Skip to main content

Error-Free Lattice-Based Key Encapsulation Mechanism Based on Ring-LWE

  • Conference paper
  • First Online:
Foundations and Practice of Security (FPS 2020)

Abstract

As most of the published lattice based encryptions and key encapsulation mechanisms have decryption failure, they are subjected to side-channel attacks. In this paper, we construct an error-free lattice-based key encapsulation mechanism (KEM) which is based on LPR encryption. We also examine some new classes of cyclotomic polynomials for the new error-free lattice-based KEM. The proposed error-free KEM has a reasonable public key size of about 1.472 Kbytes for 128-bit quantum security level. This is comparable to those submitted to the NIST PQC standardization.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Ajtai, M., Dwork, C.: A public-key cryptosystem with worst-case/average-case equivalence. In: 29th ACM STOC, pp. 284–293. ACM Press, May 1997

    Google Scholar 

  2. Ajtai, M.: The shortest vector problem in \(L_2\) is NP-hard for randomized reductions (extended abstract). In: Vitter, J.S. (ed.) Proceedings of the Thirtieth Annual ACM Symposium on the Theory of Computing, Dallas, Texas, USA, 23–26 May 1998, pp. 10–19. ACM (1998). https://doi.org/10.1145/276698.276705

  3. Albrecht, M.R., Player, R., Scott, S.: On the concrete hardness of learning with errors. J. Math. Cryptol. 9(3), 169–203 (2015)

    Article  MathSciNet  Google Scholar 

  4. Alkim, E., et al.: NewHope. https://newhopecrypto.org/data/NewHope_2019_04_10.pdf

  5. Alkim, E., et al.: FrodoKEM learning with errors key encapsulation. https://frodokem.org/files/FrodoKEM-specification-20190702.pdf

  6. Baan, H., et al.: Round5: KEM and PKE based on (ring) learning with rounding. https://round5.org/Supporting_Documentation/Round5_Submission.pdf

  7. Bernstein, D.J., Chuengsatiansup, C., Lange, T., van Vredendaal, C.: NTRU Prime: reducing attack surface at low cost. In: Adams, C., Camenisch, J. (eds.) SAC 2017. LNCS, vol. 10719, pp. 235–260. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-72565-9_12

    Chapter  Google Scholar 

  8. Bernstein, D.J., Chuengsatiansup, C., Lange, T., van Vredendaal, C.: NTRU Prime. NIST submission “Supporting Documentation”. https://ntruprime.cr.yp.to/nist.html

  9. Bernstein, D.J., Persichetti, E.: Towards KEM unification. Cryptology ePrint Archive, report 2018/526 (2018). https://eprint.iacr.org/2018/526

  10. Bindel, N., Schanck, J.M.: Decryption failure is more likely after success. In: Ding, J., Tillich, J.-P. (eds.) PQCrypto 2020. LNCS, vol. 12100, pp. 206–225. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-44223-1_12

    Chapter  Google Scholar 

  11. 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)

    Article  MathSciNet  Google Scholar 

  12. van Emde Boas, P.: Another NP-complete partition problem and the complexity of computing short vectors in lattices. Technical report 81-04, Mathematics Department, University of Amsterdam (1981)

    Google Scholar 

  13. Chen, Y., Nguyen, P.Q.: BKZ 2.0: better lattice security estimates. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 1–20. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_1

    Chapter  Google Scholar 

  14. Chatterjee, S., Koblitz, N., Menezes, A., Sarkar, P.: Another look at tightness II: practical issues in cryptography. In: Phan, R.C.-W., Yung, M. (eds.) Mycrypt 2016. LNCS, vol. 10311, pp. 21–55. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-61273-7_3

    Chapter  Google Scholar 

  15. Dachman-Soled, D., Ducas, L., Gong, H., Rossi, M.: LWE with side information: attacks and concrete security estimation. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12171, pp. 329–358. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56880-1_12

    Chapter  Google Scholar 

  16. D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption failure attacks on IND-CCA secure lattice-based schemes. In: Lin, D., Sako, K. (eds.) PKC 2019. LNCS, vol. 11443, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19

    Chapter  Google Scholar 

  17. D’Anvers, J.-P., Rossi, M., Virdia, F.: (One) failure is not an option: bootstrapping the search for failures in lattice-based encryption schemes. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12107, pp. 3–33. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45727-3_1

