Skip to main content
SpringerLink
Log in

Security Comparisons and Performance Analyses of Post-quantum Signature Algorithms

  • Conference paper
  • First Online:
Applied Cryptography and Network Security (ACNS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12727))

Included in the following conference series:

Abstract

Quantum computing challenges the computational hardness assumptions anchoring the security of public-key ciphers, such as the prime factorization and the discrete logarithm problem. To prepare for the quantum era and withstand the attacks equipped with quantum computing, the security and cryptography communities are designing new quantum-resistant public-key ciphers. National Institute of Standards and Technology (NIST) is collecting and standardizing the post-quantum ciphers, similarly to its past involvements in establishing DES and AES as symmetric cipher standards. The NIST finalist algorithms for public-key signatures are Dilithium, Falcon, and Rainbow. Finding common ground to compare these algorithms can be difficult because of their design, the underlying computational hardness assumptions (lattice based vs. multivariate based), and the different metrics used for security strength analyses in the previous research (qubits vs. quantum gates). We overcome such challenges and compare the security and the performances of the finalist post-quantum ciphers of Dilithium, Falcon, and Rainbow. For security comparison analyses, we advance the prior literature by using the depth-width cost for quantum circuits (DW cost) to measure the security strengths and by analyzing the security in Universal Quantum Gate Model and with Quantum Annealing. For performance analyses, we compare the algorithms’ computational loads in the execution time as well as the communication costs and implementation overheads when integrated with Transport Layer Security (TLS) and Transmission Control Protocol (TCP)/Internet Protocol (IP). Our work presents a security comparison and performance analysis as well as the trade-off analysis to inform the post-quantum cipher design and standardization to protect computing and networking in the post-quantum era.

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 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
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.

    Our work has been shared with NIST.

  2. 2.

    In addition to DW metrics, Jaques and Schanck [34] introduce G cost metrics for self-correcting quantum memory. However, self-correcting quantum memory is not available even theoretically. The two dimensional toric code [37], is not thermally stable [6]. Even though in a non-physical case of four spatial dimensions, it is thermally stable [7], it remains an open question if it is possible to implement it in three dimensions in which we live. Therefore, for our purposes, we use conservative DW cost metrics.

  3. 3.

    If they are comparable, using one-time pad can be an option for information-theoretic security resistant against (quantum-)computationally capable adversaries.

References

  1. ETSI-Standards. https://www.etsi.org. Accessed 1 Sept 2020

  2. Wireshark tool. https://www.wireshark.org. Accessed 1 Sept 2020

  3. Workshops and timeline. https://csrc.nist.gov/projects/post-quantum-cryptography/workshops-and-timeline. Accessed 1 Sept 2020

  4. Alagic, G., et al.: Status report on the first round of the NIST post-quantum cryptography standardization process. US Department of Commerce, National Institute of Standards and Technology (2019)

    Google Scholar 

  5. Alagic, G., et al.: Status report on the second round of the NIST post-quantum cryptography standardization process, NIST, Technical report, July 2020

    Google Scholar 

  6. Alicki, R., Fannes, M., Horodecki, M.: On thermalization in Kitaev’s 2D model. J. Phys. A: Math. Theoret. 42(6), 065303 (2009)

    Article  MathSciNet  Google Scholar 

  7. Alicki, R., Horodecki, M., Horodecki, P., Horodecki, R.: On thermal stability of topological qubit in Kitaev’s 4D model. Open Syst. Inf. Dyn. 17(01), 1–20 (2010)

    Article  MathSciNet  Google Scholar 

  8. Alkim, E., Ducas, L., Pöppelmann, T., Schwabe, P.: Post-quantum key exchange-a new hope. In: 25th USENIX Security Symposium (USENIX Security 16), pp. 327–343 (2016)

    Google Scholar 

  9. Alsina, D., Latorre, J.I.: Experimental test of Mermin inequalities on a five-qubit quantum computer. Phys. Rev. A 94(1), 012314 (2016)

    Article  Google Scholar 

  10. Amin, M.H.: Consistency of the adiabatic theorem. Phys. Rev. Lett. 102(22), 220401 (2009)

    Article  MathSciNet  Google Scholar 

  11. Basu, K., Soni, D., Nabeel, M., Karri, R.: NIST post-quantum cryptography-A hardware evaluation study. IACR Cryptology ePrint Archives, p. 47 (2019)

    Google Scholar 

  12. Bernstein, D.J.: Visualizing size-security tradeoffs for lattice-based encryption. IACR Cryptology ePrint Archives, p. 655 (2019)

