The advantage of truncated permutations

Shoni Gilboa; Shay Gueron

doi:10.1007/978-3-030-20951-3_11

The advantage of truncated permutations

Shoni Gilboa, Shay Gueron

Mathematics

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

Abstract

Constructing a Pseudo Random Function (PRF) from a pseudorandom permutation is a fundamental problem in cryptology. Such a construction, implemented by truncating the last m bits of permutations of (formula presented) was suggested by Hall et al. (1998). They conjectured that the distinguishing advantage of an adversary with q quesires, (formula presented), is small if (formula presented), established an upper bound on (formula presented) that confirms the conjecture for (formula presented), and also declared a general lower bound (formula presented). The conjecture was essentially confirmed by Bellare and Impagliazzo in 1999. Nevertheless, the problem of estimating (formula presented) remained open. Combining the trivial bound 1, the birthday bound, and a result by Stam (1978) leads to the following upper bound: (formula presented) This upper bound shows that the number of times that a truncated permutation can be used as a PRF can exceed the birthday bound by at least a factor of (formula presented). In this paper we show that this upper bound is tight for every (formula presented) and (formula presented). This, in turn, verifies that the converse to the conjecture of Hall et al. is also correct, i.e., that (formula presented) is negligible only for (formula presented).

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	111-120
Number of pages	10
ISBN (Print)	9783030209506
DOIs	https://doi.org/10.1007/978-3-030-20951-3_11
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

Advantage
Pseudo random functions
Pseudo random permutations

Access to Document

10.1007/978-3-030-20951-3_11

Cite this

Gilboa, S., & Gueron, S. (2019). The advantage of truncated permutations. In S. Dolev, D. Hendler, S. Lodha, & M. Yung (Eds.), Cyber Security Cryptography and Machine Learning - 3rd International Symposium, CSCML 2019, Proceedings (pp. 111-120). (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_11

Gilboa, Shoni ; Gueron, Shay. / The advantage of truncated permutations. 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. 111-120 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Constructing a Pseudo Random Function (PRF) from a pseudorandom permutation is a fundamental problem in cryptology. Such a construction, implemented by truncating the last m bits of permutations of (formula presented) was suggested by Hall et al. (1998). They conjectured that the distinguishing advantage of an adversary with q quesires, (formula presented), is small if (formula presented), established an upper bound on (formula presented) that confirms the conjecture for (formula presented), and also declared a general lower bound (formula presented). The conjecture was essentially confirmed by Bellare and Impagliazzo in 1999. Nevertheless, the problem of estimating (formula presented) remained open. Combining the trivial bound 1, the birthday bound, and a result by Stam (1978) leads to the following upper bound: (formula presented) This upper bound shows that the number of times that a truncated permutation can be used as a PRF can exceed the birthday bound by at least a factor of (formula presented). In this paper we show that this upper bound is tight for every (formula presented) and (formula presented). This, in turn, verifies that the converse to the conjecture of Hall et al. is also correct, i.e., that (formula presented) is negligible only for (formula presented).",

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Gilboa, S & Gueron, S 2019, The advantage of truncated permutations. 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. 111-120, 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_11

The advantage of truncated permutations. / Gilboa, Shoni; 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. 111-120 (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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N2 - Constructing a Pseudo Random Function (PRF) from a pseudorandom permutation is a fundamental problem in cryptology. Such a construction, implemented by truncating the last m bits of permutations of (formula presented) was suggested by Hall et al. (1998). They conjectured that the distinguishing advantage of an adversary with q quesires, (formula presented), is small if (formula presented), established an upper bound on (formula presented) that confirms the conjecture for (formula presented), and also declared a general lower bound (formula presented). The conjecture was essentially confirmed by Bellare and Impagliazzo in 1999. Nevertheless, the problem of estimating (formula presented) remained open. Combining the trivial bound 1, the birthday bound, and a result by Stam (1978) leads to the following upper bound: (formula presented) This upper bound shows that the number of times that a truncated permutation can be used as a PRF can exceed the birthday bound by at least a factor of (formula presented). In this paper we show that this upper bound is tight for every (formula presented) and (formula presented). This, in turn, verifies that the converse to the conjecture of Hall et al. is also correct, i.e., that (formula presented) is negligible only for (formula presented).

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Gilboa S, Gueron S. The advantage of truncated permutations. 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. 111-120. (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_11

The advantage of truncated permutations

Abstract

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Bibliographical note

Keywords

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