Re-visiting the One-Time Pad

TL;DR

This paper challenges the traditional understanding of the One-Time Pad by showing it can be shorter than the message while maintaining perfect secrecy, and introduces a new interpretative framework and cryptographic paradigm.

Contribution

It proves OTP can be shorter than message length without losing secrecy and introduces private-object cryptography with a new interpretation of OTP encryption.

Findings

OTP length can be less than message length without compromising secrecy

A new interpretation treats message bits as statements about a secret-object

Proposes formal axiomatic systems for secret investment

Abstract

In 1949, Shannon proved the perfect secrecy of the Vernam cryptographic system,also popularly known as the One-Time Pad (OTP). Since then, it has 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 which actually contains useful information need not be compromised and could be less than the message length without sacrificing perfect secrecy. We also provide a new interpretation for the OTP encryption by treating the message bits as making True/False statements about the pad, which we define as a private-object. We introduce the paradigm of private-object cryptography where messages are transmitted by verifying statements about a secret-object. We conclude by suggesting the use of Formal Axiomatic Systems for investing N bits of secret.