The article takes a verifier of equivalence of the quality of indistinguishability (uncertainty) of the semantic security for the cryptosystems defense against of attacker's cryptanalyses based on matched (selected) open text. The issues of analysis and research of security models of post-quantum cryptoalgorithms in relation to cryptoprimitives of all types, the definition of criteria for assessing their compliance with different security models (according to different types of crypto-transformations) are relevant and of practical importance. The indistinguishability (uncertainty) of encrypted text is an important property of the security of many encryption schemes. The indistinguishability (uncertainty) property when attacking on the basis of matched (selected) plain text is considered a basic requirement for the majority of reliably protected public-key cryptosystems. Some schemes also provide an indistinguishability for attack based on selected (selected) encrypted text and attack based on adaptively picked (selected) encrypted text. The indistinguishability (uncertainty) of an attack on the basis of a selected (selected) open text is equivalent to the properties of semantic security. If the cryptosystem has the property of indistinguishability, the attacker will not be able to distinguish between pairs of encrypted texts based on the message that they encrypt. In the case of non-differentiation (uncertainty) of ciphertext protects all known cryptosystems from the intruder which: is a probabilistic Turing machine of polynomial time; has all algorithms; has full access to communications. Using the property of the indeterminacy (uncertainty) of the encrypted text at the present time, it is guaranteed to protect all known symmetric and asymmetric cryptosystems from the classical or quantum cryptanalysis of the intruder. Here are a review of mostly attacks on the encryption security namely an attack based on adaptively matched (selected) ciphertexts, an attack based on adaptively matched (selected) open texts, an attack based on both of this types of texts, an attack based on matched (selected) ciphertexts, an attack based on matched (selected) open texts and a recognition attacks (recognizability).
The article takes a verifier of equivalence of the quality of indistinguishability (uncertainty) of the semantic security for the cryptosystems defense against of attacker's cryptanalyses based on matched (selected) open text. The issues of analysis and research of security models of post-quantum cryptoalgorithms in relation to cryptoprimitives of all types, the definition of criteria for assessing their compliance with different security models (according to different types of crypto-transformations) are relevant and of practical importance. The indistinguishability (uncertainty) of encrypted text is an important property of the security of many encryption schemes. The indistinguishability (uncertainty) property when attacking on the basis of matched (selected) plain text is considered a basic requirement for the majority of reliably protected public-key cryptosystems. Some schemes also provide an indistinguishability for attack based on selected (selected) encrypted text and attack based on adaptively picked (selected) encrypted text. The indistinguishability (uncertainty) of an attack on the basis of a selected (selected) open text is equivalent to the properties of semantic security. If the cryptosystem has the property of indistinguishability, the attacker will not be able to distinguish between pairs of encrypted texts based on the message that they encrypt. In the case of non-differentiation (uncertainty) of ciphertext protects all known cryptosystems from the intruder which: is a probabilistic Turing machine of polynomial time; has all algorithms; has full access to communications. Using the property of the indeterminacy (uncertainty) of the encrypted text at the present time, it is guaranteed to protect all known symmetric and asymmetric cryptosystems from the classical or quantum cryptanalysis of the intruder. Here are a review of mostly attacks on the encryption security namely an attack based on adaptively matched (selected) ciphertexts, an attack based on adaptively matched (selected) open texts, an attack based on both of this types of texts, an attack based on matched (selected) ciphertexts, an attack based on matched (selected) open texts and a recognition attacks (recognizability).
