Variants of rZK:

• rZK arguments: The same except that soundness is guaranteed for polynomial-time provers.

• rWI: Modify the security requirement to:

For any V*, x in L, and for any two witnesses w,wí for x, (P(w),V*)(x) _ (P(wí),V*)(x)

• rWH: Modify the security requirement to:

For any V*, x in L, and witness w for x,

Prob(V* will be able to compute w after the protocol) < neg

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