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On the Impossibility of Constructing Non-interactive Statistically-Secret Protocols from Any Trapdoor One-Way Function

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Topics in Cryptology — CT-RSA 2002 (CT-RSA 2002)

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Abstract

We show that non-interactive statistically-secret bit commitment cannot be constructed from arbitrary black-box one-to-one trapdoor functions and thus from general public-key cryptosystems. Reducing the problems of non-interactive crypto-computing, rerandomizable encryption, and non-interactive statistically-sender-private oblivious transfer and low-communication private information retrieval to such commitment schemes, it follows that these primitives are neither constructible from one-to-one trapdoor functions and public-key encryption in general. Furthermore, our separation sheds some light on statistical zero-knowledge proofs. There is an oracle relative to which one-to-one trapdoor functions and one-way permutations exist, while the class of promise problems with statistical zero-knowledge proofs collapses in P. This indicates that nontrivial problems with statistical zero-knowledge proofs require more than (trapdoor) one-wayness.

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  1. Johann Wolfgang Goethe-University, Frankfurt am Main, Germany

    Marc Fischlin

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  1. Marc Fischlin
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  1. Department of Electrical Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, 3001, Leuven-Heverlee, Belgium

    Bart Preneel

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Fischlin, M. (2002). On the Impossibility of Constructing Non-interactive Statistically-Secret Protocols from Any Trapdoor One-Way Function. In: Preneel, B. (eds) Topics in Cryptology — CT-RSA 2002. CT-RSA 2002. Lecture Notes in Computer Science, vol 2271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45760-7_7

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  • DOI: https://doi.org/10.1007/3-540-45760-7_7

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