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1. Output Compression, MPC, and iO for Turing Machines

   https://doi.org/10.1007/978-3-030-34578-5_13  

   Badrinarayanan, S.; Fernando, R.; Koppula, Venkata; Sahai, Amit; Waters, Brent (November 2019, Advances in Cryptology ASIACRYPT 2019 - 25th International Conference on the Theory and Application of Cryptology and Information Securit)

   In this work, we study the fascinating notion of output-compressing randomized encodings for Turing Machines, in a shared randomness model. In this model, the encoder and decoder have access to a shared random string, and the efficiency requirement is, the size of the encoding must be independent of the running time and output length of the Turing Machine on the given input, while the length of the shared random string is allowed to grow with the length of the output. We show how to construct output-compressing randomized encodings for Turing machines in the shared randomness model, assuming iO for circuits and any assumption in the set {LWE, DDH, N𝑡ℎ Residuosity}. We then show interesting implications of the above result to basic feasibility questions in the areas of secure multiparty computation (MPC) and indistinguishability obfuscation (iO): 1.Compact MPC for Turing Machines in the Random Oracle Model. In the context of MPC, we consider the following basic feasibility question: does there exist a malicious-secure MPC protocol for Turing Machines whose communication complexity is independent of the running time and output length of the Turing Machine when executed on the combined inputs of all parties? We call such a protocol as a compact MPC protocol. Hubácek and Wichs [HW15] showed via an incompressibility argument, that, even for the restricted setting of circuits, it is impossible to construct a malicious secure two party computation protocol in the plain model where the communication complexity is independent of the output length. In this work, we show how to evade this impossibility by compiling any (non-compact) MPC protocol in the plain model to a compact MPC protocol for Turing Machines in the Random Oracle Model, assuming output-compressing randomized encodings in the shared randomness model. 2. Succinct iO for Turing Machines in the Shared Randomness Model. In all existing constructions of iO for Turing Machines, the size of the obfuscated program grows with a bound on the input length. In this work, we show how to construct an iO scheme for Turing Machines in the shared randomness model where the size of the obfuscated program is independent of a bound on the input length, assuming iO for circuits and any assumption in the set {LWE, DDH, N𝑡ℎ Residuosity}. 

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2. Adaptive Security via Deletion in Attribute-Based Encryption: Solutions from Search Assumptions in Bilinear Groups

   https://doi.org/10.1007/978-3-030-92068-5_11  

   Goyal, Rishab; Liu, Jiahui; Waters, Brent (December 2021, Asiacrypt 2021)

   One of the primary research challenges in Attribute-Based Encryption (ABE) is constructing and proving cryptosystems that are adaptively secure. To date the main paradigm for achieving adaptive security in ABE is dual system encryption. However, almost all such solutions in bilinear groups rely on (variants of) either the subgroup decision problem over composite order groups or the decision linear assumption. Both of these assumptions are decisional rather than search assumptions and the target of the assumption is a source or bilinear group element. This is in contrast to earlier selectively secure ABE systems which can be proven secure from either the decisional or search Bilinear Diffie-Hellman assumption. In this work we make progress on closing this gap by giving a new ABE construction for the subset functionality and prove security under the Search Bilinear Diffie-Hellman assumption. We first provide a framework for proving adaptive security in Attribute-Based Encryption systems. We introduce a concept of ABE with deletable attributes where any party can take a ciphertext encrypted under the attribute string and modify it into a ciphertext encrypted under any string where is derived by replacing any bits of with symbols (i.e. ``deleting" attributes of ). The semantics of the system are that any private key for a circuit can be used to decrypt a ciphertext associated with if none of the input bits read by circuit are symbols and . We show a pathway for combining ABE with deletable attributes with constrained psuedorandom functions to obtain adaptively secure ABE building upon the recent work of Tsabary. Our new ABE system will be adaptively secure and be a ciphertext-policy ABE that supports the same functionality as the underlying constrained PRF as long as the PRF is ``deletion conforming". Here we also provide a simple constrained PRF construction that gives subset functionality. Our approach enables us to access a broader array of Attribute-Based Encryption schemes support deletion of attributes. For example, we show that both the Goyal~et al.~(GPSW) and Boyen ABE schemes can trivially handle a deletion operation. And, by using a hardcore bit variant of GPSW scheme we obtain an adaptively secure ABE scheme under the Search Bilinear Diffie-Hellman assumption in addition to pseudo random functions in NC1. This gives the first adaptively secure ABE from a search assumption as all prior work relied on decision assumptions over source group elements. 

