We introduce the notion of non-malleable noninteractive zero-knowledge (NIZK) proof systems. We show how to transform any ordinary NIZK proof system into one that has strong non-m...
We present a fully proof-producing implementation of a quantifier elimination procedure for real closed fields. To our knowledge, this is the first generally useful proof-producing...
A zero-knowledge proof allows a prover to convince a verifier of an assertion without revealing any further information beyond the fact that the assertion is true. Secure multipar...
Let Λ : {0, 1}n ×{0, 1}m → {0, 1} be a Boolean formula of size d, or more generally, an arithmetic circuit of degree d, known to both Alice and Bob, and let y ∈ {0, 1}m be a...
We show that if a language L has a 4-round, black-box, computational zero-knowledge proof system with negligible soundness error, then ¯L ∈ MA. Assuming the polynomial hierarch...