Constructions of symmetric-key encryption with guessing secrecy

Constructions of symmetric-key encryption with guessing secrecy are discussed. In the previous works, only a construction of symmetric-key encryption with average guessing secrecy is proposed for one-bit plaintexts. In this paper, we analyze a symmetric-key encryption with average guessing secrecy through OTP (one-time pad) constructions for a wide class of probability distributions of plaintexts and keys. As a result, we show a necessary and sufficient condition that such class of distributions satisfies average guessing secrecy in OTP constructions. On the other hand, we prove that optimal guessing secrecy is essentially equivalent to perfect secrecy under several natural restrictions. Therefore, only average guessing secrecy is meaningful for considering guessing secrecy other than perfect secrecy.