    Google Scholar 

  13. Brassard, G., Høyer, P., Tapp, A.: Quantum cryptanalysis of hash and claw-free functions. ACM SIGACT News 28(2), 14–19 (1997)

    Article  Google Scholar 

  14. Caelli, W.J., Dawson, E.P., Rea, S.A.: PKI, elliptic curve cryptography, and digital signatures. Comput. Secur. 18(1), 47–66 (1999)

    Article  Google Scholar 

  15. Casanova, A., Faugere, J.C., Macario-Rat, G., Patarin, J., Perret, L., Ryckeghem, J.: GeMSS: a great multivariate short signature. Submission to NIST (2017)

    Google Scholar 

  16. Castelvecchi, D.: IBM’s quantum cloud computer goes commercial. Nat. News 543(7644), 159 (2017)

    Article  Google Scholar 

  17. Chen, L., et al.: Report on post-quantum cryptography, vol. 12. US Department of Commerce, National Institute of Standards and Technology (2016)

    Google Scholar 

  18. Cheung, D., Høyer, P., Wiebe, N.: Improved error bounds for the adiabatic approximation. J. Phys. A: Math. Theoret. 44(41), 415302 (2011)

    Article  MathSciNet  Google Scholar 

  19. Chuang, I.L., Gershenfeld, N., Kubinec, M.: Experimental implementation of fast quantum searching. Phys. Rev. Lett. 80(15), 3408 (1998)

    Article  Google Scholar 

  20. Dachman-Soled, D., Ducas, L., Gong, H., Rossi, M.: LWE with side information: attacks and concrete security estimation. IACR Cryptology ePrint Archives 2020, 292 (2020)

    Google Scholar 

  21. Deutsch, D.E.: Quantum computational networks. Proc. R. Soc. Lond. A Math. Phys. Sci. 425(1868), 73–90 (1989)

    MathSciNet  MATH  Google Scholar 

  22. Ding, J., Schmidt, D.: Rainbow, a new multivariable polynomial signature scheme. In: Ioannidis, J., Keromytis, A., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164–175. Springer, Heidelberg (2005). https://doi.org/10.1007/11496137_12

    Chapter  Google Scholar 

  23. Ducas, L., et al.: Crystals-dilithium: a lattice-based digital signature scheme. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2018, 238–268 (2018)

    Article  Google Scholar 

  24. Duong, D.H., Tran, H.T.N., et al.: Choosing subfields for LUOV and lifting fields for rainbow. IET Inf. Secur. 14(2), 196–201 (2020)

    Article  Google Scholar 

  25. Durr, C., Hoyer, P.: A quantum algorithm for finding the minimum. arXiv preprint quant-ph/9607014 (1996)

    Google Scholar 

  26. Finnila, A.B., Gomez, M., Sebenik, C., Stenson, C., Doll, J.D.: Quantum annealing: a new method for minimizing multidimensional functions. Chem. Phys. Lett. 219(5–6), 343–348 (1994)

    Article  Google Scholar 

  27. FIPS, P.: 186–4: Federal information processing standards publication. Digital Signature Standard (DSS). Information Technology Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD, pp. 20899–8900 (2013)

    Google Scholar 

  28. Fouque, P.A., et al.: Falcon: fast-Fourier lattice-based compact signatures over NTRU. Submission to the NIST’s post-quantum cryptography standardization process (2018)

    Google Scholar 

  29. Gao, Y.L., Chen, X.B., Chen, Y.L., Sun, Y., Niu, X.X., Yang, Y.X.: A secure cryptocurrency scheme based on post-quantum blockchain. IEEE Access 6, 27205–27213 (2018)

    Article  Google Scholar 

  30. Gottesman, D.: Theory of fault-tolerant quantum computation. Phys. Rev. A 57(1), 127 (1998)

    Article  Google Scholar 

  31. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 212–219 (1996)

    Google Scholar 

  32. Hauke, P., Katzgraber, H.G., Lechner, W., Nishimori, H., Oliver, W.D.: Perspectives of quantum annealing: methods and implementations. Rep. Prog. Phys. 83(5), 054401 (2020)

    Article  Google Scholar 

  33. Jacobson, V., Leres, C., McCanne, S.: TCPDUMP public repository (2003). http://www.tcpdump.org

  34. Jaques, S., Schanck, J.M.: Quantum cryptanalysis in the RAM model: claw-finding attacks on SIKE. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11692, pp. 32–61. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26948-7_2

