@inproceedings{f06554a468964247aac29796a6a40466,
title = "New techniques for obfuscating conjunctions",
abstract = "A conjunction is a function (Formula presented) where S⊆[n] and each li is xi or -xi. Bishop et al. (CRYPTO 2018) recently proposed obfuscating conjunctions by embedding them in the error positions of a noisy Reed-Solomon codeword and placing the codeword in a group exponent. They prove distributional virtual black box (VBB) security in the generic group model for random conjunctions where |S| ≥ 0.226n. While conjunction obfuscation is known from LWE [31, 47], these constructions rely on substantial technical machinery. In this work, we conduct an extensive study of simple conjunction obfuscation techniques. We abstract the Bishop et al. scheme to obtain an equivalent yet more efficient “dual” scheme that can handle conjunctions over exponential size alphabets. This scheme admits a straightforward proof of generic group security, which we combine with a novel combinatorial argument to obtain distributional VBB security for |S| of any size. If we replace the Reed-Solomon code with a random binary linear code, we can prove security from standard LPN and avoid encoding in a group. This addresses an open problem posed by Bishop et al. to prove security of this simple approach in the standard model.We give a new construction that achieves information theoretic distributional VBB security and weak functionality preservation for |S| ≥ n-nδ and δ ˂ 1. Assuming discrete log and δ > 1/2, we satisfy a stronger notion of functionality preservation for computationally bounded adversaries while still achieving information theoretic security.",
author = "James Bartusek and Tancr{\`e}de Lepoint and Fermi Ma and Mark Zhandry",
year = "2019",
month = jan,
day = "1",
doi = "10.1007/978-3-030-17659-4_22",
language = "English (US)",
isbn = "9783030176587",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "636--666",
editor = "Yuval Ishai and Vincent Rijmen",
booktitle = "Advances in Cryptology – EUROCRYPT 2019 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings",
address = "Germany",
note = "38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2019 ; Conference date: 19-05-2019 Through 23-05-2019",
}