique in the masking of lattice-based post-quantum cryptography. It is also a crucial part of building a masked comparison which is one of the hardest to mask building blocks for active secure lattice-based encryption. We first present a new method, called one-hot conversion, to efficiently convert from higher-order arithmetic masking to Boolean masking using a variant of the higher-order table-based conversion of Coron et al. Secondly, we specialize our method to perform arithmetic to 1-bit Boolean functions. Our one-hot function can be applied to masking lattice-based encryption building blocks such as masked comparison or to determine the most significant bit of an arithmetically masked variable. In our benchmarks on a Cortex M4 processor, a speedup of 15 times is achieved over state-of-the-art table-based A2B conversions, bringing table-based A2B conversions within the performance range of the Boolean circuit-based A2B conversions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Note that the numbers given in [16] (Table 6) depict algorithmic operation counts and not cycles in an actual implementation. As there is no one-to-one match between the algorithmic operation count and the cycle count (e.g., memory accesses might be more expensive than local operations) one should be careful in comparing these numbers.

References

  1. Alagic, G., et al.: Status Report on the Second Round of the NIST Post-Quantum Cryptography Standardization Process (2020). https://csrc.nist.gov/publications/detail/nistir/8309/final

  2. Amiet, D., Curiger, A., Leuenberger, L., Zbinden, P.: Defeating NewHope with a single trace. In: Ding, J., Tillich, J.-P. (eds.) PQCrypto 2020. LNCS, vol. 12100, pp. 189–205. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-44223-1_11

    Chapter  Google Scholar 

  3. Atici, A.C., Batina, L., Gierlichs, B., Verbauwhede, I.: Power analysis on ntru implementations for RFIDs: First results (2008)

    Google Scholar 

  4. Bache, F., Paglialonga, C., Oder, T., Schneider, T., Güneysu, T.: High-speed masking for polynomial comparison in lattice-based kems. IACR TCHES 2020(3), 483–507 (2020). https://doi.org/10.13154/tches.v2020.i3.483-507, https://tches.iacr.org/index.php/TCHES/article/view/8598

  5. Barthe, G., et al.: Strong non-interference and type-directed higher-order masking. In: Weippl, E.R., Katzenbeisser, S., Kruegel, C., Myers, A.C., Halevi, S. (eds.) ACM CCS 2016, pp. 116–129. ACM Press (2016). https://doi.org/10.1145/2976749.2978427

  6. Barthe, G., et al.: Masking the GLP lattice-based signature scheme at any order. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10821, pp. 354–384. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78375-8_12

    Chapter  Google Scholar 

  7. Bhasin, S., D’Anvers, J.P., Heinz, D., Pöppelmann, T., Van Beirendonck, M.: Attacking and defending masked polynomial comparison. IACR TCHES 2021(3), 334–359 (2021). https://doi.org/10.46586/tches.v2021.i3.334-359, https://tches.iacr.org/index.php/TCHES/article/view/8977

  8. Bos, J.W., Gourjon, M., Renes, J., Schneider, T., van Vredendaal, C.: Masking kyber: first- and higher-order implementations. IACR TCHES 2021(4), 173–214 (2021). https://doi.org/10.46586/tches.v2021.i4.173-214, https://tches.iacr.org/index.php/TCHES/article/view/9064

  9. Chari, S., Jutla, C.S., Rao, J.R., Rohatgi, P.: Towards sound approaches to counteract power-analysis attacks. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 398–412. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48405-1_26

    Chapter  Google Scholar 

  10. Coron, J.-S., Großschädl, J., Tibouchi, M., Vadnala, P.K.: Conversion from arithmetic to boolean masking with logarithmic complexity. In: Leander, G. (ed.) FSE 2015. LNCS, vol. 9054, pp. 130–149. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48116-5_7

    Chapter  Google Scholar 

  11. Coron, J.-S., Großschädl, J., Vadnala, P.K.: Secure conversion between boolean and arithmetic masking of any order. In: Batina, L., Robshaw, M. (eds.) CHES 2014. LNCS, vol. 8731, pp. 188–205. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44709-3_11

    Chapter  MATH  Google Scholar 

  12. Coron, J.S., Gérard, F., Trannoy, M., Zeitoun, R.: High-order masking of ntru. Cryptology ePrint Archive, Paper 2022/1188 (2022). https://eprint.iacr.org/2022/1188, https://eprint.iacr.org/2022/1188

  13. Coron, J.S., Rondepierre, F., Zeitoun, R.: High order masking of look-up tables with common shares. IACR TCHES 2018(1), 40–72 (2018). https://doi.org/10.13154/tches.v2018.i1.40-72, https://tches.iacr.org/index.php/TCHES/article/view/832

