Security Of Cryptographic Primitives Research Articles

Quantum Computers and Algorithms: A Threat to Classical Cryptographic Systems

Contemporary cryptographic algorithms are resistant to the strongest threats to cybersecurity and high-profile cyber-attacks. In recent times, information security scientists and researchers had developed various cryptographic schemes that defeated attacks using the most sophisticated (in terms of processor speed) classical computer. However, this resistance will soon erode with the arrival of quantum computers. In this paper, we profiled quantum computers and quantum algorithms based on their widely believed threat against currently secure cryptographic primitives. We found that Grover’s and Shor’s quantum-based algorithms actually pose a threat to the continued security of symmetric cryptosystems (e.g. 128-bit AES) and asymmetric (public key) cryptosystems (e.g. RSA, Elgamal, elliptic curve Diffie Hellman (ECDH), etc.) respectively.We discovered that the source of the algorithms’ cryptanalytic power against the current systems, stems from the fact that they (Grover and Shor) both equipped their respective algorithms with a quantum circuit component that can execute the oracle in parallel by applying a single circuit to all possible states of an n-qubit input. With this exponential level of processing characteristic of quantum computers and quantum-based algorithms, it is easy for the current cryptosystems to be broken since the algorithms can existentially solve the underlying mathematical problems such as integer factorization, discrete logarithm problem and elliptic curve problem, which formed the basis of the security of the affected cryptosystems. Based on this realization and as part of our readiness for a post quantum era, we explored other mathematical structures (lattices, hashes, codes, isogenies, high entropy-based symmetric key resistance, and multivariate quadratic problems) whose hardness could surpass the cryptanalytic nightmare posed by quantum computers and quantum-based algorithms. Our contribution is that, based on the findings of this research work, we can confidently assert that all hope is not lost for organizations heavily relying on protocols and applications like HTTPS, TLS, PGP, Bitcoin, etc., which derived their security from the endangered cryptosystems.

An Extensive Study on Lattice-Based Cryptography and its Applications for RLWE-Based Problems

Lattice-based cryptography has emerged as a powerful paradigm for constructing secure cryptographic primitives, offering resistance to quantum attacks and providing a versatile framework for building post-quantum cryptographic systems. This research paper provides an in-depth exploration of lattice-based cryptography, focusing specifically on its applications for problems based on Ring Learning with Errors (RLWE). We analyze the fundamental concepts of lattice theory, delve into the RLWE problem, and highlight the security properties and challenges associated with lattice-based schemes. Furthermore, we discuss various real-world applications of lattice-based cryptography, demonstrating its potential for secure communication, privacy-preserving protocols, and post-quantum cryptography.

Identity-Based Encryption With Continuous Leakage-Resilient CCA Security From Static Complexity Assumption

Abstract Although a large number of provably secure cryptographic primitives have been proposed in the literature, many of these schemes might be broken in practice because of various leakage attacks. Therefore, the leakage resilience should be considered in designing these primitives. However, in identity-based cryptography, most of the existing leakage-resilient identity-based encryption (IBE) schemes suffer some limitations: they either resist the leakage attacks in the selective identity security model or achieve the chosen-ciphertext attack (CCA) security based on a non-static assumption. In this paper, an IBE scheme with adaptive leakage-resilient CCA security is proposed, and its security is rigorously proved in the random oracle model under a classic static complexity assumption, e.g. decisional bilinear Diffie–Hellman assumption. In our construction, all elements of ciphertext are randomly distributed in the adversary’s view. Hence, the adversary cannot obtain any useful information of the user’s private key from the given ciphertexts. Moreover, a unique property of our construction is that the leakage parameter is independent of the plaintext space, which contributes a better leakage rate.

Signcryption Based Authenticated and Key Exchange Protocol for EI-Based V2G Environment

In this paper, we introduce a robust authentication protocol for Vehicle-to-Grid (V2G) communication through lightweight and secure cryptographic primitives. In addition, we utilize signcrypt and unsigncrypt functions which facilitate the consumers to have secure access to the services. The security evaluation of the introduced framework shows its resilience against well-known security attacks. Moreover, the performance analysis shows that our protocol is efficient and reliable as compared to various related protocols but energy and computation cost is slightly higher than four other related protocols.

