diff --git a/chap-OT-LWE.tex b/chap-OT-LWE.tex index fb0840b..b1a36e2 100644 --- a/chap-OT-LWE.tex +++ b/chap-OT-LWE.tex @@ -535,7 +535,7 @@ Adapting the technique of \cite{CNS07} to the lattice setting requires the foll (i) A signature scheme allowing to sign ciphertexts while remaining compatible with ZK proofs; (ii) A ZK protocol allowing to prove knowledge of a signature on some hidden ciphertext which belongs to a public set and was transformed into a given ciphertext; (iii) A protocol for proving the correct decryption of a ciphertext; (iv) A method of statistically re-randomizing an $\LWE$-encrypted ciphertext in a way that enables oblivious decryption. The first three ingredients can be obtained from \cref{ch:gs-lwe}. Since component (i) only needs to be secure against random-message attacks as long as the adversary obtains at most $N$ signatures, we use the simplified $\SIS$-based signature scheme of Section \ref{RMA-sec}. -The statistical re-randomization of Regev ciphertexts is handled via the noise flooding technique \cite{AJL+12}, which consists in drowning the initial noise with a super-polynomially larger +The statistical re-randomization of Regev ciphertexts is handled via the noise flooding technique \cite{AJL+12}, which consists in drowning the initial noise with a sub-exponentially larger noise. While recent results \cite{DS16,BDPMW16} provide potentially more efficient alternatives, we chose the flooding technique for simplicity because it does not require the use of FHE (and also because the known multi-bit version \cite{HAO15} of the GSW FHE~\cite{GSW13} incurs an \textit{ad hoc} circular security assumption).