Arithmetic Cryptography
Constructions whose algorithms are arithmetic circuits making only black-box use of the underlying field or ring.
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Degree-2 Statistical RE Question 1.6 of the harvested paper, attributed there to Ishai-Kushilevitz and Applebaum-Ishai-Kushilevitz and described as open for almost 20 years. Degree-3 statistical encodings exist for every finite function; negative results are known for perfectly private degree 2. The harvested paper adds a new consequence, its Proposition 1.7. 4 open |
Arithmetic CryptographyNon Interactive Secure ComputationRandomized Encodingscharacterizationbarrier (ai) | |
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Arithmetic Two-Server PIR Optimality O(n^{1/3}) is achieved by arithmetizing the classical two-server schemes. The source states that whether it can be improved – let alone brought to sub-polynomial – is unknown, and supplies a linear-algebraic characterization of exactly what an improvement would require. 5 open |
Arithmetic CryptographyPrivate Information Retrievaltight-bound |
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