Pseudorandom FE, iO and Applications

2026
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Authors: Shweta Agrawal; Simran Kumari; Shota Yamada
Published in: Theory of Cryptography
Publisher: Springer Nature Switzerland

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Abstract

The chapter delves into the realm of pseudorandom functional encryption (PRFE) and its applications in advanced cryptographic systems. It begins by introducing attribute-based encryption (ABE) and its generalization to predicate encryption, highlighting the challenges and recent progress in constructing ABE for circuits of unbounded depth. The text explores the use of evasive LWE assumptions and their implications for secure cryptographic constructions. It presents new tools such as functional encryption for pseudorandom functionalities and discusses their applications in achieving secure ABE schemes. The chapter also addresses recent attacks on evasive LWE assumptions and proposes solutions to mitigate these vulnerabilities. Additionally, it covers the construction of multi-input predicate encryption (MIPE) and its applications, as well as the instantiation of random oracles using PRFE. The text concludes with a technical overview and a discussion on the security and efficiency of the proposed constructions, providing a comprehensive overview of the latest advancements in the field of cryptography.

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Abstract

We propose the abstractions of Functional Encryption (FE) and Indistinguishability Obfuscation (iO) for pseudorandom functionalities which are strictly weaker than their general counterparts. Intuitively, a pseudorandom functionality means that the output of the circuit is indistinguishable from uniform for every input seen by the adversary. We then leverage weak indistinguishability style security of these tools to obtain the following applications:

Attribute Based Encryption for Unbounded Depth Circuits. Assuming \(\text {IND}\)-secure FE for pseudorandom functionalities and LWE, we construct Attribute Based Encryption (ABE) for circuits of unbounded depth. Previously, such ABE required the circular Evasive LWE assumption (Hseih, Lin and Luo, Focs 2023) which has recently been subject to zeroizing attacks.

Attribute Based Encryption for Turing Machines. Assuming \(\text {IND}\)-secure FE for pseudorandom functionalities and circular small-secret LWE, we construct Attribute Based Encryption (ABE) for Turing machines. Previously, such ABE required either private coin Evasive LWE (Agrawal, Kumari and Yamada, Crypto 2024) or circular Evasive LWE (Cini and Wee, Eurocrypt 2025), both of which admit attacks in the general case.

Multi Input Predicate Encryption for Polynomial Arity. Assuming \(\text {IND}\)-secure multi-input FE for pseudorandom functionalities, we construct Multi Input Predicate Encryption (\(\textsf{MIPE}\)) for \(\textsf{P}\) for polynomial arity. Previously, \(\textsf{MIPE}\) for \(\textsf{P}\) was known only for constant arity, using private coin evasive LWE (Agrawal, Rossi, Yadav and Yamada, Crypto 2023).

Instantiating the Random Oracle. We use our \(\text {IND}\)-secure iO for pseudorandom functionalities to instantiate the random oracle in several applications that previously used iO (Hohenberger, Sahai and Waters, Eurocrypt 2014) such as full-domain hash signature based on trapdoor permutations and more.

We provide heuristic constructions of FE and MIFE for pseudorandom functionalities from private coin evasive LWE and plain LWE, where private coin evasive LWE is suitably parametrized to avoid all know attacks for the functionalities we consider in this work. This implies iO for pseudorandom functionalities from the same assumptions.

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previous chapter Obfuscating Pseudorandom Functions is Post-quantum Complete

next chapter Zeroizing Attacks Against Evasive and Circular Evasive LWE

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Title: Pseudorandom FE, iO and Applications
Authors: Shweta Agrawal
Simran Kumari
Shota Yamada
Publisher: Springer Nature Switzerland
Book: Theory of Cryptography
Print ISBN: 978-3-032-12292-6

Electronic ISBN: 978-3-032-12293-3

Copyright Year: 2026
DOI: https://doi.org/10.1007/978-3-032-12293-3_8

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