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Title:
KDM-Secure Public-Key Encryption from Constant-Noise LPN
Authors: Shuai Han, Shengli Liu
Abstract:The Learning Parity with Noise (LPN) problem has found many applications in cryptography due to its conjectured post-quantum hardness and simple algebraic structure. Over the years, constructions of different public-key primitives were proposed from LPN, but most of them are based on the LPN assumption with low noise rate rather than constant noise rate. A recent breakthrough was made by Yu and Zhang (Crypto’16), who constructed the first Public-Key Encryption (PKE) from constant-noise LPN. However, the problem of designing a PKE with Key-Dependent Message (KDM) security from constant-noise LPN is still open. In this paper, we present the first PKE with KDM-security assuming certain sub-exponential hardness of constant-noise LPN, where the number of users is predefined. The technical tool is two types of multi-fold LPN on squared-log entropy, one having independent secrets and the other independent sample subspaces. We establish the hardness of the multi-fold LPN variants on constant-noise LPN. Two squared-logarithmic entropy sources for multi-fold LPN are carefully chosen, so that our PKE is able to achieve correctness and KDM-security simultaneously.
ePrint: https://eprint.iacr.org/2017/310
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