Amplification of Non-interactive Zero Knowledge, Revisited

In an \((\varepsilon _s,\varepsilon _z)\) -weak non-interactive zero knowledge (NIZK), the soundness error is at most \(\varepsilon _s\) and the zero-knowledge error is at most \(\varepsilon _z\) . Goyal, Jain, and Sahai (CRYPTO 2019) stated that if \(\varepsilon _s+\varepsilon _z < 1\) for some constants \(\varepsilon _s,\varepsilon _z\) , then \((\varepsilon _s,\varepsilon _z)\) -weak NIZK can be turned into fully-secure NIZK, assuming sub-exponentially-secure public-key encryption. Later, however, they have discovered a gap in their proof. We revisit the problem of NIZK amplification: Our results take a different route than that of Goyal, Jain, and Sahai. They are based on the hidden-bits paradigm, and can be viewed as a reduction from NIZK amplification to the better understood problem of pseudorandomness amplification.