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08 December 2025
Tapas Pal, Robert Schädlich
ePrint Report
We present a unified framework for constructing registered attribute-based encryption (RABE) and registered functional encryption (RFE) from the standard (bilateral) $k$-Lin assumption in asymmetric bilinear pairing groups. Specifically, our schemes capture the following functionalities.
- RABE for logspace Turing machines. We present the first RABE for deterministic and nondeterministic logspace Turing machines (TMs), corresponding to the uniform complexity classes $\mathsf L$ and $\mathsf{NL}$. That is, we consider policies $g$ computable by a TM with a polynomial time bound $T$ and a logarithmic space bound $S$. The public parameters of our schemes scale only with the number of states of the TM, but remain independent of the attribute length and the bounds $T,S$. Thus, our system is capable of verifying unbounded-length attributes $\mathbf y$ while the maximum number of states needs to be fixed upfront.
- RFE for attribute-based attribute-weighted sums (AB-AWS). Building upon our RABE, we develop RFE for AB-AWS. In this functionality, a function is described by a tuple $f=(g,h)$, takes $(\mathbf y, \{(\mathbf x_j, \mathbf z_j)\}_{j\in[N]})$ as input for an unbounded integer $N$, and outputs $\sum_{j\in[N]}\mathbf z_jh(\mathbf x_j)^\top$ if and only if $g(\mathbf y) = 0$. Here, $\{\mathbf z_j\}_j$ are private inputs that are hidden in the ciphertext, whereas $\mathbf y$ and $\{\mathbf x_j\}_j$ can be public. Our construction can instantiate $g,h$ with deterministic logspace TMs, while a previous construction due to [Pal and Schädlich, Eprint 2025] only supports arithmetic branching programs (ABPs), i.e. a non-uniform model of computation.
- RFE for attribute-based quadratic functions (AB-QF). Furthermore, we build the first RFE for AB-QF with compact ciphertexts. In this functionality, a function is described by a tuple $f=(g,\mathbf h)$, takes input $(\mathbf y,(\mathbf z_1,\mathbf z_2))$ and outputs $(\mathbf z_1\otimes\mathbf z_2)\mathbf h^\top$ if and only if $g(\mathbf y)=0$. Here, $(\mathbf z_1, \mathbf z_2)$ are private inputs whereas the attribute $\mathbf y$ is public. Policies can be computed by ABPs or deterministic logspace TMs. Prior to our work, the only known construction of RFE for quadratic functions from standard assumptions [Zhu et al., Eurocrypt 2024] did not provide any access control.
Conceptually, we transfer the framework of [Lin and Luo, Eurocrypt 2020], which combines linear FE with information-theoretic garbling schemes, from standard to registered FE. At the core of our constructions, we introduce a novel RFE for inner products with user-specific pre-constraining of the functions which enables the on-the-fly randomization of garbling schemes akin to standard inner-product FE. This solves an open question raised in [Zhu et al., Asiacrypt 2023] who constructed RABE from predicate encodings but left open the problem of building RABE in a more general setting from linear garbling schemes.
- RABE for logspace Turing machines. We present the first RABE for deterministic and nondeterministic logspace Turing machines (TMs), corresponding to the uniform complexity classes $\mathsf L$ and $\mathsf{NL}$. That is, we consider policies $g$ computable by a TM with a polynomial time bound $T$ and a logarithmic space bound $S$. The public parameters of our schemes scale only with the number of states of the TM, but remain independent of the attribute length and the bounds $T,S$. Thus, our system is capable of verifying unbounded-length attributes $\mathbf y$ while the maximum number of states needs to be fixed upfront.
- RFE for attribute-based attribute-weighted sums (AB-AWS). Building upon our RABE, we develop RFE for AB-AWS. In this functionality, a function is described by a tuple $f=(g,h)$, takes $(\mathbf y, \{(\mathbf x_j, \mathbf z_j)\}_{j\in[N]})$ as input for an unbounded integer $N$, and outputs $\sum_{j\in[N]}\mathbf z_jh(\mathbf x_j)^\top$ if and only if $g(\mathbf y) = 0$. Here, $\{\mathbf z_j\}_j$ are private inputs that are hidden in the ciphertext, whereas $\mathbf y$ and $\{\mathbf x_j\}_j$ can be public. Our construction can instantiate $g,h$ with deterministic logspace TMs, while a previous construction due to [Pal and Schädlich, Eprint 2025] only supports arithmetic branching programs (ABPs), i.e. a non-uniform model of computation.
- RFE for attribute-based quadratic functions (AB-QF). Furthermore, we build the first RFE for AB-QF with compact ciphertexts. In this functionality, a function is described by a tuple $f=(g,\mathbf h)$, takes input $(\mathbf y,(\mathbf z_1,\mathbf z_2))$ and outputs $(\mathbf z_1\otimes\mathbf z_2)\mathbf h^\top$ if and only if $g(\mathbf y)=0$. Here, $(\mathbf z_1, \mathbf z_2)$ are private inputs whereas the attribute $\mathbf y$ is public. Policies can be computed by ABPs or deterministic logspace TMs. Prior to our work, the only known construction of RFE for quadratic functions from standard assumptions [Zhu et al., Eurocrypt 2024] did not provide any access control.
Conceptually, we transfer the framework of [Lin and Luo, Eurocrypt 2020], which combines linear FE with information-theoretic garbling schemes, from standard to registered FE. At the core of our constructions, we introduce a novel RFE for inner products with user-specific pre-constraining of the functions which enables the on-the-fly randomization of garbling schemes akin to standard inner-product FE. This solves an open question raised in [Zhu et al., Asiacrypt 2023] who constructed RABE from predicate encodings but left open the problem of building RABE in a more general setting from linear garbling schemes.