Impossibility of strong kdm security with auxiliary input

Cody Freitag; Ilan Komargodski; Rafael Pass

doi:10.1007/978-3-030-57990-6_25

Impossibility of strong kdm security with auxiliary input

Cody Freitag^*
, Ilan Komargodski
, Rafael Pass

^*Corresponding author for this work

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

Abstract

We show that a strong notion of KDM security cannot be obtained by any encryption scheme in the auxiliary input setting, assuming Learning With Errors (LWE) and one-way permutations. The notion of security we deal with guarantees that for any (possibly inefficient) function f, it is computationally hard to distinguish between an encryption of $$\mathbf {0}$$ and an encryption of $$f(\mathsf {pk}, z)$$, where $$\mathsf {pk} $$ is the public key and z is the auxiliary input. Furthermore, we show that this holds even when restricted to bounded-length auxiliary input where z is much shorter than $$\mathsf {pk} $$ under the additional assumption that (non-leveled) fully homomorphic encryption exists.

Original language	English
Title of host publication	Security and Cryptography for Networks - 12th International Conference, SCN 2020, Proceedings
Editors	Clemente Galdi, Vladimir Kolesnikov
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	512-524
Number of pages	13
ISBN (Print)	9783030579890
DOIs	https://doi.org/10.1007/978-3-030-57990-6_25
State	Published - 2020
Externally published	Yes
Event	12th International Conference on Security and Cryptography for Networks, SCN 2020 - Amalfi, Italy Duration: 14 Sep 2020 → 16 Sep 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12238 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	12th International Conference on Security and Cryptography for Networks, SCN 2020
Country/Territory	Italy
City	Amalfi
Period	14/09/20 → 16/09/20

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2020.

Access to Document

10.1007/978-3-030-57990-6_25

Cite this

Freitag, C., Komargodski, I., & Pass, R. (2020). Impossibility of strong kdm security with auxiliary input. In C. Galdi, & V. Kolesnikov (Eds.), Security and Cryptography for Networks - 12th International Conference, SCN 2020, Proceedings (pp. 512-524). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12238 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-57990-6_25

Freitag, Cody ; Komargodski, Ilan ; Pass, Rafael. / Impossibility of strong kdm security with auxiliary input. Security and Cryptography for Networks - 12th International Conference, SCN 2020, Proceedings. editor / Clemente Galdi ; Vladimir Kolesnikov. Springer Science and Business Media Deutschland GmbH, 2020. pp. 512-524 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Impossibility of strong kdm security with auxiliary input",

abstract = "We show that a strong notion of KDM security cannot be obtained by any encryption scheme in the auxiliary input setting, assuming Learning With Errors (LWE) and one-way permutations. The notion of security we deal with guarantees that for any (possibly inefficient) function f, it is computationally hard to distinguish between an encryption of \$\$\textbackslash{}mathbf \{0\}\$\$ and an encryption of \$\$f(\textbackslash{}mathsf \{pk\}, z)\$\$, where \$\$\textbackslash{}mathsf \{pk\} \$\$ is the public key and z is the auxiliary input. Furthermore, we show that this holds even when restricted to bounded-length auxiliary input where z is much shorter than \$\$\textbackslash{}mathsf \{pk\} \$\$ under the additional assumption that (non-leveled) fully homomorphic encryption exists.",

author = "Cody Freitag and Ilan Komargodski and Rafael Pass",

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020.; 12th International Conference on Security and Cryptography for Networks, SCN 2020 ; Conference date: 14-09-2020 Through 16-09-2020",

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Freitag, C, Komargodski, I & Pass, R 2020, Impossibility of strong kdm security with auxiliary input. in C Galdi & V Kolesnikov (eds), Security and Cryptography for Networks - 12th International Conference, SCN 2020, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12238 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 512-524, 12th International Conference on Security and Cryptography for Networks, SCN 2020, Amalfi, Italy, 14/09/20. https://doi.org/10.1007/978-3-030-57990-6_25

Impossibility of strong kdm security with auxiliary input. / Freitag, Cody; Komargodski, Ilan; Pass, Rafael.
Security and Cryptography for Networks - 12th International Conference, SCN 2020, Proceedings. ed. / Clemente Galdi; Vladimir Kolesnikov. Springer Science and Business Media Deutschland GmbH, 2020. p. 512-524 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12238 LNCS).

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

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AB - We show that a strong notion of KDM security cannot be obtained by any encryption scheme in the auxiliary input setting, assuming Learning With Errors (LWE) and one-way permutations. The notion of security we deal with guarantees that for any (possibly inefficient) function f, it is computationally hard to distinguish between an encryption of $$\mathbf {0}$$ and an encryption of $$f(\mathsf {pk}, z)$$, where $$\mathsf {pk} $$ is the public key and z is the auxiliary input. Furthermore, we show that this holds even when restricted to bounded-length auxiliary input where z is much shorter than $$\mathsf {pk} $$ under the additional assumption that (non-leveled) fully homomorphic encryption exists.

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Freitag C, Komargodski I, Pass R. Impossibility of strong kdm security with auxiliary input. In Galdi C, Kolesnikov V, editors, Security and Cryptography for Networks - 12th International Conference, SCN 2020, Proceedings. Springer Science and Business Media Deutschland GmbH. 2020. p. 512-524. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-57990-6_25

Impossibility of strong kdm security with auxiliary input

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