Communications in Cryptology IACR CiC

Cracking the Mask: SASCA Against Local-Masked NTT for CRYSTALS-Kyber

Authors

Rafael Carrera Rodriguez, Florent Bruguier, Emanuele Valea, Pascal Benoit
Rafael Carrera Rodriguez ORCID
LIRMM, University of Montpellier, CNRS, Montpellier, France
Univ. Grenoble Alpes, CEA, List, Grenoble, France
rafael dot carrera-rodriguez at lirmm dot fr
Florent Bruguier ORCID
LIRMM, University of Montpellier, CNRS, Montpellier, France
florent dot bruguier at lirmm dot fr
Emanuele Valea ORCID
Univ. Grenoble Alpes, CEA, List, Grenoble, France
emanuele dot valea at cea dot fr
Pascal Benoit ORCID
LIRMM, University of Montpellier, CNRS, Montpellier, France
pascal dot benoit at lirmm dot fr

Abstract

Soft-Analytical Side-Channel Attacks (SASCAs) on lattice-based cryptography implementations have become a prominent vector of attack in the recent years, specially against the Number-Theoretic Transform (NTT). To address this issue, local masking with twiddle factors has been proposed as a countermeasure to protect the NTT against such attacks. In this paper we propose an adaptation of SASCA to local-masked NTT implementations, by modifying the factor graph representation to include the masking nodes. We evaluate the success rate of the attack with respect to the level of noise of simulated traces and the number of masks $u$ per layer. We show that the attack proves very successful in the lower values of $u$, by even outperforming the attack on the unmasked case. When $u$ is increased there is a gradual augmentation of security, which comes with an important overhead on performance. Thus, we question the practicality of this countermeasure when compared to other analyzed countermeasures in the state of the art, such as shuffling.

