Although pNE is a new and unique provably secure variant of famous NTRU cryptosystem so far, the messageexpansion factor of pNE, similar to other variants of NTRU, is rather larger than that of other traditional public-key cryptosystems. In this paper, beside introducing RISKE, a new probabilistic secret-key cryptosystem based-on characteristics of invertible elements in binary truncated quotient polynomial rings, we combine it with pNE to construct a novel hybrid cryptosystem, named HpNE, which not only is IND-CPA secure but also has smaller message-expansion factor than pNE does.
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