Guessing Based on Compressed Side Information

A source sequence is to be guessed with some fidelity based on a rate-limited description of an observed which it correlated. The tension between the rate and exponential growth power mean required number guesses quantified. This can viewed as guessing version classical indirect-rate-distortion problem Dobrushin-Tsybakov’62 Witsenhausen’80. Judicious choices correlated sequence, rate, criterion recover recent results guessing. In context security, paper provides conservative estimates password’s remaining security after bits from database have been leaked.