Abstract
Lossy trapdoor functions (LTDF) and all-but-one trapdoor functions (ABO-TDF) are fundamental cryptographic primitives. And given the recent advances in quantum computing, it would be much desirable to develop new and improved lattice-based LTDF and ABO-TDF. In this work, we provide more compact cons
Highlights
It is well known that trapdoor functions (TDFs) and security under chosen ciphertext attack (CCA security)[1,2,3] are very important notions in public-key cryptosystem.Injective one-way trapdoor function F specifies, for each public key pk, a deterministic map Fpk that can be inverted given an associated trapdoor
In this work, following the general paradigm proposed in [8] we provide improved and more compact constructions of lossy trapdoor functions (LTDF) and all-but-one trapdoor functions (ABO-TDF) based on the learning with errors (LWE) problem
As a core building tool we provide a more compact homomorphic symmetric encryption schemes based on LWE, which might be of independent interest
Summary
It is well known that trapdoor functions (TDFs) and security under chosen ciphertext attack (CCA security)[1,2,3] are very important notions in public-key cryptosystem. In this work, following the general paradigm proposed in [8] we provide improved and more compact constructions of LTDF and ABO-TDF based on the LWE problem. To further reduce the size of the encrypted matrix of function indices of ABO-TDF, we make use of the full rank difference encoding (FRD) proposed in [23] (instead of the pairwise independent hash function originally used in [8]); The FRD technique reduces the matrix size, and can allow smaller system parameters to support super-polynomially many injective branches in the construction of CCA secure public key encryption, which further optimize the construction of ABO-TDF. The results presented in this work can substantially improve the performance of all the previous LWEbased cryptographic constructions based upon LTDF and ABO-TDF
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