Biblio

The NIST standardization process for post-quantum cryptography has been drawing the attention of researchers to the submitted candidates. One direction of research consists in implementing those candidates on embedded systems and that exposes them to physical attacks in return. The Classic McEliece cryptosystem, which is among the four finalists of round 3 in the Key Encapsulation Mechanism category, builds its security on the hardness of the syndrome decoding problem, which is a classic hard problem in code-based cryptography. This cryptosystem was recently targeted by a laser fault injection attack leading to message recovery. Regrettably, the attack setting is very restrictive and it does not tolerate any error in the faulty syndrome. Moreover, it depends on the very strong attacker model of laser fault injection, and does not apply to optimised implementations of the algorithm that make optimal usage of the machine words capacity. In this article, we propose a to change the angle and perform a message-recovery attack that relies on side-channel information only. We improve on the previously published work in several key aspects. First, we show that side-channel information, obtained with power consumption analysis, is sufficient to obtain an integer syndrome, as required by the attack framework. This is done by leveraging classic machine learning techniques that recover the Hamming weight information very accurately. Second, we put forward a computationally-efficient method, based on a simple dot product and information-set decoding algorithms, to recover the message from the, possibly inaccurate, recovered integer syndrome. Finally, we present a masking countermeasure against the proposed attack.

We discuss the performance of a new quantumsafe multivariate digital signature scheme proposed recently, called the Multivariate Polynomial Public Key Digital Signature (MPPK DS) scheme. Leveraging MPPK KEM or key exchange mechanism, the MPPK DS scheme is established using modular exponentiation with a randomly chosen secret base from a prime field. The security of the MPPK DS algorithm largely benefits from a generalized safe prime associated with the said field and the Euler totient function. We can achieve NIST security levels I, III, and V over a 64-bit prime field, with relatively small public key sizes of 128 bytes, 192 bytes, and 256 bytes for security levels I, III, and V, respectively. The signature sizes are 80 bytes for level I, 120 bytes for level III, and 160 bytes for level V. The MPPK DS scheme offers probabilistic procedures for signing and verification. That is, for each given signing message, a signer can randomly pick a base integer to be used for modular exponentiation with a private key, and a verifier can verify the signature with the digital message, based on the verification relationship, using any randomly selected noise variables. The verification process can be repeated as many times as the verifier wishes for different noise values, however, for a true honest signature, the verification will always pass. This probabilistic feature largely restricts an adversary to perform spoofing attacks. In this paper, we conduct some performance analyses by implementing MPPK DS in Java. We compare its performance with benchmark performances of NIST PQC Round 3 finalists: Rainbow, Dilithium, and Falcon. Overall, the MPPK DS scheme demonstrates equivalent or better performance, and much smaller public key, as well as signature sizes, compared to the three NIST PQC Round 3 finalists.

This research investigates efficient architectures for the implementation of the CRYSTALS-Dilithium post-quantum digital signature scheme on reconfigurable hardware, in terms of speed, memory usage, power consumption and resource utilisation. Post quantum digital signature schemes involve a significant computational effort, making efficient hardware accelerators an important contributor to future adoption of schemes. This is work in progress, comprising the establishment of a comprehensive test environment for operational profiling, and the investigation of the use of novel architectures to achieve optimal performance.

This article describes the process of synchronizing the generation of random sequences by a quantum random number generator (QRNG) that can be used as secret keys for known cryptographic transformations. The subject of the research is a method for synchronizing the generation of random QRNG sequences based on L1 (C/A) signals of the global positioning system (GPS) using control correcting information received from control correcting stations.

The Multivariate Polynomial Public Key (MPPK) algorithm, over a prime Galois field, takes a multiplier multivariate polynomial and two multiplicand univariate solvable polynomials to create two product multivariate polynomials. One of variables is for secret message and all others are for noises. The public key consists of all coefficients of the product multivariate polynomials, except the two constant terms for the message variable. The private key is made of both multiplicands. Encryption takes a list of random numbers, over the prime Galois field. The first number is the secret to exchange. The other random numbers generate noise automatically cancelled by decryption. The secret is easily extracted from the evaluation of a solvable equation. The level of security provided by MPPK is adaptable. The algorithm can be used in several different ways. In this paper, we review the performance achieved by MPPK for several combinations of polynomial configurations and Galois field sizes. For every combination, we calculated key generation time, encryption time and decryption time. We also compare the effectiveness of MPPK with the performance of all four NIST PQC finalists. For MPPK, the data has been collected from the execution of an implementation in Java. In comparison to the NIST PQC finalists, MPPK key generation, encryption and decryption performance is excellent.

