Polynomial-Time, Semantically-Secure Encryption Achieving the Secrecy Capacity

TL;DR

This paper presents the first polynomial-time encryption scheme that achieves the secrecy capacity of the wiretap channel while ensuring semantic security, combining optimal rate with strong security guarantees.

Contribution

It introduces a novel polynomial-time scheme that attains the secrecy capacity and achieves semantic security, surpassing previous schemes limited to weaker security notions.

Findings

Achieves secrecy capacity with polynomial-time encryption and decryption.

Ensures semantic security, a stronger security notion than traditional wiretap security.

Demonstrates that optimal secure communication rate is feasible with efficient algorithms.

Abstract

In the wiretap channel setting, one aims to get information-theoretic privacy of communicated data based only on the assumption that the channel from sender to receiver is noisier than the one from sender to adversary. The secrecy capacity is the optimal (highest possible) rate of a secure scheme, and the existence of schemes achieving it has been shown. For thirty years the ultimate and unreached goal has been to achieve this optimal rate with a scheme that is polynomial-time. (This means both encryption and decryption are proven polynomial time algorithms.) This paper finally delivers such a scheme. In fact it does more. Our scheme not only meets the classical notion of security from the wiretap literature, called MIS-R (mutual information security for random messages) but achieves the strictly stronger notion of semantic security, thus delivering more in terms of security without loss of rate.