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3. How to Make Any Computational Secret Sharing Scheme Adaptively Secure

   Lu, George; Waters, Brent (August 2025, CRYPTO 2025)

   Secret sharing (SS) is a foundational cryptographic primitive with diverse applications, including secure multiparty computation and conditional disclosure of secrets. While traditional schemes have primarily emphasized information-theoretic security, recent advancements have increasingly leveraged computational assumptions to achieve more efficient constructions and support broader access policies. Despite these successes, most existing computational secret sharing (CSS) schemes are limited to a static security model, where adversaries must commit to their choice of corrupted participants at the outset. A critical challenge in CSS lies in achieving adaptive security, where adversaries can dynamically select participants to corrupt, better reflecting real-world threat models. In this paper, we present a novel transformation that converts any statically secure CSS scheme into an adaptively secure one while preserving the original access policy and computational assumptions, providing a framework for bridging the gap between static and adaptive security. Our construction introduces a multiplicative share size overhead of where is the number of parties. Additionally, we explore trade-offs in efficiency and security, offering more efficient adaptive CSS constructions for specific, restricted policy classes. This work addresses key limitations in the current landscape of CSS and paves the way for broader adoption of adaptively secure secret sharing in cryptographic applications. 

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4. Registered Attribute-Based Encryption

   https://doi.org/10.1007/978-3-031-30620-4_17  

   Hohenberger, Susan; Lu, George; Waters, Brent; Wu, David J. (April 2023, EUROCRYPT 2023)

   Attribute-based encryption (ABE) generalizes public-key encryption and enables fine-grained control to encrypted data. However, ABE upends the traditional trust model of public-key encryption by requiring a single trusted authority to issue decryption keys. If an adversary compromises the central authority and exfiltrates its secret key, then the adversary can decrypt every ciphertext in the system. This work introduces registered ABE, a primitive that allows users to generate secret keys on their own and then register the associated public key with a “key curator” along with their attributes. The key curator aggregates the public keys from the different users into a single compact master public key. To decrypt, users occasionally need to obtain helper decryption keys from the key curator which they combine with their own secret keys. We require that the size of the aggregated public key, the helper decryption keys, the ciphertexts, as well as the encryption/decryption times to be polylogarithmic in the number of registered users. Moreover, the key curator is entirely transparent and maintains no secrets. Registered ABE generalizes the notion of registration-based encryption (RBE) introduced by Garg et al. (TCC 2018), who focused on the simpler setting of identity-based encryption. We construct a registered ABE scheme that supports an a priori bounded number of users and policies that can be described by a linear secret sharing scheme (e.g., monotone Boolean formulas) from assumptions on composite-order pairing groups. Our approach deviates sharply from previous techniques for constructing RBE and only makes black-box use of cryptography. All existing RBE constructions (a weaker notion than registered ABE) rely on heavy non-black-box techniques. The encryption and decryption costs of our construction are comparable to those of vanilla pairing-based ABE. Two limitations of our scheme are that it requires a structured reference string whose size scales quadratically with the number of users (and linearly with the size of the attribute universe) and the running time of registration scales linearly with the number of users. Finally, as a feasibility result, we construct a registered ABE scheme that supports general policies and an arbitrary number of users from indistinguishability obfuscation and somewhere statistically binding hash functions. 

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5. Opening Up the Distinguisher: A Hardness to Randomness Approach for BPL = L that Uses Properties of BPL

   Doron, Dean; Pyne, Ted; Tell, Roei (June 2024, 56th Annual ACM Symposium on Theory of Computing (STOC 2024))

   We provide compelling evidence for the potential of hardness-vs.-randomness approaches to make progress on the long-standing problem of derandomizing space-bounded computation. Our first contribution is a derandomization of bounded-space machines from hardness assumptions for classes of uniform deterministic algorithms, for which strong (but non-matching) lower bounds can be unconditionally proved. We prove one such result for showing that BPL=L “on average”, and another similar result for showing that BPSPACE[O(n)]=DSPACE[O(n)]. Next, we significantly improve the main results of prior works on hardness-vs.-randomness for logspace. As one of our results, we relax the assumptions needed for derandomization with minimal memory footprint (i.e., showing BPSPACE[S]⊆ DSPACE[c · S] for a small constant c), by completely eliminating a cryptographic assumption that was needed in prior work. A key contribution underlying all of our results is non-black-box use of the descriptions of space-bounded Turing machines, when proving hardness-to-randomness results. That is, the crucial point allowing us to prove our results is that we use properties that are specific to space-bounded machines. 

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