Skip to main content
SpringerLink
Log in
Book cover

International Colloquium on Theoretical Aspects of Computing

ICTAC 2022: Theoretical Aspects of Computing – ICTAC 2022 pp 272–289Cite as

Local XOR Unification: Definitions, Algorithms and Application to Cryptography

  • Conference paper
  • First Online:

  • 279 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13572))

Abstract

Unification techniques have been proven to be useful for formal analysis of cryptographic systems. In this paper, we introduce a new unification problem called local XOR unification, motivated by formal analysis of security of modes of operation. The goal in local XOR unification is to find a substitution making two terms equivalent modulo the theory of exclusive-or, but each variable is only allowed to be mapped to a term from a given set of terms. We present two versions of the local XOR unification problem, and give algorithms to solve them, proving soundness, completeness and termination.

The work is supported by NRL under contract N00173-19-1-G012.

This is a preview of subscription content, 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   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Notes

  1. 1.

    https://symcollab.github.io/CryptoSolve/.

References

  1. Akinyele, J.A., Green, M., Hohenberger, S.: Using SMT solvers to automate design tasks for encryption and signature schemes. In: Sadeghi, A., Gligor, V.D., Yung, M. (eds.) 2013 ACM SIGSAC Conference on Computer and Communications Security, CCS 2013, Berlin, Germany, 4–8 November 2013, pp. 399–410. ACM (2013)

    Google Scholar 

  2. Ambrona, M., Barthe, G., Schmidt, B.: Automated unbounded analysis of cryptographic constructions in the generic group model. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 822–851. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_29

    Chapter  MATH  Google Scholar 

  3. Anantharaman, S., Lin, H., Lynch, C., Narendran, P., Rusinowitch, M.: Cap unification: application to protocol security modulo homomorphic encryption. In: Feng, D., Basin, D.A., Liu, P. (eds.) Proceedings of the 5th ACM Symposium on Information, Computer and Communications Security, ASIACCS 2010, Beijing, China, 13–16 April 2010, pp. 192–203. ACM (2010). https://doi.org/10.1145/1755688.1755713

  4. Bellare, M., Rogaway, P., Wagner, D.: The EAX Mode of operation. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 389–407. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-25937-4_25

    Chapter  Google Scholar 

  5. Carmer, B., Rosulek, M.: Linicrypt: a model for practical cryptography. In: 36th Annual International Cryptology Conference, pp. 416–445 (2016)

    Google Scholar 

  6. Chichester, D., et al.: CryptoSolve: towards a tool for the symbolic analysis of cryptographic algorithms. In: 13th International Symposium on Games, Automata, Logics, and Formal Verification, Madrid, Spain (2022)

    Google Scholar 

  7. Erbatur, S., et al.: Asymmetric unification: a new unification paradigm for cryptographic protocol analysis. In: Bonacina, M.P. (ed.) CADE 2013. LNCS (LNAI), vol. 7898, pp. 231–248. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38574-2_16

    Chapter  Google Scholar 

  8. Escobar, S., et al.: Protocol analysis in Maude-NPA using unification modulo homomorphic encryption. In: Schneider-Kamp, P., Hanus, M. (eds.) Proceedings of the 13th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming, 20–22 July 2011, Odense, Denmark, pp. 65–76. ACM (2011). https://doi.org/10.1145/2003476.2003488

  9. Hoang, V.T., Katz, J., Malozemof, A.J.: Automated analysis and synthesis of authenticated encryption schemes. In: Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, pp. 84–95 (2015)

    Google Scholar 

  10. Knudsen, L.R. (ed.): Block chaining modes of operation. Department of Informatics, University of Bergen, Norway (2000)

    Google Scholar 

  11. Li, B., Micciancio, D.: Equational security proofs of oblivious transfer protocols. In: Abdalla, M., Dahab, R. (eds.) PKC 2018. LNCS, vol. 10769, pp. 527–553. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76578-5_18

    Chapter  Google Scholar 

  12. Li, B., Micciancio, D.: Symbolic security of garbled circuits. In: 31st IEEE Computer Security Foundations Symposium, CSF 2018, Oxford, United Kingdom, 9–12 July 2018, pp. 147–161. IEEE Computer Society (2018)

    Google Scholar 

  13. Lin, H., et al.: Algorithmic problems in the symbolic approach to the verification of automatically synthesized cryptosystems. In: Konev, B., Reger, G. (eds.) FroCoS 2021. LNCS (LNAI), vol. 12941, pp. 253–270. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-86205-3_14

    Chapter  Google Scholar 

  14. Liu, Z., Lynch, C.: Efficient general unification for XOR with homomorphism. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 407–421. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22438-6_31

    Chapter  Google Scholar 

  15. Malozemoff, A.J., Katz, J., Green, M.D.: Automated analysis and synthesis of block-cipher modes of operation. In: Computer Security Foundations Symposium (CSF), pp. 140–152 (2014)

    Google Scholar 

  16. Meadows, C.: Moving the bar on computationally sound exclusive-or. In: Bertino, E., Shulman, H., Waidner, M. (eds.) ESORICS 2021. LNCS, vol. 12973, pp. 275–295. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-88428-4_14

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Clarkson University, Potsdam, NY, 13699, USA

    Hai Lin & Christopher Lynch

Authors
  1. Hai Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christopher Lynch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Hai Lin or Christopher Lynch .

Editor information

Editors and Affiliations

  1. TU München, München, Germany

    Helmut Seidl

  2. Southwest University, Chongqing, China

    Zhiming Liu

  3. NASA Ames Research Center, Moffett Field, CA, USA

    Corina S. Pasareanu

Rights and permissions

Reprints and permissions

Copyright information

© 2022 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

Lin, H., Lynch, C. (2022). Local XOR Unification: Definitions, Algorithms and Application to Cryptography. In: Seidl, H., Liu, Z., Pasareanu, C.S. (eds) Theoretical Aspects of Computing – ICTAC 2022. ICTAC 2022. Lecture Notes in Computer Science, vol 13572. Springer, Cham. https://doi.org/10.1007/978-3-031-17715-6_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-17715-6_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-17714-9

  • Online ISBN: 978-3-031-17715-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation