One-Time Padding Still Matters in Modern Cryptography

A proof sketch for Theorem 1, which establishes achievability for safe and private source coding utilizing the output statistics of random binning (OSRB) approach, is shown in this section. Prior to adjusting the privacy leakage using the key's entropy contribution through one-time padding, a virtual situation without private keys is analyzed. This method shows how privacy and secrecy constraints can be met in the asymptotic regime as block length increases. Using common tools from information theory, the proof emphasizes how private keys can drastically lower leakage rates.