Abstract
In 2011, Chris Peikert and Brent Waters proposed the concept of lossy trapdoor functions, which is an inherent and powerful cryptographic concept. Lossy trapdoor functions can be used for simple black-box constructing CCA encryption schemes, collision-resistent hash functions and oblivious transfer schemes. Chris Peikert and Brent Waters constructed lossy trapdoor functions based on decisional Diffie–Hellman assumption and learning with errors problem separately, which can be generalized to all-but-one trapdoor functions. In this paper, we generalize the lossy trapdoor functions and all-but-one trapdoor functions based on the polynomial ring separately, and we construct two types of trapdoor functions based on polynomial learning with errors assumption, which have more throughput and efficiency.
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