Framework for faster key search using related‐key higher‐order differentialproperties: applications to Agrasta

The relevance of the related-key model is usually controversial. However, in some cases, related-key properties have already been used to reduce the effective key length of the cipher in the single-key model. Hence, research into this direction can be helpful to bridge the gap between theory and practice aspects of the related-key model. Motivated by this challenge, the authors develop a new framework to provide further evidence that deterministic related-key characteristics can be utilised in the single-key model. The authors describe a sound framework for utilising related-key higher-order differential distinguishers that can beat the boundaries given by exhaustive key search. The data required is only one known as plaintext–ciphertext pair if the number of ciphertext bits matches the key length. From a theoretical point of view, the connection between related-key higher-order differential properties and the security of cryptographic primitives in the single-key model are precised. From a practical point of view, the proposed framework is used to evaluate the security of Agrasta cipher which is a variant of Rasta cipher presented at CRYPTO 2018. The proposed method is the first analysis of Agrasta reduced to three rounds that performs better than exhaustive key search and is independent of the used linear layers.

Continuous Leakage-Resilient Certificate-Based Encryption Scheme Without Bilinear Pairings

Abstract Recently, much attention has been focused on designing provably secure cryptographic primitives in the presence of key leakage, even the continuous leakage attacks. However, several constructions on the (continuous) leakage-resilient certificate-based encryption (CBE) scheme were proposed based on the bilinear pairings, and the corresponding computational efficiency is lower. Also, the leakage on the master secret key is omitted in the previous constructions. In this paper, to further achieve the better performance, a new construction method of continuous leakage-resilient CBE scheme without bilinear pairings is proposed, and the chosen-ciphertext attacks security of designed scheme is proved based on the hardness of the classic decisional Diffie–Hellman assumption. The performance analysis shows that our method not only can obtain higher computational efficiency but also enjoys better security performances, such as the leakage parameter of secret key of user has the constant size, and an adversary cannot obtain any leakage on the secret key of user from the corresponding given ciphertext etc. The advantage is that our proposal allows leakage attacks of multiple keys, i.e. continuous leakage resilience of the secret key of user and bounded leakage resilience of the master secret key. Additionally, to provide the leakage resilience for the cloud computing, a novel data access control scheme for cloud storage service is proposed from our continuous leakage-resilient CBE scheme, which can keep its claimed security in the leakage seting.

Parallel Platform for Supporting Stream Ciphers Over Multi-core Processors

Designing secure and fast cryptographic primitives is one of the critical issues in the current era. Several domains, including Internet of Things (IoT), military and banking, require fast and secure data encryption over public channels. Most of the existing stream ciphers are designed to work sequentially and therefore not utilizing available computing power. Also, other stream ciphers are designed based on complex mathematical problems which makes these ciphers slower due to the complex computations. For this purpose, a novel parallel platform for enhancing the performance of stream ciphers is presented. The platform is designed to work efficiently over multi-core processors using multithreading techniques. The architecture of the platform relies on independent components that can operate over multiple cores available on the corresponding communication ends. Two groups of stream ciphers were considered as case studies in our experiments. The first category includes stream ciphers of a sequential design, while the second category includes parallelizable stream ciphers. Performance tests and analysis shows that the parallel platform was able to maximize the encryption throughput of the selected stream ciphers dramatically. The enhancements on the encryption throughput is relative to the constructional design of the stream ciphers. Parallelized stream ciphers (Salsa20, DSP-128, and ECSC-128) was able to achieve higher throughput compared to other sequentially designed stream ciphers.

Aleakage-resilient certificateless public key encryption scheme with CCA2 security

In recent years, much attention has been focused on designing provably secure cryptographic primitives in the presence of key leakage. Many constructions of leakage-resilient cryptographic primitives have been proposed. However, for any polynomial time adversary, most existing leakage-resilient cryptographic primitives cannot ensure that their outputs are random, and any polynomial time adversary can obtain a certain amount of leakage on the secret key from the corresponding output of a cryptographic primitive. In this study, to achieve better performance, a new construction of a chosen ciphertext attack 2 (CCA2) secure, leakage-resilient, and certificateless public-key encryption scheme is proposed, whose security is proved based on the hardness of the classic decisional Diffie-Hellman assumption. According to our analysis, our method can tolerate leakage attacks on the private key. This method also achieves better performance because polynomial time adversaries cannot achieve leakage on the private key from the corresponding ciphertext, and a key leakage ratio of 1/2 can be achieved. Because of these good features, our method may be significant in practical applications.

