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Lecture notes in computer science

Public-Key Encryption and Injective Trapdoor Functions from LWE with Large Noise Rate

Liheng Ji, Yilei Chen

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.1007/978-3-032-10536-3_17

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Lossy Trapdoor Functions (LTFs) was introduced by Peikert and Waters in 2008. The importance of the LTFs was justified by their numerous cryptographic applications, like the construction of injective one-way trapdoor functions, CCA-secure public-key encryption, etc. However, little research on application of LTFs to key-leakage resilient public-key encryption was done. In this article we introduce a new variant of LTFs featuring leakage-resilience, namely lrLTFs and give a realization of lrLTFs with leakage rate 1/Θ(κ) (where κ is the security parameter) under the Decisional Diffie-Hellman (DDH) assumption. We further improve the leakage rate to 1-o(1) over a composite-order group in which the Decisional Composite Residuosity (DCR) assumption holds. We also introduce a new notion of key-leakage attacks, which we call weak key-leakage attacks, for bridging the adaptive and non-adaptive key-leakage attacks in the setting of public-key cryptosystem. In this model, the leakage adversary only gets a part of public key before accessing to a leakage oracle. We show that lrLTFs imply public-key encryption schemes secure against chosen-ciphertext weak key-leakage attacks in a black-box sense.
Proxy re-encryption (PRE) can guarantee the security of data sharing in the cloud making it important in ciphertext sharing in the cloud computing environment. Plenty of the current PRE algorithms based on the learning with errors (LWE) problem are constructed under the random oracle model or have problems such as long public parameter size, large ciphertext expansion rate, etc. We propose an identity-based PRE (IB-PRE) scheme using the LWE problem with short public parameters which can solve the mentioned challenges. Our scheme uses the blocking operation to decrease the public parameter size and a more useful trapdoor generation algorithm to reduce the trapdoor size. These two technologies improve the computational efficiency of the public key. We think that when we divide the identity id into 16 blocks, without much increase in computational overhead, the public key size can be reduced by 88.34%, and the scheme’s security level can remain unchanged. Our scheme achieves adaptive IND-ID-CPA security. It is unidirectional, collusion-resistant, and constructed under the standard model.