New Multilinear Maps from CLT13 with Provable Security Against Zeroizing Attacks

We devise the first weak multilinear map model for CLT13 multilinear maps (Coron et al., CRYPTO 2013) that captures all known classical polynomial-time attacks on the maps. We then show important applications of our model. First, we show that in our model, several existing obfuscation and order-revealing encryption schemes, when instantiated with CLT13 maps, are secure against known attacks under a mild algebraic complexity assumption used in prior work. These are schemes that are actually being implemented for experimentation. However, until our work, they had no rigorous justification for security. Next, we turn to building constant degree multilinear maps on top of CLT13 for which there are no known attacks. Precisely, we prove that our scheme achieves the ideal security notion for multilinear maps in our weak CLT13 model, under a much stronger variant of the algebraic complexity assumption used above. Our multilinear maps do not achieve the full functionality of multilinear maps as envisioned by Boneh and Silverberg (Contemporary Mathematics, 2003), but do allow for re-randomization and for encoding arbitrary plaintext elements.