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Universal Proxy Re-Encryption

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Public-Key Cryptography – PKC 2021 (PKC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12710))

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Abstract

We put forward the notion of universal proxy re-encryption (UPRE). A UPRE scheme enables a proxy to convert a ciphertext under a (delegator) public key of any existing public-key encryption (PKE) scheme into another ciphertext under a (delegatee) public key of any existing PKE scheme (possibly different from the delegator one). The proxy has a re-encryption key generated from the delegator’s secret key and the delegatee public key. Thus UPRE generalizes proxy re-encryption by supporting arbitrary PKE schemes and allowing to convert ciphertexts into ones of possibly different PKE schemes. In this work, we

  • provide syntax and definitions for both UPRE and a variant we call relaxed UPRE. The relaxed variant means that decryption algorithms for re-encrypted ciphertexts are slightly modified but still only use the original delegatee secret keys for decryption.

  • construct a UPRE based on probabilistic indistinguishability obfuscation (PIO). It allows us to re-encrypt ciphertexts polynomially many times.

  • construct relaxed UPRE from garbled circuits (GCs). We provide two variants of this construction, one which allows us to re-encrypt ciphertexts polynomially many times, and a second one which satisfies a stronger security requirement but only allows us to re-encrypt ciphertexts a constant number of times.

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Notes

  1. 1.

    A.k.a. “heavy hammers”.

  2. 2.

    Derler, Krenn, Lorünser, Ramacher, Slamanig, and Striecks also proposed a similar security notion in the forward secret setting as (fs)-RIND-CPA [DKL+18].

  3. 3.

    Note that the corrupted delegator does not have a ciphertext to be re-encrypted here.

  4. 4.

    Davidson, Deo, Lee, and Martin [DDLM19] independently introduced a stronger notion called strong post-compromised security in the standard PRE setting. Note that our work appeared before their publication. Our work appeared on September 7th in 2018 while their work [DDLM19] did on April 5th in 2019. (See the submission dates on Cryptology ePrint Archive.).

  5. 5.

    Of course, a re-encryption query from an honest user to a corrupted user is also prohibited in PRE-CPA security.

  6. 6.

    If we prefer longer security parameters, then we can change the condition to \(\lambda _i < c \lambda \) for some constant \(c>1\).

  7. 7.

    The circular security issue arises in constructions that use general PKE schemes. If there exists a cycle, we have no way to use the CPA-security of a PKE scheme in the cycle since the information of each secret key in the cycle is in a re-encryption key in the cycle. This does not happen in concrete constructions based on some hard problems such as the DDH.

  8. 8.

    Note that Cohen does not use key-privacy of PRE [ABH09] to prove PRE-HRA security.

  9. 9.

    We could define a weaker variant of re-encryption simulatability for UPRE (and PRE) that still implies HRA security. However, such a definition is not simple, and proofs are not simplified. Proving such a weak re-encryption simulatability takes almost the same efforts to prove HRA security directly. Thus, we do not use re-encryption simulatability.

  10. 10.

    If there exists \((\widehat{i},j_1,k_1)\) and \((\widehat{i},j_2,k_2)\) such that \((\widehat{i},j_1)\) and \((\widehat{i},j_2)\) are not admissible and \(k_1,k_2 \notin \mathsf {Drv}\), then we can use the same simulation process described in hybrid experiments for those queries.

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Authors and Affiliations

  1. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Nico Döttling

  2. NTT Secure Platform Laboratories, Tokyo, Japan

    Ryo Nishimaki

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  1. Nico Döttling
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Correspondence to Ryo Nishimaki .

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  1. Texas A&M University, College Station, TX, USA

    Juan A. Garay

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Döttling, N., Nishimaki, R. (2021). Universal Proxy Re-Encryption. In: Garay, J.A. (eds) Public-Key Cryptography – PKC 2021. PKC 2021. Lecture Notes in Computer Science(), vol 12710. Springer, Cham. https://doi.org/10.1007/978-3-030-75245-3_19

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