Abstract
The notion of Registration-Based Encryption (RBE) was recently introduced by Garg, Hajiabadi, Mahmoody, and Rahimi [TCC’18] with the goal of removing the private-key generator (PKG) from IBE. Specifically, RBE allows encrypting to identities using a (compact) master public key, like how IBE is used, with the benefit that the PKG is substituted with a weaker entity called “key curator” who has no knowledge of any secret keys. Here individuals generate their secret keys on their own and then publicly register their identities and their corresponding public keys to the key curator. Finally, individuals obtain “rare” decryption-key updates from the key curator as the population grows. In their work, they gave a construction of RBE schemes based on the combination of indistinguishability obfuscation and somewhere statistically binding hash functions. However, they left open the problem of constructing RBE schemes based on standard assumptions.
In this work, we resolve the above problem and construct RBE schemes based on standard assumptions (e.g., CDH or LWE). Furthermore, we show a new application of RBE in a novel context. In particular, we show that anonymous variants of RBE (which we also construct under standard assumptions) can be used for realizing abstracts forms of anonymous messaging tasks in simple scenarios in which the parties communicate by writing messages on a shared board in a synchronized way.
S. Garg—Research supported in part from DARPA/ARL SAFEWARE Award W911NF15C0210, AFOSR Award FA9550-15-1-0274, AFOSR YIP Award, DARPA and SPAWAR under contract N66001-15-C-4065, a Hellman Award and research grants by the Okawa Foundation, Visa Inc., and Center for Long-Term Cybersecurity (CLTC, UC Berkeley). The views expressed are those of the author and do not reflect the official policy or position of the funding agencies.
M. Hajiabadi—Supported by NSF award CCF-1350939 and AFOSR Award FA9550-15-1-0274.
M. Mahmoody—Supported by NSF CAREER award CCF-1350939, and two University of Virginia’s SEAS Research Innovation Awards.
A. Rahimi—Supported by NSF award CCF-1350939.
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Notes
- 1.
This will guarantee that the leaf nodes are sorted in ascending order of the timestamps of the identities.
- 2.
Looking ahead, we need to store the root hashes of \(\mathsf {TimeTree}\) at mulitple times in order to ensure that the number of updates required by each person remains \(\log n\).
- 3.
The main advantage of having a Red-Black Merkle tree is that after each insertion, the depth of the tree does not increase beyond \(\log n\), where n is the number of people registered in the system. The balancing is not perfect, but ensures that further insertions, rearrangement after insertion to balance, searches, all take time \(O(\log n)\).
- 4.
Note that we must store the versions of the same \(\mathsf {TimeTree}\) at times corresponding to last updation of each \(\mathsf {Tree}_i\) in \(\mathcal {T}\). But there would only be \(\log n\) such versions.
- 5.
Alternately, we could have performed these operations for each i, which would be the number of trees in \(\mathcal {T}\). Here, we would have obtained a value \(\ne \bot \) only for one i.
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Garg, S., Hajiabadi, M., Mahmoody, M., Rahimi, A., Sekar, S. (2019). Registration-Based Encryption from Standard Assumptions. In: Lin, D., Sako, K. (eds) Public-Key Cryptography – PKC 2019. PKC 2019. Lecture Notes in Computer Science(), vol 11443. Springer, Cham. https://doi.org/10.1007/978-3-030-17259-6_3
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