research-article

Secure Delegation of Isogeny Computations and Cryptographic Applications

Authors:

Osmanbey UzunkolAuthors Info & Claims

CCSW'19: Proceedings of the 2019 ACM SIGSAC Conference on Cloud Computing Security Workshop

Pages 29 - 42

https://doi.org/10.1145/3338466.3358913

Published: 11 November 2019 Publication History

Abstract

We address the problem of speeding up isogeny computation for supersingular elliptic curves over finite fields using untrusted computational resources like third party servers or cloud service providers (CSPs). We first propose new, efficient and secure delegation schemes. This especially enables resource-constrained devices (e.g. smart cards, RFID tags, tiny sensor nodes) to effectively deploy post-quantum isogeny-based cryptographic protocols. To the best of our knowledge, these new schemes are the first attempt to generalize the classical secure delegation schemes for group exponentiations and pairing computation to an isogeny-based post-quantum setting. Then, we apply these secure delegation subroutines to improve the performance of supersingular isogeny-based zero-knowledge proofs of identity. Our experimental results show that, at the 128-bit quantum-security level, the proving party only needs about 3% of the original protocol cost, while the verifying party's effort is fully reduced to comparison operations. Lastly, we also apply our delegation schemes to decrease the computational cost of the decryption step for the NIST postquantum standardization candidate SIKE.

References

[1]

Reza Azarderakhsh, Matthew Campagna, Craig Costello, LD De Feo, Basil Hess, A Jalali, D Jao, B Koziel, B LaMacchia, P Longa, et almbox. 2017. Supersingular isogeny key encapsulation. Submission to the NIST Post-Quantum Standardization project (2017).

[2]

DJ Bernstein and T Lange. 2019. Explicit-formulas database. https://www.hyperelliptic.org/EFD (2019).

[3]

Victor Boyko, Marcus Peinado, and Ramarathnam Venkatesan. 1998. Speeding up discrete log and factoring based schemes via precomputations. In International Conference on the Theory and Applications of Cryptographic Techniques. Springer, 221--235.

[4]

Denis X. Charles, Kristin E. Lauter, and Eyal Z." Goren. 2009. Cryptographic Hash Functions from Expander Graphs. Journal of Cryptology (2009), 93--113.

[5]

Xiaofeng Chen, Jin Li, Jianfeng Ma, Qiang Tang, and Wenjing Lou. 2014. New algorithms for secure outsourcing of modular exponentiations. IEEE Transactions on Parallel and Distributed Systems, Vol. 25, 9 (2014), 2386--2396.

[6]

Céline Chevalier, Fabien Laguillaumie, and Damien Vergnaud. 2016. Privately outsourcing exponentiation to a single server: cryptanalysis and optimal constructions. In European Symposium on Research in Computer Security. Springer, 261--278.

[7]

Andrew M. Childs, David Jao, and Vladimir Soukharev. 2014. Constructing elliptic curve isogenies in quantum subexponential time. J. Mathematical Cryptology, Vol. 8, 1 (2014), 1--29.

[8]

Craig Costello and Huseyin Hisil. 2017a. A Simple and Compact Algorithm for SIDH with Arbitrary Degree Isogenies. In Advances in Cryptology -- ASIACRYPT 2017. 303--329.

[9]

Craig Costello and Huseyin Hisil. 2017b. A simple and compact algorithm for SIDH with arbitrary degree isogenies. In International Conference on the Theory and Application of Cryptology and Information Security. Springer, 303--329.

[10]

Craig Costello and Benjamin Smith. 2017. Montgomery curves and their arithmetic: The case of large characteristic fields. IACR Cryptology ePrint Archive, Vol. 2017 (2017), 212.

[11]

Jean-marc Couveignes. 2006. Hard Homogeneous Spaces. https://eprint.iacr.org/2006/291.pdf.

[12]

Giacomo De Meulenaer, Francc ois Gosset, Francc ois-Xavier Standaert, and Olivier Pereira. 2008. On the energy cost of communication and cryptography in wireless sensor networks. In 2008 IEEE International Conference on Wireless and Mobile Computing, Networking and Communications. IEEE, 580--585.

Digital Library

[13]

Peter De Rooij. 1994. Efficient exponentiation using precomputation and vector addition chains. In Workshop on the Theory and Application of of Cryptographic Techniques. Springer, 389--399.

[14]

Javad Doliskani, Geovandro CCF Pereira, and Paulo SLM Barreto. 2017. Faster Cryptographic Hash Function From Supersingular Isogeny Graphs. IACR Cryptology ePrint Archive, Vol. 2017 (2017), 1202.