Reliable Inversion in GF(28) With Redundant Arithmetic for Secure Error Detection of Cryptographic Architectures

In secure cryptographic primitives, such as block ciphers, the reliability of hardware implementations needs to be closely considered because faults in the hardware implementations can potentially reduce or impact on the underlying security. In this paper, we present approaches to detect errors in hardware implementations of the inversion in GF(28). The proposed approaches are based on both nonredundant and redundant arithmetic, utilizing normal basis (nonredundant) and two redundant Galois field representations, i.e., polynomial ring representation and redundantly represented basis through tower fields. To the best of our knowledge, this is the first work focusing on the error detection architectures for redundant arithmetic-based inversion in GF(28). The presented signature-based schemes in this paper are general and can be applied to block ciphers with 8-bit S-boxes, such as Camellia, SMS4, the advanced encryption standard, and CLEFIA. We present the results of error simulations and application-specific integrated circuit implementations to demonstrate the utility of the presented schemes. Based on the specific implementation’s security/reliability objectives and the overhead/degradation tolerance for implementation/performance metrics, one can fine-tune and tailor the proposed work to achieve more reliable inversions in GF(28).

Security of weak secrets based cryptographic primitives via the Rényi entropy

In ideality, cryptographic primitives take for granted that the secret sources are derived from uniform distribution. However, in reality, we may only obtain some ‘weak’ random sources guaranteed with high unpredictability (e.g. biometric data, physical sources, and secrets with partial leakage). Formally, the security of cryptographic primitives is measured by the expectation of some function, called ‘perfect’ expectation in the ideal model and ‘weak’ expectation in the real model. The authors propose some elementary inequalities which show that the ‘weak’ expectation is not much worse than the ‘perfect’ expectation. The authors present how to overcome weak expectations dependent on the Renyi entropy other than the min and collision entropies by Dodis and Yu [TCC 2013]. The authors achieve these results by capturing on two approaches: one is by observing a new relationship between the collision entropy and other Renyi entropy, the other is by developing the connection between different moments of a variable. Furthermore, pseudorandom generator, and pairwise independent hash function family, the authors extend key derivation functions based on the Renyi entropy. The results are applied to all unpredictability applications and ‘square-friendly’ indistinguishability applications including CPA-secure symmetric-key encryption schemes.

A limitation on security evaluation of cryptographic primitives with fixed keys

AbstractIn this paper, we discuss security of public‐key cryptographic primitives in the case that the public key is fixed. In the standard argument, security of cryptographic primitives are evaluated by estimating the average probability of being successfully attacked where keys are treated as random variables. In contrast to this, in practice, a user is mostly interested in the security under his specific public key, which has been already fixed. However, it is obvious that such security cannot be mathematically guaranteed because for any given public key, there always potentially exists an adversary, which breaks its security. Therefore, the best what we can do is just to use a public key such that its effective adversary is not likely to be constructed in the real life and, thus, it is desired to provide a method for evaluating this possibility. The motivation of this work is to investigate (in)feasibility of predicting whether for a given fixed public key, its successful adversary will actually appear in the real life or not. As our main result, we prove that for any digital signature scheme or public key encryption scheme, it is impossible to reduce any fixed key adversary in any weaker security notion than the de facto ones (i.e., existential unforgery against adaptive chosen message attacks or indistinguishability against adaptive chosen ciphertext attacks) to fixed key adversaries in the de facto security notion in a black‐box manner. This result means that, for example, for any digital signature scheme, impossibility of extracting the secret key from a fixed public key will never imply existential unforgery against chosen message attacks under the same key as long as we consider only black‐box analysis. Copyright © 2016 John Wiley & Sons, Ltd.

Influence of addition modulo 2 n on algebraic attacks

Many modern ciphers have a substitution-permutation (SP) network as a main component. This design is well researched in relation to Advanced Encryption Standard (AES). One of the ways to improve the security of cryptographic primitives is the use of additional nonlinear layers. However, this replacement may not have any effect against particular cryptanalytic attacks. In this paper we use algebraic attacks to analyze an SP network with addition modulo 2n as the key mixing layer. In particular, we show how to reduce the number of intermediate variables in round functions based on SP networks. We also apply the proposed method to the GOST 28147-89 block cipher that allows us to break reduced 8- and 14-round versions with complexity at most 2155 and 2215.4, respectively.

