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Unique-Path Identity Based Encryption with Applications to Strongly Secure Messaging

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Advances in Cryptology – EUROCRYPT 2023 (EUROCRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14008))

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Abstract

Hierarchical Identity Based Encryption (HIBE) is a well studied, versatile tool used in many cryptographic protocols. Yet, since the performance of all known HIBE constructions is broadly considered prohibitive, some real-world applications avoid relying on HIBE at the expense of security. A prominent example for this is secure messaging: Strongly secure messaging protocols are provably equivalent to Key-Updatable Key Encapsulation Mechanisms (KU-KEMs; Balli et al., Asiacrypt 2020); so far, all KU-KEM constructions rely on adaptive unbounded-depth HIBE (Poettering and Rösler, Jaeger and Stepanovs, both CRYPTO 2018). By weakening security requirements for better efficiency, many messaging protocols dispense with using HIBE.

      In this work, we aim to gain better efficiency without sacrificing security. For this, we observe that applications like messaging only need a restricted variant of HIBE for strong security. This variant, that we call Unique-Path Identity Based Encryption (UPIBE), restricts HIBE by requiring that each secret key can delegate at most one subordinate secret key. However, in contrast to fixed secret key delegation in Forward-Secure Public Key Encryption, the delegation in UPIBE, as in HIBE, is uniquely determined by variable identity strings from an exponentially large space. We investigate this mild but surprisingly effective restriction and show that it offers substantial complexity and performance advantages.

      More concretely, we generically build bounded-depth UPIBE from only bounded-collusion IBE in the standard model; and we generically build adaptive unbounded-depth UPIBE from only selective bounded-depth HIBE in the random oracle model. These results significantly extend the range of underlying assumptions and efficient instantiations. We conclude with a rigorous performance evaluation of our UPIBE design. Beyond solving challenging open problems by reducing complexity and improving efficiency of KU-KEM and strongly secure messaging protocols, we offer a new definitional perspective on the bounded-collusion setting.

The full version [38] of this article is available in the IACR eprint archive as article 2023/248, at https://eprint.iacr.org/2023/248.

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Notes

  1. 1.

    E.g., the chronological succession of presidents in a particular state or a ranking list that results from a competition.

  2. 2.

    We stress that the construction of selective-secure HIBE with unbounded delegations from CDH [17] or from any fully secure IBE [16] is an impressive, yet rather theoretic result.

  3. 3.

    An alternative approach from standard assumptions would be to rely on the fully secure IBE from CDH by Garg and Döttling [17]. Unfortunately, this will not yield a practical instantiation.

  4. 4.

    With the exposed UPIBE decapsulation key, the adversary can compute all subsequent delegations and decapsulations itself, so further exposures are meaningless.

  5. 5.

    Branching here means that for two identity strings \( id , id ^*\) with \(\ell ^*=\min (| id |,| id ^*|)\), strings \( id \) and \( id ^*\) differ in at least one of the first \(\ell ^*\) bits.

  6. 6.

    E.g., the number of conducted key delegations in the bidirectional messaging protocol in [36, see page 22] is upper-bounded by the maximal number of ciphertexts that cross the wire during a round-trip time (i.e., at most a few dozens).

  7. 7.

    Consider asymmetric communication for which ciphertexts should be small and encapsulation keys can be large: E.g., sending large encapsulation keys on hardware memory from time to time via resupply flights to the International Space Station, and sending ciphertexts over the air back to earth.

  8. 8.

    For clarity in our explanation, we slightly deviate from the original BTE-to-FS-PKE idea by Canetti et al. [8]: We do not use all nodes in the BTE tree as epoch starting points but only nodes in the lowest level of this BTE component.

  9. 9.

    We would sample a random key k and derive \((r_0,\ldots ,r_{l-1},k')=G(k)\) from a random oracle G and encapsulate \(k_i\) with randomness \(r_i\) for the i’th instance such that \(K=k_0\oplus \ldots \oplus k_{l-1}\) and then use \(k'\) as the overall encapsulation key.

  10. 10.

    In our concrete setting, for standard-model HIBEs, we use Groth’s pairing-free signature scheme [26] while for HIBEs in the ROM, we use Schnorr signatures [40].

  11. 11.

    Essentially, GCTC [24] improves Lewko [35] towards shorter ciphertext sizes and LP [34] deals with tightness of the Lewko scheme [35], at the expense of rather large encapsulation keys (see \(\gamma \)-factor).

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Acknowledgements

This work was supported by the ECSEL Joint Undertaking (JU) under grant agreement No 826610 (Comp4Drones) and by the Austrian Science Fund (FWF) and netidee SCIENCE under grant agreement P31621-N38 (Profet).

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Authors and Affiliations

  1. FAU Erlangen-Nürnberg, Erlangen, Germany

    Paul Rösler

  2. AIT Austrian Institute of Technology, Vienna, Austria

    Daniel Slamanig & Christoph Striecks

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  1. Paul Rösler
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Correspondence to Paul Rösler .

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  1. Bar-Ilan University, Ramat Gan, Israel

    Carmit Hazay

  2. Simula UiB, Bergen, Norway

    Martijn Stam

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Rösler, P., Slamanig, D., Striecks, C. (2023). Unique-Path Identity Based Encryption with Applications to Strongly Secure Messaging. In: Hazay, C., Stam, M. (eds) Advances in Cryptology – EUROCRYPT 2023. EUROCRYPT 2023. Lecture Notes in Computer Science, vol 14008. Springer, Cham. https://doi.org/10.1007/978-3-031-30589-4_1

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