Recent advancements in quantum information theory and quantum computation intend the possibilities of breaking the existing classical cryptographic systems. To mitigate these kinds of threats with quantum computers we need some advanced quantum-based cryptographic systems. The research orientation towards this is tremendous in recent years, and many excellent approaches have been reported. In this article, we discuss the probable approaches of the quantum cryptographic systems from implementation point of views to handle the post-quantum cryptographic attacks.

Cloud computing has changed the paradigm of using computing resources. It has shifted from traditional storage and computing to Internet based computing leveraging economy of scale, cost saving, elimination of data redundancy, scalability, availability and regulatory compliance. With these, cloud also brings plenty of security issues. As security is not a one-time solution, there have been efforts to investigate and provide countermeasures. In the wake of emerging quantum computers, the aim of post-quantum cryptography is to develop cryptography schemes that are secure against both classical computers and quantum computers. Since cloud is widely used across the globe for outsourcing data, it is essential to strive at providing betterment of security schemes from time to time. This paper reviews recent development, methods of cloud data security in post-quantum perspectives. It provides useful insights pertaining to the security schemes used to safeguard data dynamics associated with cloud computing. The findings of this paper gives directions for further research in pursuit of more secure cloud data storage and retrieval.

This paper proposes an efficient face template protection system based on homomorphic encryption. By developing a message packing method suitable for the calculation of the squared Euclidean distance, the proposed system computes the squared Euclidean distance between facial features by a single homomorphic multiplication. Our experimental results show the transaction time of the proposed system is about 14 times faster than that of the existing face template protection system based on homomorphic encryption presented in BIOSIG2020.

We tackle the problem where a server owns a trained Machine Learning (ML) model and a client/user has an unclassified query that he wishes to classify in secure and private fashion using the server’s model. During the process the server learns nothing, while the user learns only his final classification and nothing else. Since several ML classification algorithms, such as deep neural networks, support vector machines-SVM (and hyperplane decisions in general), Logistic Regression, Naïve Bayes, etc., can be expressed in terms of matrix operations, initially we propose novel secure matrix operations as our building blocks. On top of them we build our secure and private ML classification algorithms under strict security and privacy requirements. As our underlying cryptographic primitives are shown to be resilient to quantum computer attacks, our algorithms are also suitable for the post-quantum world. Our theoretical analysis and extensive experimental evaluations show that our secure matrix operations, hence our secure ML algorithms build on top of them as well, outperform the state of the art schemes in terms of computation and communication costs. This makes our algorithms suitable for devices with limited resources that are often found in Industrial IoT (Internet of Things)

The design of public-key cryptography algorithm based on LWE hard problem is a hot topic in the field of post-quantum cryptography. In this paper, we design a new homomorphic encryption algorithm based on LWE problem. Firstly, to solve the problem that the existing encryption algorithms can only encrypt a single 0 or 1 bit, a new encryption algorithm based on LWE over integer is proposed, and its correctness and security are proved by theoretical analysis. Secondly, an additive homomorphism algorithm is constructed based on the algorithm, and the correctness of the algorithm is proved. The homomorphism algorithm can carry out multi-level homomorphism addition under certain parameters. Finally, the public key cryptography algorithm and homomorphic encryption algorithm are simulated through experiments, which verifies the correctness of the algorithm again, and compares the efficiency of the algorithm with existing algorithms. The experimental data shows that the algorithm has certain efficiency advantages.

Post-quantum digital signature is a critical primitive of computer security in the era of quantum hegemony. As a finalist of the post-quantum cryptography standardization process, the theoretical security of the CRYSTALS-Dilithium (Dilithium) signature scheme has been quantified to withstand classical and quantum cryptanalysis. However, there is an inherent power side-channel information leakage in its implementation instance due to the physical characteristics of hardware.This work proposes an efficient non-profiled Correlation Power Analysis (CPA) strategy on Dilithium to recover the secret key by targeting the underlying polynomial multiplication arithmetic. We first develop a conservative scheme with a reduced key guess space, which can extract a secret key coefficient with a 99.99% confidence using 157 power traces of the reference Dilithium implementation. However, this scheme suffers from the computational overhead caused by the large modulus in Dilithium signature. To further accelerate the CPA run-time, we propose a fast two-stage scheme that selects a smaller search space and then resolves false positives. We finally construct a hybrid scheme that combines the advantages of both schemes. Real-world experiment on the power measurement data shows that our hybrid scheme improves the attack’s execution time by 7.77×.

