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# Blind Evaluation of Polynomials

How to make Blind Evaluation of Polynomials Verifiable

**How to make Blind Evaluation of Polynomials Verifiable**\
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Suppose that Jennifer has a polynomial P of degree d and Ted has a point s ∈ F p that he chose randomly. We want to construct a protocol that allows Ted to learn E ( P ( s ) ) , i.e. the hiding of P evaluated at s , with two additional properties:\
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Blindness: Jennifer will not learn s (and Ted will not learn P ). Verifiability: \
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The probability that Jennifer sends a value not of the form E ( P ( s ) ) for P of degree d that is known to her, but Ted still accepts – is negligible. \
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This is what we call verifiable blind evaluation of a polynomial. The protocol in Part II gave us the first item but not the second. To get verifiability we need an extended version of the Knowledge of Coefficient Assumption (KCA). \
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The verifiability and blindness properties are useful together because they make Jennifer decide what polynomial P she will use without seeing s . \
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This, in a sense, commits Jennifer to an “answer polynomial” without seeing the “challenge point” s .