Re-visiting the One-Time Pad

In 1949, Shannon proved the perfect secrecy of the Vernam cryptographic system (One-Time Pad or OTP). It has generally been believed that the perfectly random and uncompressible OTP which is transmitted needs to have a length equal to the message length for this result to be true. In this paper, we prove that the length of the transmitted OTP actually contains useful information and could be exploited to compress the transmittedOTP while retaining perfect secrecy. The message bits can be interpreted as True/False statements about the OTP, a private object, leading to the notion of privateobject cryptography.