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Key-Oblivious Encryption from Isogenies with Application to Accountable Tracing Signatures

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Progress in Cryptology – INDOCRYPT 2021 (INDOCRYPT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13143))

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Abstract

Key-oblivious encryption (KOE) is a promising cryptographic primitive that randomizes the public keys of an encryption scheme in an oblivious manner. It has applications in designing accountable tracing signature (ATS) that facilitates the group manager to revoke the anonymity of traceable users in a group signature while preserving the anonymity of non-traceable users. KOE is an independent primitive and may serve as a technical building block in designing privacy preserving protocols.

In this work, we introduce the first isogeny-based KOE scheme. Isogeny-based cryptography is a fairly young post-quantum cryptography with sophisticated algebraic structures and unique security properties. Our KOE scheme is resistant to quantum attacks and derives its security from Commutative Supersingular Decisional Diffie-Hellman (CSSDDH), which is an isogeny-based hard problem. More concretely, we show that our construction exhibits key randomizability, plaintext indistinguishability under key randomization and key privacy under key randomization in the standard model adapting the security framework of [12]. Furthermore, we have manifested an instantiation of our scheme from cryptosystem based on Commutative Supersingular Isogeny Diffie-Hellman (CSIDH-512) [3] parameter set. Additionally, we demonstrate the utility of our KOE scheme by leveraging it to construct an isogeny-based ATS scheme preserving anonymity under tracing, traceability, non-frameability, anony-mity with accountability and trace obliviousness in the random oracle model following the security framework of [14].

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Notes

  1. 1.

    The quadratic twist of an elliptic curve \(E : y^{2} = f(x)\) defined over a field K is given by \(E^{t} : dy^{2} = f(x)\) where \(d \in K\) has Legendre symbol value \(-1\).

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    Surbhi Shaw & Ratna Dutta

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  1. Surbhi Shaw
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  2. Ratna Dutta
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Correspondence to Surbhi Shaw .

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Editors and Affiliations

  1. Presidency University, Kolkata, India

    Avishek Adhikari

  2. University of Stuttgart, Stuttgart, Germany

    Ralf Küsters

  3. University of Leuven and imec, Leuven, Belgium

    Bart Preneel

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Shaw, S., Dutta, R. (2021). Key-Oblivious Encryption from Isogenies with Application to Accountable Tracing Signatures. In: Adhikari, A., Küsters, R., Preneel, B. (eds) Progress in Cryptology – INDOCRYPT 2021. INDOCRYPT 2021. Lecture Notes in Computer Science(), vol 13143. Springer, Cham. https://doi.org/10.1007/978-3-030-92518-5_17

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  • DOI: https://doi.org/10.1007/978-3-030-92518-5_17

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