Zeroizing Attacks Against Evasive and Circular Evasive LWE

2026
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Authors: Shweta Agrawal; Anuja Modi; Anshu Yadav; Shota Yamada
Published in: Theory of Cryptography
Publisher: Springer Nature Switzerland

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Abstract

This chapter delves into the vulnerabilities of evasive and circular evasive Learning With Errors (LWE) assumptions, focusing on zeroizing attacks. It introduces new counterexamples that challenge the security of these assumptions in both public and private-coin regimes. The text explores the implications of these attacks on various cryptographic constructions, including broadcast encryption and witness encryption. It also discusses the repercussions of these attacks on existing schemes and the need for refined assumptions to recover validity. The chapter provides a technical overview of the attacks, highlighting the conditions under which they are effective and the methods used to exploit the evasive LWE assumptions. Additionally, it compares these attacks with previous works, emphasizing the novelty and significance of the findings. The text concludes with a discussion on the impossibility of certain functional encryption schemes for pseudorandom functionalities, further underscoring the impact of these attacks on the field of lattice-based cryptography.

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Abstract

We develop new attacks against the Evasive LWE family of assumptions, in both the public and private-coin regime. To the best of our knowledge, ours are the first attacks against Evasive LWE in the public-coin regime, for any instantiation from the family. Our attacks are summarized below.

Public-Coin Attacks.

1.

The recent work by Hseih, Lin and Luo [17] constructed the first Attribute Based Encryption (ABE) for unbounded depth circuits by relying on the “circular” evasive LWE assumption. This assumption has been popularly considered as a safe, public-coin instance of Evasive LWE in contrast to its “private-coin” cousins (for instance, see [10, 11]).

We provide the first attack against this assumption, challenging the widely held belief that this is a public-coin assumption.

2.

We demonstrate a counter-example against vanilla public-coin evasive LWE by Wee [26] in an unnatural parameter regime. Our attack crucially relies on the error in the pre-condition being larger than the error in the post-condition, necessitating a refinement of the assumption.
Private-Coin Attacks.

1.

The recent work by Agrawal, Kumari and Yamada [2] constructed the first functional encryption scheme for pseudorandom functionalities (\(\textsf{PRFE}\)) and extended this to obfuscation for pseudorandom functionalities (\(\textsf{PRIO}\)) [4] by relying on private-coin evasive LWE. We provide a new attack against the assumption stated in the first posting of their work (subsequently refined to avoid these attacks).

2.

The recent work by Branco et al. [8] (concurrently to [4]) provides a construction of obfuscation for pseudorandom functionalities by relying on private-coin evasive LWE. We provide a new attack against their stated assumption.

3.

Branco et al. [8] showed that there exist contrived, “self-referential” classes of pseudorandom functionalities for which pseudorandom obfuscation cannot exist. We extend their techniques to develop an analogous result for pseudorandom functional encryption.

While Evasive LWE was developed to specifically avoid “zeroizing attacks”, our work shows that in certain settings, such attacks can still apply.

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Title: Zeroizing Attacks Against Evasive and Circular Evasive LWE
Authors: Shweta Agrawal
Anuja Modi
Anshu Yadav
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_9

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Zeroizing Attacks Against Evasive and Circular Evasive LWE

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