The use of public key cryptosystems ranges from securely encrypting bitcoin transactions and creating digital signatures for non-repudiation. The cryptographic systems security of public key depends on the complexity in solving mathematical problems. Quantum computers pose a threat to the current day algorithms used. This research presents analysis of two Hash-based Signature Schemes (MSS and W-OTS) and provides a comparative analysis of them. The comparisons are based on their efficiency as regards to their key generation, signature generation and verification time. These algorithms are compared with two classical algorithms (RSA and ECDSA) used in bitcoin transaction security. The results as shown in table II indicates that RSA key generation takes 0.2012s, signature generation takes 0.0778s and signature verification is 0.0040s. ECDSA key generation is 0.1378s, signature generation takes 0.0187s, and verification time for the signature is 0.0164s. The W-OTS key generation is 0.002s. To generate a signature in W-OTS, it takes 0.001s and verification time for the signature is 0.0002s. Lastly MSS Key generation, signature generation and verification has high values which are 16.290s, 17.474s, and 13.494s respectively. Based on the results, W-OTS is recommended for bitcoin transaction security because of its efficiency and ability to resist quantum computer attacks on the bitcoin network.

The paper deals with the design and principles of functioning of code-based schemes for formation and verification of electronic digital signature. Comparative studies of the effectiveness of the known CFS scheme and the proposed scheme have been carried out, as well as their possibilities, disadvantages and prospects for use in the post-quantum period.

Modern computing devices use classical algorithms such as Rivest Shamir Adleman (RSA) and Elliptic Curve Digital Signature Algorithm (ECDSA) for their security. The securities of these algorithms relied on the problem and difficulty of integer factorization and also calculating the Discrete Logarithm Problems. With the introduction of quantum computers, recent research is focusing on developing alternative algorithms which are supposed to withstand attacks from quantum computers. One of such alternatives is the Hash-based Digital Signature Schemes. Chosen hash-based signature schemes over classical algorithms is because their security is on the hash function used and that they are metaheuristic in nature. This research work presents basic analysis and the background understanding of Stateful Hash-based Signature Schemes, particularly the Lamport One-Time Signature Scheme, Winternitz One-Time Signature Scheme, and the Merkle Signature Scheme. The three schemes selected are stateful, hence has common features and are few-time hash-based signature schemes. The selected Stateful Hash-based Digital Signature Schemes were analyzed based on their respective key generation, signature generation, signature verification, and their security levels. Practical working examples were given for better understanding. With the analyses, Merkle Signature Scheme proves to be the best candidate to be used in the Bitcoin Proof of Work protocol because of its security and its advantage of signing many messages.

This paper presents an authentication protocol specifically tailored for IoT devices that inherently limits the number of times that an entity can authenticate itself with a given key pair. The protocol we propose is based on a stateful hash-based digital signature system called eXtended Merkle Signature Scheme (XMSS), which has increased its popularity of late due to its resistance to quantum-computer-aided attacks. We propose a 1-pass authentication protocol that can be customized according to the server capabilities to keep track of the key pair state. In addition, we present results when ported to ARM Cortex-M3 and M0 processors.

The Supersingular Isogeny Diffie-Hellman protocol (SIDH) has recently been the subject of increased attention in the cryptography community. Conjecturally quantum-resistant, SIDH has the feature that it shares the same data flow as ordinary Diffie-Hellman: two parties exchange a pair of public keys, each generated from a private key, and combine them to form a shared secret. To create a potentially quantum-resistant scheme, SIDH depends on a new family of computational assumptions involving isogenies between supersingular elliptic curves which replace both the discrete logarithm problem and the computational and decisional Diffie-Hellman problems. As in the case of ordinary Diffie-Hellman, one is interested in knowing if these problems are related. In fact, more is true: there is a rich network of reductions between the isogeny problems securing the private keys of the participants in the SIDH protocol, the computational and decisional SIDH problems, and the problem of validating SIDH public keys. In this article we explain these relationships, which do not appear elsewhere in the literature, in hopes of providing a clearer picture of the SIDH problem landscape to the cryptography community at large.