Parallel chaotic hash function based on the shuffle-exchange network

In recent years, cryptologists have been delving into chaos theory to design more secure cryptographic primitives. However, many existing chaos-based algorithms are slow due to floating point operations. They are mostly sequential in nature and therefore cannot take advantage of multicore processors for faster speed. In this paper, a new chaos-based hash function is proposed that utilizes multiple instances of chaotic maps that run in parallel to improve hashing speed. Parallelization is realized using the baseline network that also strengthens the security of the hash function due to its shuffling mechanism. The combination of linear and nonlinear chaotic maps is used to provide a high level of sensitivity to initial conditions, confusion and diffusion characteristics as well as strong collision resistance. Results show that the proposed design has strong security strength with near-perfect statistical qualities and fast hashing speed that surpasses both chaotic hash functions and the MD5 hash function.

Feebly secure cryptographic primitives

In 1992, A. Hiltgen provided first construction of provably (slightly) secure cryptographic primitives, namely, feebly one-way functions. These functions are provably harder to invert than to compute, but the complexity (viewed as the circuit complexity over circuits with arbitrary binary gates) is amplified only by a constant factor (in Hiltgen’s works, the factor approaches 2). In traditional cryptography, one-way functions are the basic primitive of private-key shemes, while public-key schemes are constructed using trapdoor functions. We continue Hiltgen’s work by providing examples of feebly secure trapdoor functions where the adversary is guaranteed to spend more time than honest participants (also by a constant factor). We give both a (simpler) linear and a (better) nonlinear construction. Bibliography: 25 titles.

Cryptographic properties of nonlinear pseudorandom number generators

The cryptographic properties of keystreams generated by stream ciphers based on t-functions are studied. These constructions are of great interest as they allow building highly efficient and secure cryptographic primitives. The randomness of the coordinate sequences generated by such mappings is analyzed in terms of the autocorrelation function. The results derived are valid for all t-functions regardless the type of construction and indicate the existence of nonrandomness. As the problem of the efficient implementation of secure s-boxes is open, the nonlinearity of t-functions is also analyzed. It is shown how some cryptographically undesirable properties, can be solved by application of similarity transformations.

Short Group Signatures Without Random Oracles

We propose short group signature (GS) schemes which are provably secure without random oracles. Our basic scheme is about 14 times shorter than the Boyen-Waters GS scheme at Eurocrypt 2006, and 42% shorter than the recent GS schemes due to Ateniese et al. The security proofs are provided in the Universally Composable model, which allows the proofs of security valid not only when our scheme is executed in isolation, but also in composition with other secure cryptographic primitives. We also present several new computational assumptions and justify them in the generic group model. These assumptions are useful in the design of high-level protocols and may be of independent interest.

Real-or-random Key Secrecy of the Otway-Rees Protocol via a Symbolic Security Proof

We present the first cryptographically sound security proof of the well-known Otway-Rees protocol. More precisely, we show that the protocol is secure against arbitrary active attacks including concurrent protocol runs if it is implemented using provably secure cryptographic primitives. We prove secrecy of the exchanged keys with respect to the accepted cryptographic definition of real-or-random secrecy, i.e., indistinguishability of exchanged keys and random ones, given the view of a general cryptographic attacker. Although we achieve security under cryptographic definitions, our proof is performed in a deterministic setting corresponding to a slightly extended Dolev-Yao model; in particular, it does not have to deal with probabilistic aspects of cryptography and is hence in the scope of current proof tools. The reason is that we exploit a recently proposed ideal cryptographic library, which has a provably secure cryptographic implementation, as well as recent results on linking symbolic and cryptographic key secrecy. Besides establishing the cryptographic security of the Otway-Rees protocol, our result also exemplifies the potential of this cryptographic library and the recent secrecy preservation theorem for symbolic yet cryptographically sound proofs of security.

A Cryptographically Sound Security Proof of the Needham–Schroeder–Lowe Public-Key Protocol

We present a cryptographically sound security proof of the well-known Needham-Schroeder-Lowe public-key protocol for entity authentication. This protocol was previously only proved over unfounded abstractions from cryptography. We show that it is secure against arbitrary active attacks if it is implemented using standard provably secure cryptographic primitives. Nevertheless, our proof does not have to deal with the probabilistic aspects of cryptography and is, hence, in the scope of current automated proof tools. We achieve this by exploiting a recently proposed Dolev-Yao-style cryptographic library with a provably secure cryptographic implementation. Besides establishing the cryptographic security of the Needham-Schroeder-Lowe protocol, our result exemplifies the potential of this cryptographic library and paves the way for the cryptographically sound verification of security protocols by automated proof tools.