Code-based Public-key Cryptosystem Research Articles

New code-based cryptosystems via the IKKR framework

One main construct for code-based public key cryptosystems is the McEliece framework that hedges upon the hardness of decoding arbitrary linear codes. Based on Goppa codes, the original McEliece cryptosystem however, suffers from having very large public keys. To alleviate this problem, we define a new IKKR problem that is NP-complete and use this assumption of the intractability of the decisional IKKR problem to construct a IND-CCA2-secure code-based public key encryption scheme. We consider generalized Reed–Solomon codes in our public-key cryptosystem and show that it resists Sidelnikov and Shestakov’s key recovery attack. Our generalized Reed–Solomon code encryption scheme achieves optimal public key size when compared with other PKE or key encapsulation mechanisms with deterministic decryption or decapsulation, as it requires only 88.1 kilobytes to store public key for schemes achieving 128-bit security level and 399.69 kilobytes to store public key for schemes achieving 256-bit security level. A public key size reduction of nearly 92% is obtained as compared to the classic McEliece PKE, and nearly 53% compared to the Reed–Solomon code-based PKE.

Some Public-key Cryptosystems Over Finite Fields

In this paper, we present two public-key cry ptosystems over finite fields. First of them is based on polynomials. The presented system also considers a digital signature algorithm. Its security is based on the difficulty of finding discrete logarithms over GF(qd+1) with sufficiently large q and d. Is is also examined along with comparison with other polynomial based public-key systems. The other public-key cryptosystem is based on linear codes. McEliece studied the first code-based public-key cryptosystem. We are inspired by McEliece system in the construction of the new system. We examine its security using linear algebra and compare it with the other code-based cryptosystems. Our new cryptosystems are too reliable in terms of security.

Reliable Architectures for Composite-Field-Oriented Constructions of McEliece Post-Quantum Cryptography on FPGA

Code-based cryptography based on binary Goppa codes is a promising solution for thwarting attacks based on quantum computers. The McEliece cryptosystem is a code-based public-key cryptosystem which is believed to be resistant against quantum attacks. In fact, it is successfully advanced to the second round of the post-quantum cryptography standardization competition early 2019. Due to its very large key size, different variants of binary Goppa codes have been proposed. Nevertheless, research has shown that such codes can be thwarted through the injection of faults, causing erroneous outputs. In this work, we present countermeasures for the implementation of different composite field arithmetic units used in the McEliece cryptosystem. The proposed architectures use overhead-aware and tailored signatures. We apply these error detection signatures to the McEliece cryptosystem and perform field-programmable gate array (FPGA) implementations to show the feasibility of adopting the proposed schemes. We benchmark the overhead and performance degradation of the proposed approaches and show their suitability for constrained embedded systems.

PKC‐PC: A variant of the McEliece public‐key cryptosystem based on polar codes

Polar codes are novel and efficient error-correcting codes with low encoding and decoding complexities. These codes have a channel-dependent generator matrix, which is determined by the code dimension, code length and transmission channel parameters. A variant of the McEliece public-key cryptosystem based on polar codes, called the PKC-PC, is studied. Since the structure of the polar codes’ generator matrix depends on the parameters of the channel, the authors have used an efficient approach to conceal their generator matrix. The proposed approach is based on a random selection of rows of the matrix by which a random generator matrix is constructed. Using the characteristics of polar codes and introducing an efficient approach, they could reduce the public and secret key sizes, and computational complexity compared to the McEliece cryptosystem. Moreover, they show that PKC-PC yields an increased security level against conventional attacks as well as possible vulnerabilities to the code-based public-key cryptosystems. Furthermore, they prove the security of the authors’ cryptosystem and show that its security is reduced to solve NP-complete problems, called polar parameterised syndrome decoding and polar parameterised codeword existence.

Encryption scheme based on expanded Reed-Solomon codes

We present a code-based public-key cryptosystem, in which we use Reed-Solomon codes over an extension field as secret codes and disguise it by considering its shortened expanded code over the base field. Considering shortened expanded codes provides a safeguard against distinguisher attacks based on the Schur product. Moreover, without using a cyclic or a quasi-cyclic structure we obtain a key size reduction of nearly $45 \%$ compared to the classic McEliece cryptosystem proposed by Bernstein et al.

A Secure and Efficient Code-Based Signature Scheme

The McEliece public key cryptosystem and the Niederreiter public key cryptosystem are the two major branches of the code-based public key cryptosystem. It has been found that the difficult problems relied by these two systems are different from the syndrome decoding problem stated by Berlekamp et al. The Hamming weight of the error vector is fixed and known to the attackers in these two systems, which leading to the disclosure of information, and through which the attacker can implement an effective attack. In this paper, an improved vision of the McEliece public key cryptosystem was given, and a new code-based signature scheme is designed based on the new cryptosystem. As a result, we achieve a more secure variant of McEliece public key cryptosystem and a more secure code-based signature scheme with high security and fast signing speed.

A new code-based public-key cryptosystem resistant to quantum computer attacks

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.

RFID Authentication Protocols Based on Error-Correcting Codes: A Survey

Code-based cryptography is a very promising research area. It allows the construction of different cryptographic mechanisms (e.g. identification protocol, public-key cryptosystem, etc.). McEliece cryptosystem is the first code-based public-key cryptosystem; several variants of this cryptosystem were proposed to design various security protocols in different systems. In this paper, we present a survey on various and recent authentication protocols in radio frequency identification systems which use diverse variants of the McEliece cryptosystem. Moreover, we discuss the security and the performance of each presented protocol.

Public-key code-based cryptography

The possibility of a quantum computer threatens the existence of many asymmetric cryptographic primitives. An important advantage of code cryptosystems is the high resistance to the quantum cryptanalysis. Therefore it is in great demand increasing the speed of the code based primitives and their protection from classical cryptanalysis. Code-Based Public-Key Cryptosystems based on algebraic coding are considered in this paper. In addition, the current state, the existing contradictions and prospects of practical use for the post-quantum period are studied. We consider estimation of resistance to attack permutation decoding and computational complexity compared to the RSA scheme. We proposed a new code cryptosystem, it significantly increases the relative information performance and keeps the main advantages of resistance to classical and quantum cryptanalysis.