International Association
for Cryptologic Research

Key-exfiltration attacks on cryptographic keys represent a significant threat to computer security. One proposed defense against such attacks is big-key cryptography which seeks to make cryptographic secrets so large that it is infeasible for an adversary to exfiltrate the key (without being detected). However, this also introduces an inconvenience to the user who must now store the large key on all of their different devices. The work of Döttling, Garg, Sekar and Wang (TCC 2022) introduces an elegant solution to this problem in the form of big-key identity-based encryption (IBE). Here, there is a large master secret key, but very short identity keys. The user can now store the large master secret key as her long-term key, and can provision each of her devices with short ephemeral identity keys (say, corresponding to the current date). In this way, the long-term secret key is protected by conventional big-key cryptography, while the user only needs to distribute short ephemeral keys to their different devices. Döttling et al. introduce and construct big-key IBE from standard pairing-based assumptions. However, their scheme only satisfies selective security where the adversary has to declare its challenge set of identities at the beginning of the security game. The more natural notion of security is adaptive security where the user can adaptively choose which identities it wants to challenge after seeing the public parameters (and part of the master secret key). In this work, we give the first adaptively-secure construction of big-key IBE from standard cryptographic assumptions. Our first construction relies on indistinguishability obfuscation (and one-way functions), while our second construction relies on witness encryption for NP together with standard pairing-based assumptions. To prove adaptive security, we rely on the dual-system methodology.

Registered attribute-based encryption (ABE) is a generalization of public-key encryption that enables fine-grained access control to encrypted data (like standard ABE), but without needing a central trusted authority. In a key-policy registered ABE scheme, users choose their own public and private keys and then register their public keys together with a decryption policy with an (untrusted) key curator. The key curator aggregates all of the individual public keys into a short master public key which serves as the public key for an ABE scheme. Currently, we can build registered ABE for restricted policies (e.g., Boolean formulas) from pairing-based assumptions and for general policies using witness encryption or indistinguishability obfuscation. In this work, we construct a key-policy registered ABE for general policies (specifically, bounded-depth Boolean circuits) from the \ell-succinct learning with errors (LWE) assumption in the random oracle model. The ciphertext size in our registered ABE scheme is poly(\lambda, d), where \lambda is a security parameter and d is the depth of the circuit that computes the policy circuit C. Notably, this is independent of the length of the attribute x and is optimal up to the poly(d) factor. Previously, the only lattice-based instantiation of registered ABE uses witness encryption, which relies on private-coin evasive LWE, a stronger assumption than \ell-succinct LWE. Moreover, the ciphertext size in previous registered ABE schemes that support general policies (i.e., from obfuscation or witness encryption) scales with poly(\lambda, |x|, |C|). The ciphertext size in our scheme depends only on the depth of the circuit (and not the length of the attribute or the size of the policy). This enables new applications to identity-based distributed broadcast encryption. Our techniques are also useful for constructing adaptively-secure (distributed) broadcast encryption, and we give the first scheme from the \ell-succinct LWE assumption in the random oracle model. Previously, the only lattice-based broadcast encryption scheme with adaptive security relied on witness encryption in the random oracle model. All other lattice-based broadcast encryption schemes only achieved selective security.

A broadcast encryption scheme allows a user to encrypt a message to $N$ recipients with a ciphertext whose size scales sublinearly with $N$. While broadcast encryption enables succinct encrypted broadcasts, it also introduces a strong trust assumption and a single point of failure; namely, there is a central authority who generates the decryption keys for all users in the system. Distributed broadcast encryption offers an appealing alternative where there is a one-time (trusted) setup process that generates a set of public parameters. Thereafter, users can independently generate their own public keys and post them to a public-key directory. Moreover, anyone can broadcast an encrypted message to any subset of user public keys with a ciphertext whose size scales sublinearly with the size of the broadcast set. Unlike traditional broadcast encryption, there are no long-term secrets in distributed broadcast encryption and users can join the system at any time (by posting their public key to the public-key directory). Previously, distributed broadcast encryption schemes were known from standard pairing-based assumptions or from powerful tools like indistinguishability obfuscation or witness encryption. In this work, we provide the first distributed broadcast encryption scheme from a falsifiable lattice assumption. Specifically, we rely on the $\ell$-succinct learning with errors (LWE) assumption introduced by Wee (CRYPTO 2024). Previously, the only lattice-based candidate for distributed broadcast encryption goes through general-purpose witness encryption, which in turn is only known from the private-coin evasive LWE assumption, a strong and non-falsifiable lattice assumption. Along the way, we also describe a more direct construction of broadcast encryption from lattices.

Zero-knowledge and succinctness are two important properties that arise in the study of non-interactive arguments. Previously, Kitagawa et al. (TCC 2020) showed how to obtain a non-interactive zero-knowledge (NIZK) argument for NP from a succinct non-interactive argument (SNARG) for NP. In particular, their work demonstrates how to leverage the succinctness property from an argument system and transform it into a zero-knowledge property. In this work, we study a similar question of leveraging succinctness for zero-knowledge. Our starting point is a batch argument for NP, a primitive that allows a prover to convince a verifier of $T$ NP statements $x_1, \ldots, x_T$ with a proof whose size scales sublinearly with $T$. Unlike SNARGs for NP, batch arguments for NP can be built from group-based assumptions in both pairing and pairing-free groups and from lattice-based assumptions. The challenge with batch arguments is that the proof size is only amortized over the number of instances, but can still encode full information about the witness to a small number of instances. We show how to combine a batch argument for NP with a local pseudorandom generator (i.e., a pseudorandom generator where each output bit only depends on a small number of input bits) and a dual-mode commitment scheme to obtain a NIZK for NP. Our work provides a new generic approach of realizing zero-knowledge from succinctness and highlights a new connection between succinctness and zero-knowledge.