New Approach for Sine and Cosine in Secure Fixed-Point Arithmetic

Stan Korzilius; Berry Schoenmakers

doi:10.1007/978-3-031-34671-2_22

New Approach for Sine and Cosine in Secure Fixed-Point Arithmetic

Stan Korzilius, Berry Schoenmakers (Corresponding author)

Coding Theory and Cryptology

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

1 Citation (Scopus)

Abstract

In this paper we present a new class of protocols for the secure computation of the sine and cosine functions. The precision for the underlying secure fixed-point arithmetic is parametrized by the number of fractional bits f and can be set to any desired value. We perform a rigorous error analysis to provide an exact bound for the absolute error of 2^- ^f in the worst case. Existing methods rely on polynomial approximations of the sine and cosine, whereas our approach relies on the random self-reducibility of the problem, using efficiently generated solved instances for uniformly random angles. As a consequence, most of the O(f²) secure multiplications can be done in preprocessing, leaving only O(f) work for the online part. The overall round complexity can be limited to O(1) using standard techniques. We have integrated our solution in MPyC.

Original language	English
Title of host publication	Cyber Security, Cryptology, and Machine Learning
Subtitle of host publication	7th International Symposium, CSCML 2023, Be'er Sheva, Israel, June 29–30, 2023, Proceedings
Editors	Shlomi Dolev, Ehud Gudes, Pascal Paillier
Place of Publication	Cham
Publisher	Springer
Pages	307-319
Number of pages	13
ISBN (Electronic)	978-3-031-34671-2
ISBN (Print)	978-3-031-34670-5
DOIs	https://doi.org/10.1007/978-3-031-34671-2_22
Publication status	Published - 21 Jun 2023
Event	7th International Symposium on Cyber Security, Cryptology, and Machine Learning, CSCML 2023 - Be'er Sheva, Israel Duration: 29 Jun 2023 → 30 Jun 2023

Publication series

Name	Lecture Notes in Computer Science (LNCS)
Volume	13914
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th International Symposium on Cyber Security, Cryptology, and Machine Learning, CSCML 2023
Country/Territory	Israel
City	Be'er Sheva
Period	29/06/23 → 30/06/23

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10.1007/978-3-031-34671-2_22

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Korzilius, S., & Schoenmakers, B. (2023). New Approach for Sine and Cosine in Secure Fixed-Point Arithmetic. In S. Dolev, E. Gudes, & P. Paillier (Eds.), Cyber Security, Cryptology, and Machine Learning: 7th International Symposium, CSCML 2023, Be'er Sheva, Israel, June 29–30, 2023, Proceedings (pp. 307-319). (Lecture Notes in Computer Science (LNCS); Vol. 13914). Springer. https://doi.org/10.1007/978-3-031-34671-2_22

Korzilius, Stan ; Schoenmakers, Berry. / New Approach for Sine and Cosine in Secure Fixed-Point Arithmetic. Cyber Security, Cryptology, and Machine Learning: 7th International Symposium, CSCML 2023, Be'er Sheva, Israel, June 29–30, 2023, Proceedings. editor / Shlomi Dolev ; Ehud Gudes ; Pascal Paillier. Cham : Springer, 2023. pp. 307-319 (Lecture Notes in Computer Science (LNCS)).

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abstract = "In this paper we present a new class of protocols for the secure computation of the sine and cosine functions. The precision for the underlying secure fixed-point arithmetic is parametrized by the number of fractional bits f and can be set to any desired value. We perform a rigorous error analysis to provide an exact bound for the absolute error of 2- f in the worst case. Existing methods rely on polynomial approximations of the sine and cosine, whereas our approach relies on the random self-reducibility of the problem, using efficiently generated solved instances for uniformly random angles. As a consequence, most of the O(f2) secure multiplications can be done in preprocessing, leaving only O(f) work for the online part. The overall round complexity can be limited to O(1) using standard techniques. We have integrated our solution in MPyC.",

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Korzilius, S & Schoenmakers, B 2023, New Approach for Sine and Cosine in Secure Fixed-Point Arithmetic. in S Dolev, E Gudes & P Paillier (eds), Cyber Security, Cryptology, and Machine Learning: 7th International Symposium, CSCML 2023, Be'er Sheva, Israel, June 29–30, 2023, Proceedings. Lecture Notes in Computer Science (LNCS), vol. 13914, Springer, Cham, pp. 307-319, 7th International Symposium on Cyber Security, Cryptology, and Machine Learning, CSCML 2023, Be'er Sheva, Israel, 29/06/23. https://doi.org/10.1007/978-3-031-34671-2_22

New Approach for Sine and Cosine in Secure Fixed-Point Arithmetic. / Korzilius, Stan; Schoenmakers, Berry (Corresponding author).
Cyber Security, Cryptology, and Machine Learning: 7th International Symposium, CSCML 2023, Be'er Sheva, Israel, June 29–30, 2023, Proceedings. ed. / Shlomi Dolev; Ehud Gudes; Pascal Paillier. Cham: Springer, 2023. p. 307-319 (Lecture Notes in Computer Science (LNCS); Vol. 13914).

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

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AB - In this paper we present a new class of protocols for the secure computation of the sine and cosine functions. The precision for the underlying secure fixed-point arithmetic is parametrized by the number of fractional bits f and can be set to any desired value. We perform a rigorous error analysis to provide an exact bound for the absolute error of 2- f in the worst case. Existing methods rely on polynomial approximations of the sine and cosine, whereas our approach relies on the random self-reducibility of the problem, using efficiently generated solved instances for uniformly random angles. As a consequence, most of the O(f2) secure multiplications can be done in preprocessing, leaving only O(f) work for the online part. The overall round complexity can be limited to O(1) using standard techniques. We have integrated our solution in MPyC.

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Korzilius S, Schoenmakers B. New Approach for Sine and Cosine in Secure Fixed-Point Arithmetic. In Dolev S, Gudes E, Paillier P, editors, Cyber Security, Cryptology, and Machine Learning: 7th International Symposium, CSCML 2023, Be'er Sheva, Israel, June 29–30, 2023, Proceedings. Cham: Springer. 2023. p. 307-319. (Lecture Notes in Computer Science (LNCS)). doi: 10.1007/978-3-031-34671-2_22

New Approach for Sine and Cosine in Secure Fixed-Point Arithmetic

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