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. However, they have since discovered a gap in their proof.

We revisit the problem of NIZK amplification: –We amplify NIZK arguments assuming only polynomially-secure public-key encryption, for any constants $\varepsilon_s+\varepsilon_z < 1$. –We amplify NIZK proofs assuming only one-way functions, for any constants $\varepsilon_s+\varepsilon_z < 1$. –When the soundness error $\varepsilon_s$ is negligible to begin with, we can also amplify NIZK arguments assuming only one-way functions.

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.