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arXiv:1307.3753

Classical Encryption and Authentication under Quantum Attacks

Maria Velema

Published Jul 14, 2013• 1 citation
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Abstract

Post-quantum cryptography studies the security of classical, i.e. non-quantum cryptographic protocols against quantum attacks. Until recently, the considered adversaries were assumed to use quantum computers and behave like classical adversaries otherwise. A more conservative approach is to assume that also the communication between the honest parties and the adversary is (partly) quantum. We discuss several options to define secure encryption and authentication against these stronger adversaries who can carry out 'superposition attacks'. We re-prove a recent result of Boneh and Zhandry, stating that a uniformly random function (and hence also a quantum-secure pseudorandom function) can serve as a message-authentication code which is secure, even if the adversary can evaluate this function in superposition.

DOI
10.48550/arxiv.1307.3753

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Post-quantum cryptography studies the security of classical, i.e. non-quantum cryptographic protocols against quantum attacks. Until recently, the considered adversaries were assumed to use quantum computers and behave like classical adversaries otherwise. A more conservative approach is to assume that also the communication between the honest parties and the adversary is (partly) quantum. We discuss several options to define secure encryption and authentication against these stronger adversaries who can carry out 'superposition attacks'. We re-prove a recent result of Boneh and Zhandry, stating that a uniformly random function (and hence also a quantum-secure pseudorandom function) can serve as a message-authentication code which is secure, even if the adversary can evaluate this function in superposition.
Quantum algorithms have demonstrated promising speed-ups over classical algorithms in the context of computational learning theory - despite the presence of noise. In this work, we give an overview of recent quantum speed-ups, revisit the Bernstein-Vazirani algorithm in a new learning problem extension over an arbitrary cyclic group and discuss applications in cryptography, such as the Learning with Errors problem. We turn to post-quantum cryptography and investigate attacks in which an adversary is given quantum access to a classical encryption scheme. In particular, we consider new notions of security under non-adaptive quantum chosen-ciphertext attacks and propose symmetric-key encryption schemes based on quantum-secure pseudorandom functions that fulfil our definitions. In order to prove security, we introduce novel relabeling techniques and show that, in an oracle model with an arbitrary advice state, no quantum algorithm making superposition queries can reliably distinguish between the class of functions that are randomly relabeled at a small subset of the domain. Finally, we discuss current progress in quantum computing technology, particularly with a focus on implementations of quantum algorithms on the ion-trap architecture, and shed light on the relevance and effectiveness of common noise models adopted in computational learning theory.
We give a new class of security definitions for authentication in the quantum setting. These definitions capture and strengthen existing definitions of security against quantum adversaries for both classical message authentication codes (MACs) and well as full quantum state authentication schemes. The main feature of our definitions is that they precisely characterize the effective behavior of any adversary when the authentication protocol accepts, including correlations with the key. Our definitions readily yield a host of desirable properties and interesting consequences; for example, our security definition for full quantum state authentication implies that the entire secret key can be re-used if the authentication protocol succeeds. Next, we present several protocols satisfying our security definitions. We show that the classical Wegman-Carter authentication scheme with 3-universal hashing is secure against superposition attacks, as well as adversaries with quantum side information. We then present conceptually simple constructions of full quantum state authentication. Finally, we prove a lifting theorem which shows that, as long as a protocol can securely authenticate the maximally entangled state, it can securely authenticate any state, even those that are entangled with the adversary. Thus, this shows that protocols satisfying a fairly weak form of authentication security automatically satisfy a stronger notion of security (in particular, the definition of Dupuis, et al (2012)).
