Fast Polynomial Inversion for Post Quantum QC-MDPC Cryptography

Nir Drucker; Shay Gueron; Dusan Kostic

doi:10.1007/978-3-030-49785-9_8

Fast Polynomial Inversion for Post Quantum QC-MDPC Cryptography

Nir Drucker, Shay Gueron, Dusan Kostic

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The NIST PQC standardization project evaluates multiple new designs for post-quantum Key Encapsulation Mechanisms (KEMs). Some of them present challenging tradeoffs between communication bandwidth and computational overheads. An interesting case is the set of QC-MDPC based KEMs. Here, schemes that use the Niederreiter framework require only half the communication bandwidth compared to schemes that use the McEliece framework. However, this requires costly polynomial inversion during the key generation, which is prohibitive when ephemeral keys are used. One example is BIKE, where the BIKE-1 variant uses McEliece and the BIKE-2 variant uses Niederreiter. This paper shows an optimized constant-time polynomial inversion method that makes the computation costs of BIKE-2 key generation tolerable. We report a speedup of$$11.8{\times }$$ over the commonly used NTL library, and$$55.5{\times }$$ over OpenSSL. We achieve additional speedups by leveraging the latest Intel’s Vector-instructions on a laptop machine,$$14.3{\times }$$ over NTL and$$96.8{\times }$$ over OpenSSL. With this, BIKE-2 becomes a competitive variant of BIKE.

Original language	English
Title of host publication	Cyber Security Cryptography and Machine Learning - 4th International Symposium, CSCML 2020, Proceedings
Editors	Shlomi Dolev, Gera Weiss, Vladimir Kolesnikov, Sachin Lodha
Publisher	Springer
Pages	110-127
Number of pages	18
ISBN (Print)	9783030497842
DOIs	https://doi.org/10.1007/978-3-030-49785-9_8
State	Published - 2020
Event	4th International Symposium on Cyber Security Cryptography and Machine Learning, CSCML 2020 - Beersheba, Israel Duration: 2 Jul 2020 → 3 Jul 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12161 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	4th International Symposium on Cyber Security Cryptography and Machine Learning, CSCML 2020
Country/Territory	Israel
City	Beersheba
Period	2/07/20 → 3/07/20

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

Keywords

BIKE
Constant-time algorithm
Constant-time implementation
Polynomial inversion
QC-MDPC codes

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-49785-9_8

Cite this

Drucker, N., Gueron, S., & Kostic, D. (2020). Fast Polynomial Inversion for Post Quantum QC-MDPC Cryptography. In S. Dolev, G. Weiss, V. Kolesnikov, & S. Lodha (Eds.), Cyber Security Cryptography and Machine Learning - 4th International Symposium, CSCML 2020, Proceedings (pp. 110-127). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12161 LNCS). Springer. https://doi.org/10.1007/978-3-030-49785-9_8

Drucker, Nir ; Gueron, Shay ; Kostic, Dusan. / Fast Polynomial Inversion for Post Quantum QC-MDPC Cryptography. Cyber Security Cryptography and Machine Learning - 4th International Symposium, CSCML 2020, Proceedings. editor / Shlomi Dolev ; Gera Weiss ; Vladimir Kolesnikov ; Sachin Lodha. Springer, 2020. pp. 110-127 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "The NIST PQC standardization project evaluates multiple new designs for post-quantum Key Encapsulation Mechanisms (KEMs). Some of them present challenging tradeoffs between communication bandwidth and computational overheads. An interesting case is the set of QC-MDPC based KEMs. Here, schemes that use the Niederreiter framework require only half the communication bandwidth compared to schemes that use the McEliece framework. However, this requires costly polynomial inversion during the key generation, which is prohibitive when ephemeral keys are used. One example is BIKE, where the BIKE-1 variant uses McEliece and the BIKE-2 variant uses Niederreiter. This paper shows an optimized constant-time polynomial inversion method that makes the computation costs of BIKE-2 key generation tolerable. We report a speedup of$$11.8{\times }$$ over the commonly used NTL library, and$$55.5{\times }$$ over OpenSSL. We achieve additional speedups by leveraging the latest Intel{\textquoteright}s Vector-instructions on a laptop machine,$$14.3{\times }$$ over NTL and$$96.8{\times }$$ over OpenSSL. With this, BIKE-2 becomes a competitive variant of BIKE.",

keywords = "BIKE, Constant-time algorithm, Constant-time implementation, Polynomial inversion, QC-MDPC codes",

author = "Nir Drucker and Shay Gueron and Dusan Kostic",

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Drucker, N, Gueron, S & Kostic, D 2020, Fast Polynomial Inversion for Post Quantum QC-MDPC Cryptography. in S Dolev, G Weiss, V Kolesnikov & S Lodha (eds), Cyber Security Cryptography and Machine Learning - 4th International Symposium, CSCML 2020, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12161 LNCS, Springer, pp. 110-127, 4th International Symposium on Cyber Security Cryptography and Machine Learning, CSCML 2020, Beersheba, Israel, 2/07/20. https://doi.org/10.1007/978-3-030-49785-9_8

Fast Polynomial Inversion for Post Quantum QC-MDPC Cryptography. / Drucker, Nir; Gueron, Shay; Kostic, Dusan.
Cyber Security Cryptography and Machine Learning - 4th International Symposium, CSCML 2020, Proceedings. ed. / Shlomi Dolev; Gera Weiss; Vladimir Kolesnikov; Sachin Lodha. Springer, 2020. p. 110-127 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12161 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Gueron, Shay

AU - Kostic, Dusan

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N2 - The NIST PQC standardization project evaluates multiple new designs for post-quantum Key Encapsulation Mechanisms (KEMs). Some of them present challenging tradeoffs between communication bandwidth and computational overheads. An interesting case is the set of QC-MDPC based KEMs. Here, schemes that use the Niederreiter framework require only half the communication bandwidth compared to schemes that use the McEliece framework. However, this requires costly polynomial inversion during the key generation, which is prohibitive when ephemeral keys are used. One example is BIKE, where the BIKE-1 variant uses McEliece and the BIKE-2 variant uses Niederreiter. This paper shows an optimized constant-time polynomial inversion method that makes the computation costs of BIKE-2 key generation tolerable. We report a speedup of$$11.8{\times }$$ over the commonly used NTL library, and$$55.5{\times }$$ over OpenSSL. We achieve additional speedups by leveraging the latest Intel’s Vector-instructions on a laptop machine,$$14.3{\times }$$ over NTL and$$96.8{\times }$$ over OpenSSL. With this, BIKE-2 becomes a competitive variant of BIKE.

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Drucker N, Gueron S, Kostic D. Fast Polynomial Inversion for Post Quantum QC-MDPC Cryptography. In Dolev S, Weiss G, Kolesnikov V, Lodha S, editors, Cyber Security Cryptography and Machine Learning - 4th International Symposium, CSCML 2020, Proceedings. Springer. 2020. p. 110-127. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-49785-9_8

Fast Polynomial Inversion for Post Quantum QC-MDPC Cryptography

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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