In this paper, the essence is considered and security models of asymmetric post-quantum cryptographic primitives of different types are investigated. The basis taken security models that are recommended by NIST USA in the requirements of the PQC competition for candidates for post-quantum cryptographic primitives. Such algorithms include asymmetric cryptographic transformations such as asymmetric encryption, digital signature, and key encapsulation mechanism. The following security models are recommended, which are related to: the asymmetric encryption — IND-CCA2 (IND-CPA, IND-CCA); the digital signature — EUF-CMA (and its variations); the key encapsulation mechanisms — СK-model. In this paper, the basic essence of such security models is considered. The use of security models in research of cryptographic primitives is relatively new. A generalization of each of these models and a definition of the necessity and conditions, and the consequences of their application are required. Such models take into account the application environment in which an unauthenticated-links adversarial model and authenticated-links adversarial model can operate. The paper considers the concept of indistinguishability and security model of post-quantum asymmetric ciphers on its basis. The property of indistinguishability under chosen plaintext attack is determined. The concept of semantic security is considered. The types of most common attacks based on indistinguishability are given. Existing versions of the EUF-CMA security model — SUF-CMA, etc. are considered. Definitions of «forward security, forward secrecy» and «perfect forward secrecy (PFS)» are given. In addition, the paper considers the peculiarities of the application regarding to perspective asymmetric transformations of the «game theory». The definition of concept «game theory» is given
Quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model which grants the adversary quantum oracle access to encryption and decryption, but where the latter is restricted to non-adaptive (i.e., pre-challenge) queries only. We define this model formally using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA1 in analogy to the classical CCA1 security model. Using a bound on quantum random-access codes, we show that the standard PRF-based encryption schemes are QCCA1-secure when instantiated with quantum-secure primitives. We then revisit standard IND-CPA-secure Learning with Errors (LWE) encryption and show that leaking just one quantum decryption query (and no other queries or leakage of any kind) allows the adversary to recover the full secret key with constant success probability. In the classical setting, by contrast, recovering the key requires a linear number of decryption queries. The algorithm at the core of our attack is a (large-modulus version of) the well-known Bernstein-Vazirani algorithm. We emphasize that our results should not be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.
Large-scale quantum computing poses a major threat to classical public-key cryptography. Recently, strong “quantum access” security models have shown that numerous symmetric-key cryptosystems are also vulnerable. In this paper, we consider classical encryption in a model that grants the adversary quantum oracle access to encryption and decryption, but where we restrict the latter to non-adaptive (i.e., pre-challenge) queries only. We formalize this model using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA 1 in analogy to the classical CCA 1 security model. We show that the standard pseudorandom function ( PRF )-based encryption schemes are QCCA 1 -secure when instantiated with quantum-secure primitives. Our security proofs use a strong bound on quantum random-access codes with shared randomness. Revisiting plain IND − CPA -secure Learning with Errors ( LWE ) encryption, we show that leaking only a single quantum decryption query (and no other leakage or queries of any kind) allows the adversary to recover the full secret key with constant success probability. Information-theoretically, full recovery of the key in the classical setting requires at least a linear number of decryption queries. Our results thus challenge the notion that LWE is unconditionally “just as secure” quantumly as it is classically. The algorithm at the core of our attack is a new variant of the well-known Bernstein–Vazirani algorithm. Finally, we emphasize that our results should not be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.
Due to the development of technologies for quantum computing and the introduction of quantum computer, there is a threat to the current state of protection of cryptographic systems with a public key. With an advent of quantum computer that would have the volume of register required for the methods of quantum cryptanalysis, the stability of existing crypto algorithms will significantly degrade. This necessitates the creation of algorithms resistant to the methods of quantum cryptanalysis. The European project «New European Schemes for Signatures, Integrity, and Encryptions» (NESSIE) and the National Institute of Standards and Technologies (NIST) of the USA announced a start of recruiting the applicants for the contest of post-quantum algorithms whose standards are planned to be adopted over 2020–2022. In order to compare, a procedure for evaluation was selected based on integral assessments of unconditional and conditional criteria. An analysis was conducted among the algorithms that fulfilled general unconditional criteria. As conditional criteria, we chose numerical characteristics of algorithms. In addition, additional unconditional criteria were put forward.A relevant task is the comparative analysis and evaluation of a possibility to use the post-quantum mechanisms, which are represented by the algorithms that already exist, depending on the conditions of applying them. At present, only the possibility of using the appropriate crypto transformations over a post-quantum period is being examined, but the analysis of advantages of one over another has not been run yet. In addition, it is necessary to evaluate the very possibility to use such algorithms taking into account those constraints that are imposed by the existing information systems.Results of present research allow us to understand current state in the development of post-quantum crypto algorithms and to predict their possible further development.This forecast is important in that the post-quantum cryptographic mechanisms represent a new stage in the development and use of cryptography. In addition, the practical value of the research consists in obtaining the evaluation for post-quantum algorithms.