[15]

Armando Faz-Hernández, Julio López, Eduardo Ochoa-Jiménez, and Francisco Rodríguez-Henríquez. 2018. A faster software implementation of the supersingular isogeny Diffie-Hellman key exchange protocol. IEEE Trans. Comput., Vol. 67, 11 (2018), 1622--1636.

Digital Library

[16]

Luca De Feo, Simon Masson, Christophe Petit, and Antonio Sanso. 2019. Verifiable Delay Functions from Supersingular Isogenies and Pairings. https://eprint.iacr.org/2019/166.pdf.

[17]

Steven D Galbraith, Christophe Petit, Barak Shani, and Yan Bo Ti. 2016. On the security of supersingular isogeny cryptosystems. In International Conference on the Theory and Application of Cryptology and Information Security. Springer, 63--91.

[18]

Lov K Grover. 1996. A fast quantum mechanical algorithm for database search. arXiv preprint quant-ph/9605043 (1996).

[19]

Susan Hohenberger and Anna Lysyanskaya. 2005. How to securely outsource cryptographic computations. In Theory of Cryptography Conference. Springer, 264--282.

Digital Library

[20]

Amir Jalali, Reza Azarderakhsh, Mehran Mozaffarin Kermani, and David Jao. 2019. Towards Optimized and Constant-Time CSIDH on Embedded Devices. https://eprint.iacr.org/2019/297.pdf.

[21]

David Jao and Luca De Feo. 2011. Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. In International Workshop on Post-Quantum Cryptography. Springer, 19--34.

Digital Library

[22]

Mehmet Sabir Kiraz and Osmanbey Uzunkol. 2016. Efficient and verifiable algorithms for secure outsourcing of cryptographic computations. International Journal of Information Security, Vol. 15, 5 (2016), 519--537.

Digital Library

[23]

Microsoft Research. 2019. PQCrypto-SIDH v3.0 Library. https://github.com/Microsoft/PQCrypto-SIDH (2019).

[24]

Peter L Montgomery. 1987. Speeding the Pollard and elliptic curve methods of factorization. Mathematics of computation, Vol. 48, 177 (1987), 243--264.

[25]

Stephan Moritz and Osmanbey Uzunkol. 2018. A More Efficient Secure Fully Verifiable Delegation Scheme for Simultaneous Group Exponentiations. In International Conference on Intelligent, Secure, and Dependable Systems in Distributed and Cloud Environments. Springer, 74--93.

[26]

Phong Q Nguyen, Igor E Shparlinski, and Jacques Stern. 2001. Distribution of modular sums and the security of the server aided exponentiation. In Cryptography and Computational Number Theory. Springer, 331--342.

[27]

NIST. 2019. NIST Reveals 26 Algorithms Advancing to the Post-Quantum Crypto 'Semifinals'. https://www.nist.gov/news-events/news/2019/01/nist-reveals-26-algorithms-advancing-post-quantum-crypto-semifinals.

[28]

Christophe Petit. 2017. Faster Algorithms for Isogeny Problems Using Torsion Point Images. In Advances in Cryptology -- ASIACRYPT 2017. 330--353.

[29]

Joost Renes. 2018. Computing isogenies between Montgomery curves using the action of (0, 0). In International Conference on Post-Quantum Cryptography. Springer, 229--247.

[30]

Claus-Peter Schnorr. 1989. Efficient identification and signatures for smart cards. In Conference on the Theory and Application of Cryptology. Springer, 239--252.

Digital Library

[31]

Claus-Peter Schnorr. 1991. Efficient signature generation by smart cards. Journal of cryptology, Vol. 4, 3 (1991), 161--174.

Digital Library

[32]

Peter W. Shor. 1994. Algorithms for Quantum Computation: Discrete Logarithms and Factoring. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science. 124--134.

Digital Library

[33]

SIKE. 2018. Supersingular Isogeny Key Encapsulation. https://sike.org.

[34]

Joseph H Silverman. 2009. The arithmetic of elliptic curves. Vol. 106. Springer Science & Business Media.

[35]

Martin Lysoe Sommerseth and Haakon Hoeiland. 2015. Pohlig-Hellman Applied in Elliptic Curve Cryptography. (2015).

[36]

Anton Stolbunov. 2010. Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves. Adv. in Math. of Comm., Vol. 4, 2 (2010), 215--235.

