Skip to main content
SpringerLink
Log in

Arithmetic Circuit Implementations of S-boxes for SKINNY and PHOTON in MPC

  • Conference paper
  • First Online:
Computer Security – ESORICS 2023 (ESORICS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14344))

Included in the following conference series:

  • 289 Accesses

Abstract

Secure multi-party computation (MPC) enables multiple distrusting parties to compute a function while keeping their respective inputs private. In a threshold implementation of a symmetric primitive, e.g., of a block cipher, each party holds a share of the secret key or of the input block. The output block is computed without reconstructing the secret key. This enables the construction of distributed TPMs or transciphering for secure data transmission in/out of the MPC context.

This paper investigates implementation approaches for the lightweight primitives SKINNY and PHOTON in arithmetic circuits. For these primitives, we identify arithmetic expressions for the S-box that result in smaller arithmetic circuits compared to the Boolean expressions from the literature. We validate the optimization using a generic actively secure MPC protocol and obtain 18% faster execution time with 49% less communication data for SKINNY-64-128 and 27% to 74% faster execution time with 49% to 81% less data for PHOTON \(P_{100}\) and \(P_{288}\). Furthermore, we find a new set of parameters for the heuristic method of polynomial decomposition, introduced by Coron, Roy and Vivek, specialized for SKINNY’s 8-bit S-box. We reduce the multiplicative depth from 9 to 5.

This work is supported by the Flemish Government through FWO SBO project MOZAIK S003321N.

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 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
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.

    https://csrc.nist.gov/Projects/Lightweight-Cryptography.

  2. 2.

    However, the players must know an upper bound on the number of required multiplication triples resp. random bits.

  3. 3.

    Since the SKINNY reference does not specify operations in a field, we are free to pick a suitable one.

  4. 4.

    The parameters cannot be used to decompose the AES S-box, for instance.

  5. 5.

    Each party runs on a separate machine with 4 cores and 16 GB RAM connected with a bandwidth of 10 Gbit/sec and <1 ms latency.

References

  1. Abidin, A., et al.: MOZAIK: an end-to-end secure data sharing platform. In: Second ACM Data Economy Workshop (DEC 2023), Seattle, WA, USA, 18 June 2023, p. 7. ACM (2023)

    Google Scholar 

  2. Albrecht, M., Grassi, L., Rechberger, C., Roy, A., Tiessen, T.: MiMC: efficient encryption and cryptographic hashing with minimal multiplicative complexity. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 191–219. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_7

    Chapter  Google Scholar 

  3. Albrecht, M.R., Rechberger, C., Schneider, T., Tiessen, T., Zohner, M.: Ciphers for MPC and FHE. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 430–454. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5_17

    Chapter  Google Scholar 

  4. Aly, A., Ashur, T., Ben-Sasson, E., Dhooghe, S., Szepieniec, A.: Design of symmetric-key primitives for advanced cryptographic protocols. IACR Trans. Symmetric Cryptol. 2020(3), 1–45 (2020)

    Article  Google Scholar 

  5. Beaver, D.: Efficient multiparty protocols using circuit randomization. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 420–432. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-46766-1_34

    Chapter  Google Scholar 

  6. Beierle, C., et al.: The SKINNY family of block ciphers and its low-latency variant MANTIS. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 123–153. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53008-5_5

    Chapter  Google Scholar 

  7. Bogdanov, A., et al.: PRESENT: an ultra-lightweight block cipher. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 450–466. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74735-2_31

    Chapter  Google Scholar 

  8. Brandão, L.T.A.N., Peralta, R.: NIST IR 8214C ipd NIST First Call for Multi-Party Threshold Schemes (Initial Public Draft) (2023)

    Google Scholar 

  9. Canteaut, A., et al.: Stream ciphers: a practical solution for efficient homomorphic-ciphertext compression. J. Cryptol. 31(3), 885–916 (2018)

    Article  MathSciNet  Google Scholar 

  10. Chase, M., et al.: Post-quantum zero-knowledge and signatures from symmetric-key primitives. In: Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, CCS 2017, pp. 1825–1842. Association for Computing Machinery (2017)

    Google Scholar 

  11. Coron, J.-S., Roy, A., Vivek, S.: Fast evaluation of polynomials over binary finite fields and application to side-channel countermeasures. In: Batina, L., Robshaw, M. (eds.) CHES 2014. LNCS, vol. 8731, pp. 170–187. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44709-3_10

    Chapter  Google Scholar 

  12. Damgård, I., Keller, M.: Secure multiparty AES. In: Sion, R. (ed.) FC 2010. LNCS, vol. 6052, pp. 367–374. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14577-3_31

    Chapter  Google Scholar 

  13. Damgård, I., Keller, M., Larraia, E., Miles, C., Smart, N.P.: Implementing AES via an actively/covertly secure dishonest-majority MPC protocol. In: Visconti, I., De Prisco, R. (eds.) SCN 2012. LNCS, vol. 7485, pp. 241–263. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32928-9_14

    Chapter  Google Scholar 

  14. Damgård, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., Smart, N.P.: Practical covertly secure MPC for dishonest majority – or: breaking the SPDZ limits. In: Crampton, J., Jajodia, S., Mayes, K. (eds.) ESORICS 2013. LNCS, vol. 8134, pp. 1–18. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40203-6_1

    Chapter  Google Scholar 

  15. Damgård, I., Pastro, V., Smart, N., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_38

    Chapter  Google Scholar 

  16. Damgård, I., Zakarias, R.: Fast oblivious AES a dedicated application of the MiniMac protocol. In: Pointcheval, D., Nitaj, A., Rachidi, T. (eds.) AFRICACRYPT 2016. LNCS, vol. 9646, pp. 245–264. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-31517-1_13

    Chapter  Google Scholar 

  17. Dobraunig, C., et al.: Rasta: a cipher with low ANDdepth and few ANDs per bit. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10991, pp. 662–692. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96884-1_22

    Chapter  Google Scholar 

  18. Dobraunig, C., Grassi, L., Guinet, A., Kuijsters, D.: Ciminion: symmetric encryption based on Toffoli-gates over large finite fields. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12697, pp. 3–34. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77886-6_1

    Chapter  Google Scholar 

  19. Durak, F.B., Guajardo, J.: Improving the efficiency of AES protocols in multi-party computation. In: Borisov, N., Diaz, C. (eds.) FC 2021. LNCS, vol. 12674, pp. 229–248. Springer, Heidelberg (2021). https://doi.org/10.1007/978-3-662-64322-8_11

    Chapter  Google Scholar 

  20. Grassi, L., Khovratovich, D., Rechberger, C., Roy, A., Schofnegger, M.: Poseidon: a new hash function for zero-knowledge proof systems. In: Bailey, M., Greenstadt, R. (eds.) 30th USENIX Security Symposium, USENIX Security 2021, pp. 519–535. USENIX Association (2021)

    Google Scholar 

  21. Grassi, L., Lüftenegger, R., Rechberger, C., Rotaru, D., Schofnegger, M.: On a generalization of substitution-permutation networks: the HADES design strategy. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 674–704. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45724-2_23

    Chapter  Google Scholar 

  22. Grassi, L., Onofri, S., Pedicini, M., Sozzi, L.: Invertible quadratic non-linear layers for MPC-/FHE-/ZK-friendly schemes over Fnp application to Poseidon. IACR Trans. Symmetric Cryptol. 2022(3), 20–72 (2022)

    Article  Google Scholar 

  23. Grassi, L., Øygarden, M., Schofnegger, M., Walch, R.: From Farfalle to Megafono via Ciminion: the PRF hydra for MPC applications. In: Hazay, C., Stam, M. (eds.) EUROCRYPT 2023. LNCS, vol. 14007, pp. 255–286. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-30634-1_9

    Chapter  Google Scholar 

  24. Grassi, L., Rechberger, C., Rotaru, D., Scholl, P., Smart, N.P.: MPC-friendly symmetric key primitives. In: Weippl, E.R., Katzenbeisser, S., Kruegel, C., Myers, A.C., Halevi, S. (eds.) Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, pp. 430–443. ACM (2016)

    Google Scholar 

  25. Guo, J., Peyrin, T., Poschmann, A.: The PHOTON family of lightweight hash functions. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 222–239. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22792-9_13

    Chapter  Google Scholar 

  26. Keller, M.: MP-SPDZ: a versatile framework for multi-party computation. In: Ligatti, J., Ou, X., Katz, J., Vigna, G. (eds.) 2020 ACM SIGSAC Conference on Computer and Communications Security, CCS 2020, pp. 1575–1590. ACM (2020)