Cryptography enables modern-day secure communication. The advancement of quantum algorithms has made classical cryptosystems ineffective. Important data has been encrypted and verified using digital signatures and cryptography. Classical cryptography systems were on the edge of collapse when quantum algorithms were introduced, since quantum computers can solve complex problems in less time. It is important to be prepared for future threats, even if standard cryptosystems are presumably safe for the moment being because quantum computing is not yet developed. One use of quantum cryptography is quantum key distribution (QKD), which is a way to safely share encryption keys between communication parties by utilizing quantum physics. Hybrid classical-quantum methods offer protection from both classical & quantum attackers, which can help smooth the way for the change. We introduce a new way to build hybrid encryption schemes from preexisting ones. First, the paper examines classical cryptosystems vulnerability to quantum computers. Then, it investigate into different families of post-quantum cryptosystems, checks in on the NIST's post-quantum cryptography consistency process, and finally, compares the performance of algorithms using post-quantum cryptography on various platforms. Along with discussing and evaluating current methods, this paper also discusses a novel hybrid quantum cryptographic system that employs message authentication codes with enhanced lattice based cryptography.
In post-quantum approach, we consider classical (non-quantum) protocols and primitives which are run by honest parties on classical computers and our aim is to keep their security in an environment where the adversary can rely on quantum computers [3].In particular, even a harder goal is set by requiring provable security guaranties in a concurrent running environment as we aim computational UC-security.Unruh [16] conjectured that classical arguments of computational UC-security remain usable in a postquantum world as long as the underlying computational UC-secure primitives are also computationally quantum UC-secure.Our proposed technique (full factorization) aims at reducing the original protocol into a statisticallysecure protocol by turning the protocol into a hybrid one where all cryptographic primitives are substituted by appropriate ideal functionalities.The considered set of primitives consists of secret key and public key encryption as well as digital signature.This way and by applying the Unruh's Quantum Lifting Theorem as well as the Quantum Universal Composition Theorem we gain a computationally quantum UC-secure protocol from a classical UC-secure protocol.We consider quantum standard-security, where the adversary can send only classical inputs to honest algorithms, i.e. honest machines cannot receive quantum superposition of inputs If we add also the practical need of efficiency our example is the class of protocols built from symmetric key primitives.A practical (fast) implementation could be based on AES encryption algorithm with appropriate key size as long as we live with the wide belief that this algorithm is secure against a quantum adversary.
We propose and develop new schemes for post-quantum cryptography based on isogenies over elliptic curves. First we show that ordinary elliptic curves are have less than exponential security against quantum computers. These results were used as the motivation for De Feo, Jao and Pl\\^ut's construction of public key cryptosystems using supersingular elliptic curve isogenies. We extend their construction and show that isogenies between supersingular elliptic curves can be used as the underlying hard mathematical problem for other quantum-resistant schemes. For our second contribution, we propose is an undeniable signature scheme based on elliptic curve isogenies. We prove its security under certain reasonable number-theoretic computational assumptions for which no efficient quantum algorithms are known. This proposal represents only the second known quantum-resistant undeniable signature scheme, and the first such scheme secure under a number-theoretic complexity assumption. Finally, we also propose a security model for evaluating the security of authenticated encryption schemes in the post-quantum setting. Our model is based on a combination of the classical Bellare-Namprempre security model for authenticated encryption together with modifications from Boneh and Zhandry to handle message authentication against quantum adversaries. We give a generic construction based on Bellare-Namprempre for producing an authenticated encryption protocol from any quantum-resistant symmetric-key encryption scheme together with any digital signature scheme or MAC admitting any classical security reduction to a quantum-computationally hard problem. We apply the results and show how we can explicitly construct authenticated encryption schemes based on isogenies.
When it became known that quantum computers could break the RSA (named for its creators – Rivest, Shamir, and Adleman) encryption algorithm within a polynomialtime, quantum cryptography began to be actively studied. Other classical cryptographic algorithms are only secure when malicious users do not have sufficient computational power to break security within a practical amount of time. Recently, many quantum authentication protocols sharing quantum entangled particles between communicators have been proposed, providing unconditional security. An issue caused by sharing quantum entangled particles is that it may not be simple to apply these protocols to authenticate a specific user in a group of many users. An authentication protocol using quantum superposition states instead of quantum entangled particles is proposed. The random number shared between a sender and a receiver can be used for classical encryption after the authentication has succeeded. The proposed protocol can be implemented with the current technologies we introduce in this paper.