Virtually all asymmetric cryptographic schemes currently in use are threatened by the potential development of powerful quantum computers. Although there is currently no definite answer and it is very unclear when or even if CRQC will ever be built and the gap between modern quantum computers and the envisioned CRQC is huge, the risk of creating CRQC means that currently deployed public key cryptography must be replaced by quantum-resistant ones alternatives. For example, information encrypted using modern public key cryptography can be recorded by cryptanalysts and then attacked if a QRQC can be created. The potential harm that CRQC could cause is the basis of the motivation to seek countermeasures, even though we have uncertainties about when and if these computers can be built. Deployed systems that use public key cryptography can also take years to update. Post-quantum cryptography is one way to combat quantum computer threats. Its security is based on the complexity of mathematical problems that are currently considered unsolvable efficiently – even with the help of quantum computers. Post-quantum cryptography deals with the development and research of asymmetric cryptosystems, which, according to current knowledge, cannot be broken even by powerful quantum computers. These methods are based on mathematical problems for the solution of which neither efficient classical algorithms nor efficient quantum algorithms are known today. Various approaches to the implementation of post-quantum cryptography are used in modern research, including: code-based cryptography, lattice-based cryptography, hashing-based cryptography, isogeny-based cryptography, and multidimensional cryptography. The purpose of this work is to review the computational model of quantum computers; quantum algorithms, which have the greatest impact on modern cryptography; the risk of creating cryptographically relevant quantum computers (CRQC); security of symmetric cryptography and public key cryptography in the presence of CRQC; NIST PQC standardization efforts; transition to quantum-resistant public-key cryptography; relevance, views and current state of development of quantum-resistant cryptography in the European Union. It also highlights the progress of the most important effort in the field: NIST's standardization of post-quantum cryptography.
Quantum computing is a transformational technology once implemented, capable of addressing problems far beyond the capacity of classical computers. But this progress is also a real challenge to the core of today's modern security. Traditional cryptographic algorithms, such as those based on RSA, ECC, and Diffie-Hellman key exchange, are based on the computational hardness of problems such as prime factorization and discrete logarithms that quantum algorithms solve in polynomial time. As a particular research interesting example, with Shor's Algorithm one can factorize large numbers efficiently, rendering insecure the majority of public key cryptosystems used nowadays. This urgently demands a reevaluation of existing encryption schemes in the context of a post-quantum world. In this paper, we take a closer look at the threats that quantum computers pose to classical security infrastructure including encryption scheme and explore the impact that quantum computation can have on current cryptographic schemes. It calculates the cost in terms of symmetric and asymmetric security, accounting for effects of both Shor's and Grover's algorithms. Symmetric key systems such as AES are also harder hit—Grover's algorithm can give only a quadratic speedup here—but they do need to double key sizes for a sufficient level of post-quantum security. In reaction to those threats, the paper investigates nextgeneration post-quantum cryptographic (PQC) solutions resistant to quantum cryptanalysis. Lattice-based cryptosystems, hash-based signature schemes, multivariate polynomial systems, and code-based cryptosystems are some of the candidates that are being considered in international standardization work, including especially at NIST. In this paper, we compare those alternatives for security, performance, scalability, and feasibility of implementation in real system. An important aspect of this contribution is a comparative study of traditional and post-quantum cryptographic protocols in the context of a number of cybersecurity applications, including secure communications, blockchain networks and IoT contexts. It also covers the quantum readiness timeline and transitional issues, such as backward compatibility, standardization lag and the associated increased computational overhead. Through a mitigated risk evaluation and cryptanalytic attack simulation based on quantum-inspired algorithms, this analysis emphasizes the need to prepare ourselves against quantum-induced security issues. It provides strategic guidance to organizations as they plan for the post-quantum future, stressing cryptographic agility, hybrid encryption models and real-time threat monitoring. Ultimately, the results of this work add to the worldwide conversation on establishing secure systems within the digital age of quantum computing and recommend proactive migration plans for the integrity, confidentiality, and trust one should have in the future cyber world.