    Chapter  Google Scholar 

  18. D’Anvers, J.-P., Karmakar, A., Sinha Roy, S., Vercauteren, F.: Saber: module-LWR based key exchange, CPA-secure encryption and CCA-secure KEM. In: Joux, A., Nitaj, A., Rachidi, T. (eds.) AFRICACRYPT 2018. LNCS, vol. 10831, pp. 282–305. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89339-6_16

    Chapter  Google Scholar 

  19. Fujisaki, E., Okamoto, T.: Secure integration of asymmetric and symmetric encryption schemes. J. Cryptol. 26(1), 80–101 (2013). https://doi.org/10.1007/s00145-011-9114-1

    Article  MathSciNet  MATH  Google Scholar 

  20. Guo, Q., Johansson, T., Yang, J.: A novel CCA attack using decryption errors against LAC. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11921, pp. 82–111. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34578-5_4

    Chapter  Google Scholar 

  21. Hamburg, M.: Post-quantum cryptography proposal: THREEBEARS. https://www.shiftleft.org/papers/threebears/nist-submission.pdf

  22. Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities, Cambridge Mathematical Library, 2nd edn. Cambridge University Press, Cambridge (1952)

    Google Scholar 

  23. Hofheinz, D., Hövelmanns, K., Kiltz, E.: A modular analysis of the Fujisaki-Okamoto transformation. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 341–371. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70500-2_12

    Chapter  MATH  Google Scholar 

  24. Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: a ring-based public key cryptosystem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 267–288. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0054868

    Chapter  Google Scholar 

  25. Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W., Bohlinger, J.D. (eds.) Complexity of Computer Computations. IRSS, pp. 85–103. Springer, Boston (1972). https://doi.org/10.1007/978-1-4684-2001-2_9

    Chapter  Google Scholar 

  26. Lu, X., et al.: LAC: lattice-based cryptosystems. https://cs.rit.edu/~ats9095/csci762/pdfs/LAC.pdf

  27. Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1–23. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_1

    Chapter  Google Scholar 

  28. Lyubashevsky, V., Peikert, C., Regev, O.: A toolkit for ring-LWE cryptography. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 35–54. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_3

    Chapter  Google Scholar 

  29. Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. J. ACM 60(6), 1–35 (2013). Article no. 43. Early version in EUROCRYPT 2010. https://doi.org/10.1145/2535925

  30. Nguyen, P., Stern, J.: Cryptanalysis of the Ajtai-Dwork cryptosystem. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 223–242. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0055731

    Chapter  Google Scholar 

  31. Peikert, C., Regev, O., Stephens-Davidowitz, N.: Pseudorandomness of ring-LWE for any ring and modulus. In: STOC, pp. 461–473. ACM (2017)

    Google Scholar 

  32. Regev O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC, pp. 84–93. ACM (2005)

    Google Scholar 

  33. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM 56(6), 1–40 (2009). Preliminary version in STOC 2005

    Article  MathSciNet  Google Scholar 

  34. Saito, T., Xagawa, K., Yamakawa, T.: Tightly-secure key-encapsulation mechanism in the quantum random oracle model. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 520–551. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_17

    Chapter  MATH  Google Scholar 

  35. Sarkar, P., Singha, S.: Verifying solutions to LWE with implications for concrete security. Adv. Math. Commun. (2020). https://www.aimsciences.org/article/doi/10.3934/amc.2020057

  36. Schnorr, C.-P., Euchner, M.: Lattice basis reduction: improved practical algorithms and solving subset sum problems. Math. Program. 66, 181–199 (1994). https://doi.org/10.1007/BF01581144

    Article  MathSciNet  MATH  Google Scholar 

  37. Xu, Z., et al.: 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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Theo Fanuela Prabowo .

Editor information

Editors and Affiliations

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

Tan, C.H., Prabowo, T.F. (2021). Error-Free Lattice-Based Key Encapsulation Mechanism Based on Ring-LWE. In: Nicolescu, G., Tria, A., Fernandez, J.M., Marion, JY., Garcia-Alfaro, J. (eds) Foundations and Practice of Security. FPS 2020. Lecture Notes in Computer Science(), vol 12637. Springer, Cham. https://doi.org/10.1007/978-3-030-70881-8_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-70881-8_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-70880-1

  • Online ISBN: 978-3-030-70881-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics