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Ronny Ramzi Dakdouk
We construct obfuscators of point functions with multibit output and
other related functions. A point function with multibit output returns a fixed string
on a single input point and zero everywhere else. Obfuscation of such functions
has a useful application as a strong form of symmetric encryption which guarantees
security even when the key has very low entropy: Essentially, learning
information about the plaintext is paramount to finding the key via exhaustive
search on the key space.
Although the constructions appear to be simple and modular, their analysis turns out to be quite intricate. In particular, we uncover some weaknesses in the current definitions of obfuscation. One weakness is that current definitions do not guarantee security even under very weak forms of composition. We thus define a notion of obfuscation that is preserved under an appropriate composition operation. The constructions can use any obfuscator of point functions under the proposed definition. Alternatively, they can use perfect one way (POW) functions with statistical indistinguishability, or with computational indistinguishability at the price of somewhat weaker security.
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