Generating a random string with a fixed weight

Nir Drucker; Shay Gueron

doi:10.1007/978-3-030-20951-3_13

Generating a random string with a fixed weight

Nir Drucker, Shay Gueron

Department of Mathematics

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

Abstract

Generating, uniformly at random, a binary or a ternary string with a fixed length L and a prescribed weight W, is a step in several quantum safe cryptosystems (e.Â g., BIKE, NTRUEncrypt, NTRU LPrime, Lizard, McEliece). This fixed weight vector selection generation is often implemented via a shuffling method or a rejection method, but not always in “constant time” side channel protected flow. A recently suggested constant time algorithm for this problem, uses Network Sorting and turns out to be quite efficient. This paper proposes a new method for this computation, with a side channel protected implementation. We compare it to the other methods for different combinations of L and W values. Our method turns out to be the fastest approach for the cases where L is (relatively) short and (formula presented). For example, this range falls within the parameters of NTRU LPrime, where our method achieves a 3× speedup in the string generation. This leads to an overall 1.14× speedup for the NTRU LPrime key generation.

Original language	English
Title of host publication	Cyber Security Cryptography and Machine Learning - 3rd International Symposium, CSCML 2019, Proceedings
Editors	Shlomi Dolev, Danny Hendler, Sachin Lodha, Moti Yung
Publisher	Springer Verlag
Pages	141-155
Number of pages	15
ISBN (Print)	9783030209506
DOIs	https://doi.org/10.1007/978-3-030-20951-3_13
State	Published - 2019
Event	3rd International Symposium on Cyber Security Cryptography and Machine Learning, CSCML 2019 - Beer Sheva, Israel Duration: 27 Jun 2019 → 28 Jun 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11527 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Symposium on Cyber Security Cryptography and Machine Learning, CSCML 2019
Country/Territory	Israel
City	Beer Sheva
Period	27/06/19 → 28/06/19

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2019.

Keywords

Coding
Combinatorics
Post Quantum Cryptography
Software optimization

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-20951-3_13

Cite this

Drucker, N., & Gueron, S. (2019). Generating a random string with a fixed weight. In S. Dolev, D. Hendler, S. Lodha, & M. Yung (Eds.), Cyber Security Cryptography and Machine Learning - 3rd International Symposium, CSCML 2019, Proceedings (pp. 141-155). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11527 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-20951-3_13

Drucker, Nir ; Gueron, Shay. / Generating a random string with a fixed weight. Cyber Security Cryptography and Machine Learning - 3rd International Symposium, CSCML 2019, Proceedings. editor / Shlomi Dolev ; Danny Hendler ; Sachin Lodha ; Moti Yung. Springer Verlag, 2019. pp. 141-155 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Generating a random string with a fixed weight",

abstract = "Generating, uniformly at random, a binary or a ternary string with a fixed length L and a prescribed weight W, is a step in several quantum safe cryptosystems (e.{\^A} g., BIKE, NTRUEncrypt, NTRU LPrime, Lizard, McEliece). This fixed weight vector selection generation is often implemented via a shuffling method or a rejection method, but not always in “constant time” side channel protected flow. A recently suggested constant time algorithm for this problem, uses Network Sorting and turns out to be quite efficient. This paper proposes a new method for this computation, with a side channel protected implementation. We compare it to the other methods for different combinations of L and W values. Our method turns out to be the fastest approach for the cases where L is (relatively) short and (formula presented). For example, this range falls within the parameters of NTRU LPrime, where our method achieves a 3× speedup in the string generation. This leads to an overall 1.14× speedup for the NTRU LPrime key generation.",

keywords = "Coding, Combinatorics, Post Quantum Cryptography, Software optimization",

author = "Nir Drucker and Shay Gueron",

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.; 3rd International Symposium on Cyber Security Cryptography and Machine Learning, CSCML 2019 ; Conference date: 27-06-2019 Through 28-06-2019",

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doi = "10.1007/978-3-030-20951-3_13",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Drucker, N & Gueron, S 2019, Generating a random string with a fixed weight. in S Dolev, D Hendler, S Lodha & M Yung (eds), Cyber Security Cryptography and Machine Learning - 3rd International Symposium, CSCML 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11527 LNCS, Springer Verlag, pp. 141-155, 3rd International Symposium on Cyber Security Cryptography and Machine Learning, CSCML 2019, Beer Sheva, Israel, 27/06/19. https://doi.org/10.1007/978-3-030-20951-3_13

Generating a random string with a fixed weight. / Drucker, Nir; Gueron, Shay.
Cyber Security Cryptography and Machine Learning - 3rd International Symposium, CSCML 2019, Proceedings. ed. / Shlomi Dolev; Danny Hendler; Sachin Lodha; Moti Yung. Springer Verlag, 2019. p. 141-155 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11527 LNCS).

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

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AU - Gueron, Shay

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2019.

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N2 - Generating, uniformly at random, a binary or a ternary string with a fixed length L and a prescribed weight W, is a step in several quantum safe cryptosystems (e.Â g., BIKE, NTRUEncrypt, NTRU LPrime, Lizard, McEliece). This fixed weight vector selection generation is often implemented via a shuffling method or a rejection method, but not always in “constant time” side channel protected flow. A recently suggested constant time algorithm for this problem, uses Network Sorting and turns out to be quite efficient. This paper proposes a new method for this computation, with a side channel protected implementation. We compare it to the other methods for different combinations of L and W values. Our method turns out to be the fastest approach for the cases where L is (relatively) short and (formula presented). For example, this range falls within the parameters of NTRU LPrime, where our method achieves a 3× speedup in the string generation. This leads to an overall 1.14× speedup for the NTRU LPrime key generation.

AB - Generating, uniformly at random, a binary or a ternary string with a fixed length L and a prescribed weight W, is a step in several quantum safe cryptosystems (e.Â g., BIKE, NTRUEncrypt, NTRU LPrime, Lizard, McEliece). This fixed weight vector selection generation is often implemented via a shuffling method or a rejection method, but not always in “constant time” side channel protected flow. A recently suggested constant time algorithm for this problem, uses Network Sorting and turns out to be quite efficient. This paper proposes a new method for this computation, with a side channel protected implementation. We compare it to the other methods for different combinations of L and W values. Our method turns out to be the fastest approach for the cases where L is (relatively) short and (formula presented). For example, this range falls within the parameters of NTRU LPrime, where our method achieves a 3× speedup in the string generation. This leads to an overall 1.14× speedup for the NTRU LPrime key generation.

KW - Coding

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ER -

Drucker N, Gueron S. Generating a random string with a fixed weight. In Dolev S, Hendler D, Lodha S, Yung M, editors, Cyber Security Cryptography and Machine Learning - 3rd International Symposium, CSCML 2019, Proceedings. Springer Verlag. 2019. p. 141-155. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-20951-3_13

Generating a random string with a fixed weight

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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