[37]

Osmanbey Uzunkol, Jothi Rangasamy, and Lakshmi Kuppusamy. 2018. Hide the Modulus: a secure non-interactive fully verifiable delegation scheme for modular exponentiations via CRT. In International Conference on Information Security. Springer, 250--267.

[38]

Yujue Wang, Qianhong Wu, Duncan S Wong, Bo Qin, Sherman SM Chow, Zhen Liu, and Xiao Tan. 2014. Securely outsourcing exponentiations with single untrusted program for cloud storage. In European Symposium on Research in Computer Security. Springer, 326--343.

Digital Library

[39]

Nolan Winkler. [n.d.]. THE DISCRETE LOG PROBLEM AND ELLIPTIC CURVE CRYPTOGRAPHY. ( [n.,d.]).

[40]

Youngho Yoo, Reza Azarderakhsh, Amir Jalali, David Jao, and Vladimir Soukharev. 2017. A Post-quantum Digital Signature Scheme Based on Supersingular Isogenies. In Financial Cryptography and Data Security. Cham, 163--181.

Cited By

Pedersen RUzunkol O(2022)Delegating Supersingular Isogenies over $$\mathbb {F}_{p^2}$$ with Cryptographic ApplicationsInformation Security and Cryptology – ICISC 202110.1007/978-3-031-08896-4_5(95-118)Online publication date: 24-Jul-2022
https://doi.org/10.1007/978-3-031-08896-4_5
Di Crescenzo GKhodjaeva MKahrobaei DShpilrain V(2022)A Survey on Delegated ComputationDevelopments in Language Theory10.1007/978-3-031-05578-2_3(33-53)Online publication date: 6-May-2022
https://doi.org/10.1007/978-3-031-05578-2_3
Di Crescenzo GKhodjaeva MShpilrain VKahrobaei DKrishnan R(2021)Single-Server Delegation of Ring Multiplications from Quasilinear-time Clients2021 14th International Conference on Security of Information and Networks (SIN)10.1109/SIN54109.2021.9699330(1-8)Online publication date: 15-Dec-2021
https://doi.org/10.1109/SIN54109.2021.9699330
Show More Cited By

Index Terms

Secure Delegation of Isogeny Computations and Cryptographic Applications
1. Security and privacy
  1. Cryptography
  2. Network security
    1. Security protocols
2. Theory of computation
  1. Computational complexity and cryptography
    1. Cryptographic protocols
  2. Design and analysis of algorithms
    1. Online algorithms
      1. Adversary models

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cover image ACM Conferences

CCSW'19: Proceedings of the 2019 ACM SIGSAC Conference on Cloud Computing Security Workshop

November 2019

209 pages

ISBN:9781450368261

DOI:10.1145/3338466

Program Chairs:
Radu Sion
Stony Brook University, USA
,
Charalampos Papamanthou
University of Maryland, College Park, USA

Copyright © 2019 ACM.

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Published: 11 November 2019

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CCS '19: 2019 ACM SIGSAC Conference on Computer and Communications Security

November 11, 2019

London, United Kingdom

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Overall Acceptance Rate 37 of 108 submissions, 34%

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Cited By

Pedersen RUzunkol O(2022)Delegating Supersingular Isogenies over $$\mathbb {F}_{p^2}$$ with Cryptographic ApplicationsInformation Security and Cryptology – ICISC 202110.1007/978-3-031-08896-4_5(95-118)Online publication date: 24-Jul-2022
https://doi.org/10.1007/978-3-031-08896-4_5
Di Crescenzo GKhodjaeva MKahrobaei DShpilrain V(2022)A Survey on Delegated ComputationDevelopments in Language Theory10.1007/978-3-031-05578-2_3(33-53)Online publication date: 6-May-2022
https://doi.org/10.1007/978-3-031-05578-2_3
Di Crescenzo GKhodjaeva MShpilrain VKahrobaei DKrishnan R(2021)Single-Server Delegation of Ring Multiplications from Quasilinear-time Clients2021 14th International Conference on Security of Information and Networks (SIN)10.1109/SIN54109.2021.9699330(1-8)Online publication date: 15-Dec-2021
https://doi.org/10.1109/SIN54109.2021.9699330
Pedersen R(2021)DeCSIDH: Delegating Isogeny Computations in the CSIDH SettingProgress in Cryptology – INDOCRYPT 202110.1007/978-3-030-92518-5_16(337-361)Online publication date: 9-Dec-2021
https://doi.org/10.1007/978-3-030-92518-5_16

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