International Association
for Cryptologic Research

In this work, we seek to optimize the efficiency of secure general-purpose obfuscation schemes. We focus on the problem of optimizing the obfuscation of general Boolean formulas -- this corresponds to optimizing the \"core obfuscator\'\' from the work of Garg, Gentry, Halevi, Raykova, Sahai, and Waters (FOCS 2013), and all subsequent works constructing general-purpose obfuscators. This core obfuscator builds upon approximate multilinear

maps, where efficiency in proposed instantiations is closely tied to the maximum number of ``levels\'\' of multilinearity required. The most efficient previous construction of a core obfuscator, due to Barak, Garg, Kalai, Paneth, and Sahai (Eurocrypt 2014) required the maximum number of levels of multilinearity to be $\\Theta(\\ell s^{6.82})$, where $s$ is the size of the Boolean formula to be obfuscated, and $\\ell$ is the number of input bits to the formula. In contrast, our construction only requires the maximum number of levels of multilinearity to be $\\Theta(\\ell s)$. This results in significant improvements in both the total size of the obfuscation, as well as the running time of evaluating an obfuscated formula.