Nowadays public-key cryptography is based on number theory problems, such as computing the discrete logarithm on an elliptic curve or factoring big integers. Even though these problems are considered difficult to solve with the help of a classical computer, they can be solved in polynomial time on a quantum computer. Which is why the research community proposed alternative solutions that are quantum-resistant. The process of finding adequate post-quantum cryptographic schemes has moved to the next level, right after NIST's announcement for post-quantum standardization. One of the oldest quantum-resistant proposition goes back to McEliece in 1978, who proposed a public-key cryptosystem based on coding theory. It benefits of really efficient algorithms as well as a strong mathematical background. Nonetheless, its security has been challenged many times and several variants were cryptanalyzed. However, some versions remain unbroken. In this paper, we propose to give some background on coding theory in order to present some of the main flawless in the protocols. We analyze the existing side-channel attacks and give some recommendations on how to securely implement the most suitable variants. We also detail some structural attacks and potential drawbacks for new variants.

In this work, we analyze the feasibility of a physically secure implementation of the quantum-resistant supersingular isogeny Diffie-Hellman (SIDH) protocol. Notably, we analyze the defense against timing attacks, simple power analysis, differential power analysis, and fault attacks. Luckily, the SIDH protocol closely resembles its predecessor, the elliptic curve Diffie-Hellman (ECDH) key exchange. As such, much of the extensive literature in side-channel analysis can also apply to SIDH. In particular, we focus on a hardware implementation that features a true random number generator, ALU, and controller. SIDH is composed of two rounds containing a double-point multiplication to generate a secret kernel point and an isogeny over that kernel to arrive at a new elliptic curve isomorphism. To protect against simple power analysis and timing attacks, we recommend a constant-time implementation with Fermat's little theorem inversion. Differential power analysis targets the power output of the SIDH core over many runs. As such, we recommend scaling the base points by secret scalars so that each iteration has a unique power signature. Further, based on recent oracle attacks on SIDH, we cannot recommend the use of static keys from both parties. The goal of this paper is to analyze the tradeoffs in elliptic curve theory to produce a cryptographically and physically secure implementation of SIDH.

Some lattice-based public key cryptosystems allow one to transform ciphertext from one lattice or ring representation to another efficiently and without knowledge of public and private keys. In this work we explore this lattice transformation property from cryptographic engineering viewpoint. We apply ciphertext transformation to compress Ring-LWE ciphertexts and to enable efficient decryption on an ultra-lightweight implementation targets such as Internet of Things, Smart Cards, and RFID applications. Significantly, this can be done without modifying the original encryption procedure or its security parameters. Such flexibility is unique to lattice-based cryptography and may find additional, unique real-life applications. Ciphertext compression can significantly increase the probability of decryption errors. We show that the frequency of such errors can be analyzed, measured and used to derive precise failure bounds for n-bit error correction. We introduce XECC, a fast multi-error correcting code that allows constant time implementation in software. We use these tools to construct and explore TRUNC8, a concrete Ring-LWE encryption and authentication system. We analyze its implementation, security, and performance. We show that our lattice compression technique reduces ciphertext size by more than 40% at equivalent security level, while also enabling public key cryptography on previously unreachable ultra-lightweight platforms. The experimental public key encryption and authentication system has been implemented on an 8-bit AVR target, where it easily outperforms elliptic curve and RSA-based proposals at similar security level. Similar results have been obtained with a Cortex M0 implementation. The new decryption code requires only a fraction of the software footprint of previous Ring-LWE implementations with the same encryption parameters, and is well suited for hardware implementation.

We propose a new class of post-quantum digital signature schemes that: (a) derive their security entirely from the security of symmetric-key primitives, believed to be quantum-secure, and (b) have extremely small keypairs, and, (c) are highly parameterizable. In our signature constructions, the public key is an image y=f(x) of a one-way function f and secret key x. A signature is a non-interactive zero-knowledge proof of x, that incorporates a message to be signed. For this proof, we leverage recent progress of Giacomelli et al. (USENIX'16) in constructing an efficient Σ-protocol for statements over general circuits. We improve this Σ-protocol to reduce proof sizes by a factor of two, at no additional computational cost. While this is of independent interest as it yields more compact proofs for any circuit, it also decreases our signature sizes. We consider two possibilities to make the proof non-interactive: the Fiat-Shamir transform and Unruh's transform (EUROCRYPT'12, '15,'16). The former has smaller signatures, while the latter has a security analysis in the quantum-accessible random oracle model. By customizing Unruh's transform to our application, the overhead is reduced to 1.6x when compared to the Fiat-Shamir transform, which does not have a rigorous post-quantum security analysis. We implement and benchmark both approaches and explore the possible choice of f, taking advantage of the recent trend to strive for practical symmetric ciphers with a particularly low number of multiplications and end up using Low MC (EUROCRYPT'15).