References

[ABD+21]
Roberto Avanzi, Joppe Bos, Léo Ducas, Eike Kiltz, Tancrède Lepoint, Vadim Lyubashevsky, John M. Schanck, Peter Schwabe, Gregor Seiler, and Damien Stehlé. CRYSTALS-Kyber: Algorithm Specifications and Supporting Documentation. 2021.
[ADPS16]
Erdem Alkim, Léo Ducas, Thomas Pöppelmann, and Peter Schwabe. Post-quantum Key Exchange - A New Hope. In Thorsten Holz and Stefan Savage, editors, 25th USENIX Security Symposium, USENIX Security 16, Austin, TX, USA, August 10-12, 2016, pages 327–343. 2016. USENIX Association.
[AG01]
Mehdi-Laurent Akkar and Christophe Giraud. An Implementation of DES and AES, Secure against Some Attacks. In Cetin K. Koç, David Naccache, and Christof Paar, editors, Cryptographic Hardware and Embedded Systems — CHES 2001, pages 309–318, Berlin, Heidelberg. 2001. Springer. DOI: 10.1007/3-540-44709-1_26
[CB23]
Gaëtan Cassiers and Olivier Bronchain. SCALib: A Side-Channel Analysis Library. Journal of Open Source Software, 8(86):5196, June 2023. DOI: 10.21105/joss.05196
[CBVB23]
Rafael Carrera Rodriguez, Florent Bruguier, Emanuele Valea, and Pascal Benoit. Correlation Electromagnetic Analysis on an FPGA Implementation of CRYSTALS-Kyber. In 2023 18th Conference on Ph.D Research in Microelectronics and Electronics (PRIME), pages 217–220, Valencia, Spain. June 2023. IEEE. DOI: 10.1109/PRIME58259.2023.10161764
[CRR03]
Suresh Chari, Josyula R. Rao, and Pankaj Rohatgi. Template Attacks. Cryptographic Hardware and Embedded Systems - CHES 2002, 2003. DOI: 10.1007/3-540-36400-5_3
[CRVBB24]
Rafael Carrera Rodriguez, Emanuele Valea, Florent Bruguier, and Pascal Benoit. Hardware Implementation and Security Analysis of Local-Masked NTT for CRYSTALS-Kyber. Publication info: Preprint.. 2024.
[CT65]
James W. Cooley and John W. Tukey. An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, 19(90):297–301, 1965. DOI: 10.1090/S0025-5718-1965-0178586-1
[FO99]
Eiichiro Fujisaki and Tatsuaki Okamoto. Secure Integration of Asymmetric and Symmetric Encryption Schemes. In Michael Wiener, editor, Advances in Cryptology — CRYPTO' 99, pages 537–554. 1999. Springer Berlin Heidelberg. DOI: 10.1007/s00145-011-9114-1
[GS66]
W. M. Gentleman and G. Sande. Fast Fourier Transforms: for fun and profit. In Proceedings of the November 7-10, 1966, fall joint computer conference on XX - AFIPS '66 (Fall), pages 563, San Francisco, California. 1966. ACM Press. DOI: 10.1145/1464291.1464352
[GT03]
Jovan D. Golić and Christophe Tymen. Multiplicative Masking and Power Analysis of AES. In Burton S. Kaliski, Cetin K. Koç, and Christof Paar, editors, Cryptographic Hardware and Embedded Systems - CHES 2002, pages 198–212, Berlin, Heidelberg. 2003. Springer. DOI: 10.1007/3-540-36400-5_16
[HHP+21]
Mike Hamburg, Julius Hermelink, Robert Primas, Simona Samardjiska, Thomas Schamberger, Silvan Streit, Emanuele Strieder, and Christine Van Vredendaal. Chosen Ciphertext k-Trace Attacks on Masked CCA2 Secure Kyber. IACR Transactions on Cryptographic Hardware and Embedded Systems, August 2021. DOI: 10.46586/tches.v2021.i4.88-113
[HSST23]
[KPP20]
Matthias J. Kannwischer, Peter Pessl, and Robert Primas. Single-Trace Attacks on Keccak. IACR Transactions on Cryptographic Hardware and Embedded Systems, June 2020. DOI: 10.46586/tches.v2020.i3.243-268
[LPR10]
Vadim Lyubashevsky, Chris Peikert, and Oded Regev. On Ideal Lattices and Learning with Errors over Rings. In Henri Gilbert, editor, Advances in Cryptology – EUROCRYPT 2010, pages 1–23, Berlin, Heidelberg. 2010. Springer. DOI: 10.1007/978-3-642-13190-5_1
[LS15]
Adeline Langlois and Damien Stehlé. Worst-Case to Average-Case Reductions for Module Lattices. Des. Codes Cryptography, 75(3):565–599, June 2015. DOI: 10.1007/s10623-014-9938-4
[LS19]
Vadim Lyubashevsky and Gregor Seiler. NTTRU: Truly Fast NTRU Using NTT. IACR Transactions on Cryptographic Hardware and Embedded Systems, May 2019. DOI: 10.46586/tches.v2019.i3.180-201
[MWK+22]
Catinca Mujdei, Lennert Wouters, Angshuman Karmakar, Arthur Beckers, Jose Maria Bermudo Mera, and Ingrid Verbauwhede. Side-Channel Analysis of Lattice-Based Post-Quantum Cryptography: Exploiting Polynomial Multiplication. ACM Transactions on Embedded Computing Systems, November 2022. DOI: 10.1145/3569420
