The purpose of this paper is to compare side-by-side the NTRU and BGV schemes in their non-scale invariant (messages in the lower bits), and their scale invariant (message in the upper bits) forms. The scale invariant versions are often called the YASHE and FV schemes. As an additional optimization, we also investigate the ffect of modulus reduction on the scale-invariant schemes. We compare the schemes using the "average case" noise analysis presented by Gentry et al. In addition we unify notation and techniques so as to show commonalities between the schemes. We find that the BGV scheme appears to be more efficient for large plaintext moduli, whilst YASHE seems more efficient for small plaintext moduli (although the benefit is not as great as one would have expected).
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