    Chapter  MATH  Google Scholar 

  35. Kelly, J.: A preview of Bristlecone, Google’s new quantum processor. Google Research Blog 5 (2018)

    Google Scholar 

  36. Kipnis, A., Patarin, J., Goubin, L.: Unbalanced oil and vinegar signature schemes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 206–222. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48910-X_15

    Chapter  Google Scholar 

  37. Kitaev, A.Y.: Fault-tolerant quantum computation by anyons. Ann. Phys. 303(1), 2–30 (2003)

    Article  MathSciNet  Google Scholar 

  38. Messiah, A.: Quantum Mechanics: Translated [from the French] by J. Potter. North-Holland (1962)

    Google Scholar 

  39. Moses, T.: Quantum computing and cryptography. Entrust Inc., January 2009

    Google Scholar 

  40. Nejatollahi, H., Dutt, N., Ray, S., Regazzoni, F., Banerjee, I., Cammarota, R.: Post-quantum lattice-based cryptography implementations: A survey. ACM Comput. Surv. (CSUR) 51(6), 1–41 (2019)

    Article  Google Scholar 

  41. Ravi, P., Jhanwar, M.P., Howe, J., Chattopadhyay, A., Bhasin, S.: Exploiting determinism in lattice-based signatures: practical fault attacks on pqm4 implementations of NIST candidates. In: Proceedings of the 2019 ACM Asia Conference on Computer and Communications Security, pp. 427–440 (2019)

    Google Scholar 

  42. Regev, O.: Lattice-based cryptography. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 131–141. Springer, Heidelberg (2006). https://doi.org/10.1007/11818175_8

    Chapter  Google Scholar 

  43. Rezakhani, A., Kuo, W.J., Hamma, A., Lidar, D., Zanardi, P.: Quantum adiabatic brachistochrone. Phys. Rev. Lett. 103(8), 080502 (2009)

    Article  Google Scholar 

  44. Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978)

    Article  MathSciNet  Google Scholar 

  45. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)

    Article  MathSciNet  Google Scholar 

  46. Sikeridis, D., Kampanakis, P., Devetsikiotis, M.: Post-quantum authentication in TLS 1.3: a performance study. IACR Cryptology ePrint Archives, p. 71 (2020)

    Google Scholar 

  47. Stebila, D., Mosca, M.: Post-quantum key exchange for the internet and the open quantum safe project. In: Avanzi, R., Heys, H. (eds.) SAC 2016. LNCS, vol. 10532, pp. 14–37. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-69453-5_2

    Chapter  Google Scholar 

  48. Vandersypen, L.M., Steffen, M., Breyta, G., Yannoni, C.S., Sherwood, M.H., Chuang, I.L.: Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414(6866), 883–887 (2001)

    Article  Google Scholar 

  49. Wheatley, M.: D-Wave debuts new 5,000-qubit quantum computer, September 2019. https://siliconangle.com/2019/09/24/d-wave-debuts-new-5000-qubit-quantum-computer

Download references

Acknowledgment

This material is based upon work supported by the National Science Foundation under Grant No. 1922410. This research is also supported in part by Colorado State Bill 18-086.

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Colorado, Colorado Springs, USA

    Manohar Raavi, Simeon Wuthier, Pranav Chandramouli, Xiaobo Zhou & Sang-Yoon Chang

  2. Department of Physics and Energy Science, University of Colorado, Colorado Springs, USA

    Yaroslav Balytskyi

Authors
  1. Manohar Raavi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Simeon Wuthier
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pranav Chandramouli
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yaroslav Balytskyi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiaobo Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Sang-Yoon Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Manohar Raavi , Simeon Wuthier or Sang-Yoon Chang .

Editor information

Editors and Affiliations

  1. Waseda University, Tokyo, Japan

    Kazue Sako

  2. CISPA Helmholtz Center for Information Security, SaarbrĂĽcken, Germany

    Nils Ole Tippenhauer

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Raavi, M., Wuthier, S., Chandramouli, P., Balytskyi, Y., Zhou, X., Chang, SY. (2021). Security Comparisons and Performance Analyses of Post-quantum Signature Algorithms. In: Sako, K., Tippenhauer, N.O. (eds) Applied Cryptography and Network Security. ACNS 2021. Lecture Notes in Computer Science(), vol 12727. Springer, Cham. https://doi.org/10.1007/978-3-030-78375-4_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-78375-4_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-78374-7

  • Online ISBN: 978-3-030-78375-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation