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The Winternitz one-time signature (WOTS) scheme, which can be described using a certain number of so-called ``function chains", plays an important role in the design of both stateless and stateful man...
We construct a graded encoding scheme (GES), an approximate form of graded multilinear maps. Our construction relies on indistinguishability obfuscation, and a pairing-friendly group in which (a suita...
We construct a general-purpose indistinguishability obfuscation (IO) scheme for all polynomial-size circuits from {\em constant-degree} graded encoding schemes in the plain model, assuming the existen...
We exploit the presence of a subfield to solve the NTRU problem for large moduli q: norming-down the public key h to a subfield may lead to an easier lattice problem, and any sufficiently good solut...
Multilinear maps have become popular tools for designing cryptographic schemes since a first approximate realisation candidate was proposed by Garg, Gentry and Halevi (GGH). This construction was la...
We present a candidate obfuscator based on composite-order Graded Encoding Schemes (GES), which are a generalization of multilinear maps. Our obfuscator operates on circuits directly without convert...
In this note we provide a more-or-less unified framework to talk about the functionality and security of graded encoding schemes, describe some variations of recent schemes, and discuss their securi...
We present a new general-purpose obfuscator for all polynomial-size circuits. The obfuscator uses graded encoding schemes, a generalization of multilinear maps. We prove that the obfuscator exposes no...

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