  14. Coron, J.-S., Tchulkine, A.: A new algorithm for switching from arithmetic to boolean masking. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds.) CHES 2003. LNCS, vol. 2779, pp. 89–97. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45238-6_8

    Chapter  Google Scholar 

  15. Coron, J.S., Gérard, F., Montoya, S., Zeitoun, R.: High-order polynomial comparison and masking lattice-based encryption. Cryptology ePrint Archive, Report 2021/1615 (2021). https://ia.cr/2021/1615

  16. Coron, J.S., Gérard, F., Montoya, S., Zeitoun, R.: High-order table-based conversion algorithms and masking lattice-based encryption. Cryptology ePrint Archive, Report 2021/1314 (2021). https://ia.cr/2021/1314

  17. D’Anvers, J.P., Heinz, D., Pessl, P., van Beirendonck, M., Verbauwhede, I.: Higher-order masked ciphertext comparison for lattice-based cryptography. Cryptology ePrint Archive, Report 2021/1422 (2021). https://ia.cr/2021/1422

  18. D’Anvers, J.P., Karmakar, A., Roy, S.S., Vercauteren, F.: SABER. Technical report, National Institute of Standards and Technology (2019). https://csrc.nist.gov/projects/post-quantum-cryptography/round-2-submissions

  19. D’Anvers, J.P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing attacks on error correcting codes in post-quantum schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop, TIS 2019, pp. 2–9. Association for Computing Machinery, New York (2019). https://doi.org/10.1145/3338467.3358948

  20. D’Anvers, J.P., Van Beirendonck, M., Verbauwhede, I.: Revisiting higher-order masked comparison for lattice-based cryptography: Algorithms and bit-sliced implementations. Cryptology ePrint Archive, Report 2022/110 (2022). https://ia.cr/2022/110

  21. Debraize, B.: Efficient and provably secure methods for switching from arithmetic to boolean masking. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 107–121. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33027-8_7

    Chapter  MATH  Google Scholar 

  22. Fritzmann, T., et al.: Masked accelerators and instruction set extensions for post-quantum cryptography. Cryptology ePrint Archive, Report 2021/479 (2021). https://eprint.iacr.org/2021/479

  23. Fujisaki, E., Okamoto, T.: Secure integration of asymmetric and symmetric encryption schemes. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 537–554. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48405-1_34

    Chapter  Google Scholar 

  24. Goubin, L.: A sound method for switching between boolean and arithmetic masking. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 3–15. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44709-1_2

    Chapter  Google Scholar 

  25. Guo, Q., Johansson, T., Nilsson, A.: A key-recovery timing attack on post-quantum primitives using the fujisaki-okamoto transformation and its application on FrodoKEM. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12171, pp. 359–386. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56880-1_13

    Chapter  Google Scholar 

  26. Heinz, D., Kannwischer, M.J., Land, G., Pöppelmann, T., Schwabe, P., Sprenkels, D.: First-order masked kyber on arm cortex-m4. Cryptology ePrint Archive, Report 2022/058 (2022). https://ia.cr/2022/058

  27. Kundu, S., D’Anvers, J.P., Beirendonck, M.V., Karmakar, A., Verbauwhede, I.: Higher-order masked saber. Cryptology ePrint Archive, Paper 2022/389 (2022). https://eprint.iacr.org/2022/389, https://eprint.iacr.org/2022/389

  28. Lyubashevsky, V., et al.: CRYSTALS-DILITHIUM. Technical report, National Institute of Standards and Technology (2020). https://csrc.nist.gov/projects/post-quantum-cryptography/round-3-submissions

  29. Migliore, V., Gérard, B., Tibouchi, M., Fouque, P.-A.: Masking dilithium. In: Deng, R.H., Gauthier-Umaña, V., Ochoa, M., Yung, M. (eds.) ACNS 2019. LNCS, vol. 11464, pp. 344–362. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21568-2_17

    Chapter  MATH  Google Scholar 

  30. NIST Computer Security Division: Post-Quantum Cryptography Standardization (2016). https://csrc.nist.gov/Projects/Post-Quantum-Cryptography

  31. Oder, T., Schneider, T., Pöppelmann, T., Güneysu, T.: Practical CCA2-secure masked Ring-LWE implementations. IACR TCHES 2018(1), 142–174 (2018). https://doi.org/10.13154/tches.v2018.i1.142-174, https://tches.iacr.org/index.php/TCHES/article/view/836

  32. Prest, T., et al.: FALCON. Technical report, National Institute of Standards and Technology (2020). https://csrc.nist.gov/projects/post-quantum-cryptography/round-3-submissions

  33. Primas, R., Pessl, P., Mangard, S.: Single-trace side-channel attacks on masked lattice-based encryption. In: Fischer, W., Homma, N. (eds.) CHES 2017. LNCS, vol. 10529, pp. 513–533. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66787-4_25

