CCA Secure Public Key Encryption Scheme Based on LWE Without Gaussian Sampling

摘要

We present a CCA secure PKE based on the problem of the LWE with uniform errors. We use one of the instantiations of parameters of LWE with uniform errors suggested by Micciancio and Peikert (CRYPTO 2013). Since the uniform errors do not bear the Fourier-properities as the Gaussian errors, the statistical techniques and tools used by Micciancio and Peikert (EUROCRYPT 2012) to construct CCA secure PKE are not available for LWE with uniform errors. However, we conquer the problem by employing the double-trapdoor mechanism to construct a tag-based encryption with CCA security and transform it to a CCA secure PKE from the generic conversion based on one-time signatures.