[Nat]
National Institute of Standards and Technology. Post-Quantum Cryptography Standardization Process.
[{Nat}24]
National Institute of Standards and Technology. Module-Lattice-Based Key-Encapsulation Mechanism Standard. August 2024.
[PP19]
Peter Pessl and Robert Primas. More Practical Single-Trace Attacks on the Number Theoretic Transform. In Progress in Cryptology – LATINCRYPT 2019, pages 130–149. Springer International Publishing 2019. DOI: 10.1007/978-3-030-30530-7_7
[PPM17]
Robert Primas, Peter Pessl, and Stefan Mangard. Single-Trace Side-Channel Attacks on Masked Lattice-Based Encryption. In Lecture Notes in Computer Science, pages 513–533. Springer International Publishing 2017. DOI: 10.1007/978-3-319-66787-4_25
[RBRC22]
Prasanna Ravi, Shivam Bhasin, Sujoy Sinha Roy, and Anupam Chattopadhyay. On Exploiting Message Leakage in (Few) NIST PQC Candidates for Practical Message Recovery Attacks. IEEE Transactions on Information Forensics and Security, 17:684–699, 2022. DOI: 10.1109/TIFS.2021.3139268
[Reg05]
Oded Regev. On lattices, learning with errors, random linear codes, and cryptography. In Proceedings of the thirty-seventh annual ACM symposium on Theory of computing - STOC '05. 2005. ACM Press. DOI: 10.1145/1060590.1060603
[RPBC20]
Prasanna Ravi, Romain Poussier, Shivam Bhasin, and Anupam Chattopadhyay. On Configurable SCA Countermeasures Against Single Trace Attacks for the NTT. In Security, Privacy, and Applied Cryptography Engineering, pages 123–146. Springer International Publishing 2020. DOI: 10.1007/978-3-030-66626-2_7
[RSRCB20]
Prasanna Ravi, Sujoy Sinha Roy, Anupam Chattopadhyay, and Shivam Bhasin. Generic Side-channel attacks on CCA-secure lattice-based PKE and KEMs. IACR Transactions on Cryptographic Hardware and Embedded Systems, 2020. DOI: 10.46586/tches.v2020.i3.307-335
[Saa17]
Markku-Juhani O. Saarinen. Arithmetic coding and blinding countermeasures for lattice signatures. Journal of Cryptographic Engineering, 8(1):71–84, January 2017. Publisher: Springer Science and Business Media LLC DOI: 10.1007/s13389-017-0149-6
[UXT+21]
Rei Ueno, Keita Xagawa, Yutaro Tanaka, Akira Ito, Junko Takahashi, and Naofumi Homma. Curse of Re-encryption: A Generic Power/EM Analysis on Post-Quantum KEMs. IACR Transactions on Cryptographic Hardware and Embedded Systems, November 2021. Publisher: Universitatsbibliothek der Ruhr-Universitat Bochum DOI: 10.46586/tches.v2022.i1.296-322
[VCGS14]
Nicolas Veyrat-Charvillon, Benoît Gérard, and François-Xavier Standaert. Soft Analytical Side-Channel Attacks. In Lecture Notes in Computer Science, pages 282–296. Springer Berlin Heidelberg 2014. DOI: 10.1007/978-3-662-45611-8_15
[Wil27]
Edwin B Wilson. Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22(158):209–212, 1927. Publisher: Taylor & Francis DOI: 10.1080/01621459.1927.10502953
[ZBT19]
Timo Zijlstra, Karim Bigou, and Arnaud Tisserand. FPGA Implementation and Comparison of Protections Against SCAs for RLWE. In Lecture Notes in Computer Science, pages 535–555. Springer International Publishing 2019. DOI: 10.1007/978-3-030-35423-7_27
[ZPM+23]
Yiqiang Zhao, Shijian Pan, Haocheng Ma, Ya Gao, Xintong Song, Jiaji He, and Yier Jin. Side Channel Security Oriented Evaluation and Protection on Hardware Implementations of Kyber. IEEE Transactions on Circuits and Systems I: Regular Papers, 70(12):5025–5035, December 2023. Conference Name: IEEE Transactions on Circuits and Systems I: Regular Papers DOI: 10.1109/TCSI.2023.3288600

PDFPDF Open access

History
Submitted: 2025-04-07
Accepted: 2025-06-02
Published: 2025-07-07
How to cite

Rafael Carrera Rodriguez, Florent Bruguier, Emanuele Valea, and Pascal Benoit, Cracking the Mask: SASCA Against Local-Masked NTT for CRYSTALS-Kyber. IACR Communications in Cryptology, vol. 2, no. 2, Jul 07, 2025, doi: 10.62056/aesgbnja5.

License

Copyright is held by the author(s)

This work is licensed under a Creative Commons Attribution (CC BY) license.