    Chapter  Google Scholar 

  34. Ravi, P., Roy, S.S., Chattopadhyay, A., Bhasin, S.: Generic side-channel attacks on CCA-secure lattice-based PKE and KEMs. IACR TCHES 2020(3), 307–335 (2020). https://doi.org/10.13154/tches.v2020.i3.307-335, https://tches.iacr.org/index.php/TCHES/article/view/8592

  35. Reparaz, O., Sinha Roy, S., Vercauteren, F., Verbauwhede, I.: A masked ring-LWE implementation. In: Güneysu, T., Handschuh, H. (eds.) CHES 2015. LNCS, vol. 9293, pp. 683–702. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48324-4_34

    Chapter  Google Scholar 

  36. Schneider, T., Paglialonga, C., Oder, T., Güneysu, T.: Efficiently masking binomial sampling at arbitrary orders for lattice-based crypto. In: Lin, D., Sako, K. (eds.) PKC 2019. LNCS, vol. 11443, pp. 534–564. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_18

    Chapter  Google Scholar 

  37. Schwabe, P., et al.: CRYSTALS-KYBER. Technical report, National Institute of Standards and Technology (2020). https://csrc.nist.gov/projects/post-quantum-cryptography/round-3-submissions

  38. Silverman, J.H., Whyte, W.: Timing attacks on NTRUEncrypt via variation in the number of hash calls. In: Abe, M. (ed.) CT-RSA 2007. LNCS, vol. 4377, pp. 208–224. Springer, Heidelberg (2006). https://doi.org/10.1007/11967668_14

    Chapter  MATH  Google Scholar 

  39. Ueno, R., Xagawa, K., Tanaka, Y., Ito, A., Takahashi, J., Homma, N.: Curse of re-encryption: a generic power/em analysis on post-quantum kems. Cryptology ePrint Archive, Report 2021/849 (2021). https://ia.cr/2021/849

  40. Van Beirendonck, M., D’Anvers, J., Karmakar, A., Balasch, J., Verbauwhede, I.: A side-channel-resistant implementation of SABER. ACM JETC 17(2), 10:1–10:26 (2021)

    Google Scholar 

  41. Van Beirendonck, M., D’Anvers, J.P., Verbauwhede, I.: Analysis and comparison of table-based arithmetic to boolean masking. IACR TCHES 2021(3), 275–297 (2021). https://doi.org/10.46586/tches.v2021.i3.275-297, https://tches.iacr.org/index.php/TCHES/article/view/8975

  42. Wang, A., Zheng, X., Wang, Z.: Power analysis attacks and countermeasures on ntru-based wireless body area networks. KSII Trans. Internet Inf. Syst. (TIIS) 7(5), 1094–1107 (2013)

    Article  Google Scholar 

  43. Xu, Z., Pemberton, O., Roy, S.S., Oswald, D.: Magnifying side-channel leakage of lattice-based cryptosystems with chosen ciphertexts: the case study of kyber. Cryptology ePrint Archive, Report 2020/912 (2020). https://eprint.iacr.org/2020/912

Download references

Acknowledgements

I would like to thank Michiel Van Beirendonck for the interesting discussions on this topic. This work was supported in part by CyberSecurity Research Flanders with reference number VR20192203, the Research Council KU Leuven (C16/15/058) and the Horizon 2020 ERC Advanced Grant (101020005 Belfort). Jan-Pieter D’Anvers is funded by FWO (Research Foundation - Flanders) as junior post-doctoral fellow (contract number 133185 / 1238822N LV).

Author information

Authors and Affiliations

  1. imec-COSIC KU Leuven, Kasteelpark Arenberg 10 - bus 2452, 3001, Leuven, Belgium

    Jan-Pieter D’Anvers

Authors
  1. Jan-Pieter D’Anvers
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jan-Pieter D’Anvers .

Editor information

Editors and Affiliations

  1. Bar-Ilan University, Ramat Gan, Israel

    Carmit Hazay

  2. Simula UiB, Bergen, Norway

    Martijn Stam

Rights and permissions

Reprints and permissions

Copyright information

© 2023 International Association for Cryptologic Research

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

D’Anvers, JP. (2023). One-Hot Conversion: Towards Faster Table-Based A2B Conversion. In: Hazay, C., Stam, M. (eds) Advances in Cryptology – EUROCRYPT 2023. EUROCRYPT 2023. Lecture Notes in Computer Science, vol 14007. Springer, Cham. https://doi.org/10.1007/978-3-031-30634-1_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-30634-1_21

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-30633-4

  • Online ISBN: 978-3-031-30634-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships

Search

Navigation