Amplification of Non-interactive Zero Knowledge, Revisited

In an (ε_s,ε_z)-weak non-interactive zero knowledge (NIZK), the soundness error is at most ε_s and the zero-knowledge error is at most ε_z. Goyal, Jain, and Sahai (CRYPTO 2019) stated that if ε_s+ε_z<1 for some constants ε_s,ε_z, then (ε_s,ε_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:We amplify NIZK arguments assuming only polynomially-secure public-key encryption, for any constants ε_s+ε_z<1.We amplify NIZK proofs assuming only one-way functions, for any constants ε_s+ε_z<1.When the soundness error ε_s is negligible to begin with, we can also amplify NIZK arguments assuming only one-way functions. We amplify NIZK arguments assuming only polynomially-secure public-key encryption, for any constants ε_s+ε_z<1. We amplify NIZK proofs assuming only one-way functions, for any constants ε_s+ε_z<1. When the soundness error ε_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.