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Incremental Cryptography Revisited: PRFs, Nonces and Modular Design

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Progress in Cryptology – INDOCRYPT 2020 (INDOCRYPT 2020)

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Abstract

This paper gives the first definitions and constructions for incremental pseudo-random functions (IPRFs). The syntax is nonce based. (Algorithms are deterministic but may take as input a non-repeating quantity called a nonce.) The design approach is modular. First, given a scheme secure only in the single-document setting (there is just one document on which incremental updates are being performed) we show how to generically build a scheme that is secure in the more realistic multi-document setting (there are many documents, and they are simultaneously being incrementally updated). Then we give a general way to build an IPRF from (1) an incremental hash function with weak collision resistance properties and (2) a symmetric encryption scheme. (This adapts the classic Carter-Wegman paradigm used to build message authentication schemes in the non-incremental setting.) This leads to many particular IPRFs. Our work has both practical and theoretical motivation and value: Incremental PRFs bring the benefits of incrementality to new applications (such as incremental key derivation), and the movement from randomized or stateful schemes to nonce based ones, and from UF (unforgeability) to PRF security, bring incremental symmetric cryptography up to speed with the broader field of symmetric cryptography itself.

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Acknowledgments

We thank Damien Vergnaud for discussions and comments in early stages of this work. We thank the IndoCrypt 2020 reviewers for their comments. Arte and Bellare are supported in part by NSF grant CNS-1717640 and a gift from Microsoft corporation.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of California, San Diego, USA

    Vivek Arte & Mihir Bellare

  2. ANSSI, Paris, France

    Louiza Khati

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  1. Vivek Arte
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  3. Louiza Khati
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Correspondence to Vivek Arte .

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  1. Inria Paris, Paris, France

    Karthikeyan Bhargavan

  2. University of Klagenfurt, Klagenfurt, Austria

    Elisabeth Oswald

  3. Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Mumbai, Maharashtra, India

    Manoj Prabhakaran

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Arte, V., Bellare, M., Khati, L. (2020). Incremental Cryptography Revisited: PRFs, Nonces and Modular Design. In: Bhargavan, K., Oswald, E., Prabhakaran, M. (eds) Progress in Cryptology – INDOCRYPT 2020. INDOCRYPT 2020. Lecture Notes in Computer Science(), vol 12578. Springer, Cham. https://doi.org/10.1007/978-3-030-65277-7_26

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  • DOI: https://doi.org/10.1007/978-3-030-65277-7_26

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