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arXiv:0903.4744 · Physical Review A

Deterministic quantum-public-key encryption: Forward search attack and randomization

Georgios M. Nikolopoulos, Lawrence M. Ioannou

Published Apr 21, 2009• 36 citations
arXivHTMLPDF

Abstract

In the classical setting, public-key encryption requires randomness in order to be secure against a forward search attack, whereby an adversary compares the encryption of a guess of the secret message with the encryption of the actual secret message. We show that this is also true in the information-theoretic setting---where the public keys are quantum systems---by defining and giving an example of a forward search attack for any deterministic quantum-public-key bit-encryption scheme. However, unlike in the classical setting, we show that any such deterministic scheme can be used as a black box to build a randomized bit-encryption scheme that is no longer susceptible to this attack.

DOI
10.1103/physreva.79.042327

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In the classical setting, public-key encryption requires randomness in order to be secure against a forward search attack, whereby an adversary compares the encryption of a guess of the secret message with the encryption of the actual secret message. We show that this is also true in the information-theoretic setting---where the public keys are quantum systems---by defining and giving an example of a forward search attack for any deterministic quantum-public-key bit-encryption scheme. However, unlike in the classical setting, we show that any such deterministic scheme can be used as a black box to build a randomized bit-encryption scheme that is no longer susceptible to this attack.
Public-key cryptosystems for quantum messages are considered from two aspects: public-key encryption and public-key authentication. Firstly, we propose a general construction of quantum public-key encryption scheme, and then construct an information-theoretic secure instance. Then, we propose a quantum public-key authentication scheme, which can protect the integrity of quantum messages. This scheme can both encrypt and authenticate quantum messages. It is information-theoretic secure with regard to encryption, and the success probability of tampering decreases exponentially with the security parameter with regard to authentication. Compared with classical public-key cryptosystems, one private-key in our schemes corresponds to an exponential number of public-keys, and every quantum public-key used by the sender is an unknown quantum state to the sender.
It is an important question to find constructions of quantum cryptographic protocols which rely on weaker computational assumptions than classical protocols. Recently, it has been shown that oblivious transfer and multi-party computation can be constructed from one-way functions, whereas this is impossible in the classical setting in a black-box way. In this work, we study the question of building quantum public-key encryption schemes from one-way functions and even weaker assumptions. Firstly, we revisit the definition of IND-CPA security to this setting. Then, we propose three schemes for quantum public-key encryption from one-way functions, pseudorandom function-like states with proof of deletion and pseudorandom function-like states, respectively.
We construct a quantum public key encryption scheme from oneway functions in the random oracle model. While our construction only has indistinguishability against restricted adversaries, who perform individual attacks and can only make classical queries to the random oracle, it possesses two practical advantages that were not achieved in previous works. First, legitimate participants can discard noisy quantum public keys. Second, the scheme only requires products of single-qubit states, and it does not require quantum computing or quantum memory for legitimate participants. Although the security does not hold against adversaries capable of large-scale quantum computation, we believe that our protocol is well-suited for the near-term stage of the quantum era.
In a public-key encryption scheme, if a sender is not concerned about the security of a message and is unwilling to generate costly randomness, the security of the encrypted message can be compromised. In this work, we characterize such lazy parties, who are regraded as honest parties, but are unwilling to perform a costly task when they are not concerned about the security. Specifically, we consider a rather simple setting in which the costly task is to generate randomness used in algorithms, and parties can choose either perfect randomness or a fixed string. We model lazy parties as rational players who behave rationally to maximize their utilities, and define a security game between the parties and an adversary. Since a standard secure encryption scheme does not work in the setting, we provide constructions of secure encryption schemes in various settings.
Randomness extraction is of fundamental importance for information-theoretic cryptography. It allows to transform a raw key about which an attacker has some limited knowledge into a fully secure random key, on which the attacker has essentially no information. Up to date, only very few randomness-extraction techniques are known to work against an attacker holding quantum information on the raw key. This is very much in contrast to the classical (non-quantum) setting, which is much better understood and for which a vast amount of different techniques are known and proven to work. We prove a new randomness-extraction technique, which is known to work in the classical setting, to be secure against a quantum attacker as well. Randomness extraction is done by XOR'ing a so-called delta-biased mask to the raw key. Our result allows to extend the classical applications of this extractor to the quantum setting. We discuss the following two applications. We show how to encrypt a long message with a short key, information-theoretically secure against a quantum attacker, provided that the attacker has enough quantum uncertainty on the message. This generalizes the concept of entropically-secure encryption to the case of a quantum attacker. As second application, we show how to do error-correction without leaking partial information to a quantum attacker. Such a technique is useful in settings where the raw key may contain errors, since standard error-correction techniques may provide the attacker with information on, say, a secret key that was used to obtain the raw key.