In this paper we analyse possibilities of application of post-quantum code based signature schemes for message authentication purposes. An error-correcting code based digital signature algorithm is presented. There also shown results of computer simulation for this algorithm in case of Reed-Solomon codes and the estimated efficiency of its software implementation. We consider perspectives of error-correcting codes for message authentication and outline further research directions.

Many lattice-based cryptosystems are based on the security of the Ring learning with errors (Ring-LWE) problem. The most critical and computationally intensive operation of these Ring-LWE based cryptosystems is polynomial multiplication. In this paper, we exploit the number theoretic transform to build a high-speed polynomial multiplier for the Ring-LWE based public key cryptosystems. We present a versatile pipelined polynomial multiplication architecture to calculate the product of two \$n\$-degree polynomials in about ((nlg n)/4 + n/2) clock cycles. In addition, we introduce several optimization techniques to reduce the required ROM storage. The experimental results on a Spartan-6 FPGA show that the proposed hardware architecture can achieve a speedup of on average 2.25 than the state of the art of high-speed design. Meanwhile, our design is able to save up to 47.06% memory blocks.

We present a method for key compression in quantumresistant isogeny-based cryptosystems, which allows a reduction in and transmission costs of per-party public information by a factor of two, with no e ect on security. We achieve this reduction by associating a canonical choice of elliptic curve to each j-invariant, and representing elements on the curve as linear combinations with respect to a canonical choice of basis. This method of compressing public information can be applied to numerous isogeny-based protocols, such as key exchange, zero-knowledge identi cation, and public-key encryption. We performed personal computer and ARM implementations of the key exchange with compression and decompression in C and provided timing results, showing the computational cost of key compression and decompression at various security levels. Our results show that isogeny-based cryptosystems achieve by far the smallest possible key sizes among all existing families of post-quantum cryptosystems at practical security levels; e.g. 3073-bit public keys at the quantum 128-bit security level, comparable to (non-quantum) RSA key sizes.

Lattice-based cryptography offers some of the most attractive primitives believed to be resistant to quantum computers. Following increasing interest from both companies and government agencies in building quantum computers, a number of works have proposed instantiations of practical post-quantum key exchange protocols based on hard problems in ideal lattices, mainly based on the Ring Learning With Errors (R-LWE) problem. While ideal lattices facilitate major efficiency and storage benefits over their non-ideal counterparts, the additional ring structure that enables these advantages also raises concerns about the assumed difficulty of the underlying problems. Thus, a question of significant interest to cryptographers, and especially to those currently placing bets on primitives that will withstand quantum adversaries, is how much of an advantage the additional ring structure actually gives in practice. Despite conventional wisdom that generic lattices might be too slow and unwieldy, we demonstrate that LWE-based key exchange is quite practical: our constant time implementation requires around 1.3ms computation time for each party; compared to the recent NewHope R-LWE scheme, communication sizes increase by a factor of 4.7x, but remain under 12 KiB in each direction. Our protocol is competitive when used for serving web pages over TLS; when partnered with ECDSA signatures, latencies increase by less than a factor of 1.6x, and (even under heavy load) server throughput only decreases by factors of 1.5x and 1.2x when serving typical 1 KiB and 100 KiB pages, respectively. To achieve these practical results, our protocol takes advantage of several innovations. These include techniques to optimize communication bandwidth, dynamic generation of public parameters (which also offers additional security against backdoors), carefully chosen error distributions, and tight security parameters.

This paper deals with the design and implementation of the post-quantum public-key algorithm McEliece. Seamless incorporation of a new error generator and new SHA-3 module provides higher indeterminacy and more randomization of the original McEliece algorithm and achieves CCA2 security standard. Due to the lightweight and high-speed implementation of SHA-3 module the proposed 128-bit secure McEliece architecture provides 6% higher performance in only 0.78 times area of the best known existing design.