TY - GEN
T1 - On Low-End Obfuscation and Learning
AU - Boyle, Elette
AU - Ishai, Yuval
AU - Meyer, Pierre
AU - Robere, Robert
AU - Yehuda, Gal
N1 - Publisher Copyright:
© Elette Boyle, Yuval Ishai, Pierre Meyer, Robert Robere, and Gal Yehuda; licensed under Creative Commons License CC-BY 4.0.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - Most recent works on cryptographic obfuscation focus on the high-end regime of obfuscating general circuits while guaranteeing computational indistinguishability between functionally equivalent circuits. Motivated by the goals of simplicity and efficiency, we initiate a systematic study of “low-end” obfuscation, focusing on simpler representation models and information-theoretic notions of security. We obtain the following results. Positive results via “white-box” learning. We present a general technique for obtaining perfect indistinguishability obfuscation from exact learning algorithms that are given restricted access to the representation of the input function. We demonstrate the usefulness of this approach by obtaining simple obfuscation for decision trees and multilinear read-k arithmetic formulas. Negative results via PAC learning. A proper obfuscation scheme obfuscates programs from a class C by programs from the same class. Assuming the existence of one-way functions, we show that there is no proper indistinguishability obfuscation scheme for k-CNF formulas for any constant k ≥ 3; in fact, even obfuscating 3-CNF by k-CNF is impossible. This result applies even to computationally secure obfuscation, and makes an unexpected use of PAC learning in the context of negative results for obfuscation. Separations. We study the relations between different information-theoretic notions of indistinguishability obfuscation, giving cryptographic evidence for separations between them.
AB - Most recent works on cryptographic obfuscation focus on the high-end regime of obfuscating general circuits while guaranteeing computational indistinguishability between functionally equivalent circuits. Motivated by the goals of simplicity and efficiency, we initiate a systematic study of “low-end” obfuscation, focusing on simpler representation models and information-theoretic notions of security. We obtain the following results. Positive results via “white-box” learning. We present a general technique for obtaining perfect indistinguishability obfuscation from exact learning algorithms that are given restricted access to the representation of the input function. We demonstrate the usefulness of this approach by obtaining simple obfuscation for decision trees and multilinear read-k arithmetic formulas. Negative results via PAC learning. A proper obfuscation scheme obfuscates programs from a class C by programs from the same class. Assuming the existence of one-way functions, we show that there is no proper indistinguishability obfuscation scheme for k-CNF formulas for any constant k ≥ 3; in fact, even obfuscating 3-CNF by k-CNF is impossible. This result applies even to computationally secure obfuscation, and makes an unexpected use of PAC learning in the context of negative results for obfuscation. Separations. We study the relations between different information-theoretic notions of indistinguishability obfuscation, giving cryptographic evidence for separations between them.
KW - Indistinguishability obfuscation
KW - cryptography
KW - learning
UR - http://www.scopus.com/inward/record.url?scp=85147540909&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ITCS.2023.23
DO - 10.4230/LIPIcs.ITCS.2023.23
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AN - SCOPUS:85147540909
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 14th Innovations in Theoretical Computer Science Conference, ITCS 2023
A2 - Kalai, Yael Tauman
T2 - 14th Innovations in Theoretical Computer Science Conference, ITCS 2023
Y2 - 10 January 2023 through 13 January 2023
ER -