LEDAcrypt: QC-LDPC Code-Based Cryptosystems with Bounded Decryption Failure Rate (original) (raw)
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LEDAkem: A Post-quantum Key Encapsulation Mechanism Based on QC-LDPC Codes
Post-Quantum Cryptography, 2018
This work presents a new code-based key encapsulation mechanism (KEM) called LEDAkem. It is built on the Niederreiter cryptosystem and relies on quasi-cyclic low-density parity-check codes as secret codes, providing high decoding speeds and compact keypairs. LEDAkem uses ephemeral keys to foil known statistical attacks, and takes advantage of a new decoding algorithm that provides faster decoding than the classical bit-flipping decoder commonly adopted in this kind of systems. The main attacks against LEDAkem are investigated, taking into account quantum speedups. Some instances of LEDAkem are designed to achieve different security levels against classical and quantum computers. Some performance figures obtained through an efficient C99 implementation of LEDAkem are provided.
Error Correcting Codes in Post-Quantum Cryptography
This thesis gives an overview of the currently most mature key encapsulation mechanisms (KEMs) based on the theory of error correcting codes. It includes an introduction to the theory of error correcting codes in so much as it applies to these systems and how it can be used to encapsulate keys through a public key (PK) cryptosystem. In order to add context to the KEMs, first the required basics of coding theory and a selection of some of the most common error correcting codes are covered. Then, we revisit public key cryptosystems, key encapsulation, and the security threat models that are being used. This is followed by a thorough description of the current NIST candidates for KEM using post-quantum cryptography: Classic McEliece, BIKE, LEDAcrypt, and HQC. We do not include rank metric methods such as ROLLO and RQC, which were NIST candidates until the second round, since they involve different features than those studied in this thesis. The thesis is intended as a survey of current methods being used in this field. We also establish some of the problems which may pose interesting for further research.
Cryptology and Network Security, 2018
Code-based public-key cryptosystems based on QC-LDPC and QC-MDPC codes are promising post-quantum candidates to replace quantum-vulnerable classical alternatives. However, a new type of attacks based on Bob's reactions have recently been introduced and appear to significantly reduce the length of the life of any keypair used in these systems. In this paper we estimate the complexity of all known reaction attacks against QC-LDPC and QC-MDPC code-based variants of the McEliece cryptosystem. We also show how the structure of the secret key and, in particular, the secret code rate affect the complexity of these attacks. It follows from our results that QC-LDPC code-based systems can indeed withstand reaction attacks, on condition that some specific decoding algorithms are used and the secret code has a sufficiently high rate.
A new code-based public-key cryptosystem resistant to quantum computer attacks
Journal of Physics: Conference Series, 2019
We propose a new type of public-key cryptosystems (PKC) which is based on repetition of different error-correcting codes. We give a brief analysis of some well known attacks on code-based PKC, including structural ones and show that the scheme could be used as a perspective post-quantum PKC.
Quantum Computers’ threat on Current Cryptographic Measures and Possible Solutions
International Journal of Wireless and Microwave Technologies, 2022
Cryptography is a requirement for confidentiality and authentic communication, and it is an indispensable technology used to protect data security. Quantum computing is a hypothetical model, still in tentative analysis but is rapidly gaining traction among scientific communities. Quantum computers have the potential to become a pre-eminent threat to all secure communication because their performance exceeds that of conventional computers. Consequently, quantum computers are capable of iterating through a large number of keys to search for secret keys or quickly calculate cryptographic keys, thereby endangering cloud security measures. This paper's main target is to summarize the vulnerability of current cryptographic measures in front of a quantum computer. The paper also aims to cover the fundamental concept of potential quantum-resilient cryptographic techniques and explain how they can be a solution to complete secure key distribution in a post-quantum future.
This paper presents a weakness in the key schedule of the AES candidate HPC (Hasty Pudding Cipher). It is shown that for the HPC version with a 128-bit key, 1 in 256 keys is weak in the sense that it has 2 30 equivalent keys. An efficient algorithm is proposed to construct these weak keys and the corresponding equivalent keys. If a weak key is used, it can be recovered by exhaustive search trying only 2 89 keys on average. This is an improvement by a factor of 2 38 over a normal exhaustive key search, which requires on average 2 127 attempts. The weakness also implies that HPC cannot be used in standard constructions for hash functions based on block ciphers. The analysis is extended to HPC with a 192-bit key and a 256-bit key, with similar results. For some other key lengths, all keys are shown to be weak. An example of this is the HPC variant with a 56-bit user key and block length of 128 bits, which can be broken in 2 31 attempts on average.
Quantum Computers and Algorithms: A Threat to Classical Cryptographic Systems 26
International Journal of Engineering and Advanced Technology (IJEAT), 2023
Contemporary cryptographic algorithms are resistant to the strongest threats to cybersecurity and high-profile cyberattacks. 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 quantumbased 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.
Using quantum key distribution for cryptographic purposes: a survey
arXiv (Cornell University), 2007
The appealing feature of quantum key distribution (QKD), from a cryptographic viewpoint, is the ability to prove the information-theoretic security (ITS) of the established keys. As a key establishment primitive, QKD however does not provide a standalone security service in its own: the secret keys established by QKD are in general then used by a subsequent cryptographic applications for which the requirements, the context of use and the security properties can vary. It is therefore important, in the perspective of integrating QKD in security infrastructures, to analyze how QKD can be combined with other cryptographic primitives.The purpose of this survey article, which is mostly centered on European research results, is to contribute to such an analysis. We first review and compare the properties of the existing key establishment techniques, QKD being one of them. We then study more specifically two generic scenarios related to the practical use of QKD in cryptographic infrastructures: 1) using QKD as a key renewal technique for a symmetric cipher over a point-to-point link ; 2) using QKD in a network containing many users with the objective of offering any-to-any key establishment service. We discuss the constraints as well as the potential interest of using QKD in these contexts. We finally give an overview of challenges relative to the development of QKD technology that also constitute potential avenues for cryptographic research. ✩ This document is the fruit of a collaborative effort initiated within the FP6 Trust and Security European integrated project SECOQC (IST-2002-506813). It is based for a large part on the SECOQC Crypto White Paper [1] that had been released in 2007.
Cryptology Column --- 25 Years of Quantum Cryptography
Sigact, 1996
I n t r o d u c t i o n The fates of S I G A C T News and Quantum Cryptography are inseparably entangled. The exact date of Stephen Wiesner's invention of "conjugate coding" is unknown but it cannot be far from April 1969, when the premier issue of SIGACT News-or rather S I C A C T News as it was known at the time-came out. Much later, it was in S I G A C T News that Wiesner's paper finally appeared [74] in the wake of the first author's early collaboration with Charles H. Bennett [7]. It was also in SIGACT News that the original experimental demonstration for quantum key distribution was announced for the first time [6] and that a thorough bibliography was published [19]. Finally, it was in S I G A C T News that Doug Wiedemann chose to publish his discovery when he reinvented quantum key distribution in 1987, unaware of all previous work but Wiesner's [73, 5].