Encryption with Weakly Random Keys Using Quantum Ciphertext

TL;DR

This paper demonstrates that quantum ciphertexts can enhance security in encryption schemes using weakly random keys, surpassing classical limitations by reducing adversary success probabilities.

Contribution

It introduces a quantum cryptosystem that bounds adversary success probabilities under weak randomness, outperforming classical bounds and showing quantum advantages in cryptography.

Findings

Quantum ciphertexts improve security bounds with weak keys.

Adversary's success probability is strictly less than 1 with non-zero entropy.

The scheme nearly matches classical bounds, except in one specific case.

Abstract

The lack of perfect randomness can cause significant problems in securing communication between two parties. McInnes and Pinkas proved that unconditionally secure encryption is impossible when the key is sampled from a weak random source. The adversary can always gain some information about the plaintext, regardless of the cryptosystem design. Most notably, the adversary can obtain full information about the plaintext if he has access to just two bits of information about the source (irrespective on length of the key). In this paper we show that for every weak random source there is a cryptosystem with a classical plaintext, a classical key, and a quantum ciphertext that bounds the adversary's probability p to guess correctly the plaintext strictly under the McInnes-Pinkas bound, except for a single case, where it coincides with the bound. In addition, regardless of the source of randomness, the adversary's probability p is strictly smaller than 1 as long as there is some uncertainty in the key (Shannon/min-entropy is non-zero). These results are another demonstration that quantum information processing can solve cryptographic tasks with strictly higher security than classical information processing.