    Google Scholar 

  27. Keller, M., Orsini, E., Rotaru, D., Scholl, P., Soria-Vazquez, E., Vivek, S.: Faster secure multi-party computation of AES and DES using lookup tables. In: Gollmann, D., Miyaji, A., Kikuchi, H. (eds.) ACNS 2017. LNCS, vol. 10355, pp. 229–249. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-61204-1_12

    Chapter  Google Scholar 

  28. Keller, M., Orsini, E., Scholl, P.: MASCOT: faster malicious arithmetic secure computation with oblivious transfer. In: Weippl, E.R., Katzenbeisser, S., Kruegel, C., Myers, A.C., Halevi, S. (eds.) Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, pp. 830–842. ACM (2016)

    Google Scholar 

  29. Keller, M., Pastro, V., Rotaru, D.: Overdrive: making SPDZ great again. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 158–189. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_6

    Chapter  Google Scholar 

  30. Lorünser, T., Wohner, F.: Performance comparison of two generic MPC-frameworks with symmetric ciphers. In: Samarati, P., di Vimercati, S.D.C., Obaidat, M.S., Ben-Othman, J. (eds.) Proceedings of the 17th International Joint Conference on e-Business and Telecommunications, ICETE 2020, SECRYPT, vol. 2, pp. 587–594. ScitePress (2020)

    Google Scholar 

  31. Mandal, K., Gong, G.: Can LWC and PEC be friends?: evaluating lightweight ciphers in privacy-enhancing cryptography. In: Fourth Lightweight Cryptography Workshop. NIST (2020)

    Google Scholar 

  32. Méaux, P., Journault, A., Standaert, F.-X., Carlet, C.: Towards stream ciphers for efficient FHE with low-noise ciphertexts. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9665, pp. 311–343. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49890-3_13

    Chapter  Google Scholar 

  33. National Institute of Standards and Technology: Specification for the ADVANCED ENCRYPTION STANDARD (AES). Federal Information Processing Standards Publications 197 (2001)

    Google Scholar 

  34. National Institute of Standards and Technology: Secure Hash Standard (SHS). Federal Information Processing Standards Publications 180-4, August 2015

    Google Scholar 

  35. Zahur, S., Rosulek, M., Evans, D.: Two halves make a whole - reducing data transfer in garbled circuits using half gates. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 220–250. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_8

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. COSIC, KU Leuven, Leuven, Belgium

    Aysajan Abidin, Erik Pohle & Bart Preneel

Authors
  1. Aysajan Abidin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erik Pohle
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bart Preneel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Erik Pohle .

Editor information

Editors and Affiliations

  1. University of California, Irvine, CA, USA

    Gene Tsudik

  2. University of Padua, Padua, Italy

    Mauro Conti

  3. Delft University of Technology, Delft, The Netherlands

    Kaitai Liang

  4. Delft University of Technology, Delft, The Netherlands

    Georgios Smaragdakis

A Appendix

A Appendix

We detail the used (inverse) embeddings in Table 7. The inversion of the embedding of \(\mathbb {F}_{2^{4}}\) and \(\mathbb {F}_{2^{8}}\) only costs 4 and 8 random bits from \(\mathcal {F}_{\textsf {Bit}}\), respectively.

Table 7. The used embeddings from \(\mathbb {F}_{2^{4}}\) and \(\mathbb {F}_{2^{8}}\) into \(\mathbb {F}_{2^{40}}\) on a bit level. Let \(b_3 X^3 + b_2 X^2 + b_1 X + b_0\) be an element in \(\mathbb {F}_{2^{4}}\) and \(b_7 X^7 + b_6 X^6 + b_5 X^5 + b_4 X^4 + b_3 X^3 + b_2 X^2 + b_1 X + b_0\) be an element in \(\mathbb {F}_{2^{8}}\). An element in \(\mathbb {F}_{2^{40}}\) is \(\sum _{i=0}^{39} b_i'Y^i\). Bits \(b_i'\) that are not set below are 0.
Full size table
Fig. 5.
figure 5

Additional figures for shortest addition chain and the trade-off between multiplication and free squares.

Full size image

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Abidin, A., Pohle, E., Preneel, B. (2024). Arithmetic Circuit Implementations of S-boxes for SKINNY and PHOTON in MPC. In: Tsudik, G., Conti, M., Liang, K., Smaragdakis, G. (eds) Computer Security – ESORICS 2023. ESORICS 2023. Lecture Notes in Computer Science, vol 14344. Springer, Cham. https://doi.org/10.1007/978-3-031-50594-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-50594-2_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-50593-5

  • Online ISBN: 978-3-031-50594-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation