McEliece Encryption Research Articles

Implementation of McEliece Encryption Scheme Based on Quasi- Cyclics Goppa Codes (QC-GOPPA)

Implementation of McEliece Encryption Scheme Based on Quasi- Cyclics Goppa Codes (QC-GOPPA)

An Optimized Intelligent Computational Security Model for Interconnected Blockchain-IoT System & Cities

Blockchain technology may provide a potential solution to the Internet of Things (IoT) security challenges by providing a decentralized and secure method for storing, managing, and sharing data. The Secure Hash Algorithm (SHA-256) hashed value of preliminary data (block) is retained in one block along with transaction data in tree form and timestamp in a chain of blocks. However, there are observations about blockchain limitations such as higher energy consumption, secure data, self-maintenance reliance, and higher cost. These constraints can be overcome by incorporating encryption algorithms into accepting blocks of data. In this paper, we propose a secure intelligent computational model for a large-scale interconnected IoT environment; an analytical modeling technique is considered for the proposed system. The proposed system takes advantage of the potential security feature of blockchain, which is considered the most appropriate secure communication system in an IoT. A computational model is built using the proposed blockchain technology to incorporate a secure and intelligent communication system. The proposed system uses the enhanced McEliece encryption approach’s potential to link the blockchain due to the faster mode of encryption and decryption process with a highly reduced number of steps.

Noise Modulation-Based Reversible Data Hiding with McEliece Encryption

McEliece cryptosystem is expected to be the next generation of the cryptographic algorithm due to its ability to resist quantum computing attacks. Few research studies have combined it with reversible data hiding in the encrypted domain (RDH-ED). In this article, we analysed and proved that there is a redundancy in the McEliece encryption process that is suitable for embedding. Then, a noise modulation-based scheme is proposed, called NM-RDHED, which is suitable for any signal and not only for images. The content owner scrambles the original image and then encrypts it with the receiver’s public key. The data hider generates a load noise by modulating additional data. After that, the load noise is added to the encrypted image, which achieves the data embedding. The reconstructed image is without any distortion after the direct decryption of the marked image, and the extracted data are no errors. The experimental results demonstrate our scheme has a higher embedding rate and more security, which is superior to existing schemes.

Reversible Data Hiding in Encrypted Domain Based on the Error-Correction Redundancy of Encryption Process

The existing reversible data hiding methods in encrypted domain separate image encryption from information embedding and do not make full use of the redundant space in the process of image encryption. In order to improve the performance of reversible data hiding by using the technical characteristics of image encryption, a reversible data hiding method based on McEliece error correction is proposed. Firstly, the segmentation position of bit plane is determined according to the embedding requirement and texture characteristic, and the image is divided into high and low significant bits. Secondly, because of the error-correcting characteristic of McEliece encryption, reversible data embedding can be realized while encrypting low significant bits. Then, the high significant bits are compressed to reserve space for the ciphertext extension of the low significant bits. Finally, the whole high significant bits information is stream-encrypted. As long as the image receiver has the decryption key, the image can be restored without distortion. By concealing the relationship between error correction and secret information mapping, the concealment of secret information transmission can be realized. In addition, due to different processing for different pixels, it can be efficiently transmitted with low computational complexity for applications that only need general images. The simulation results show that this scheme can not only realize the separable operation of information extraction and image recovery but also resist the noise attack to a certain extent. The maximum embedding rates of 10 standard images from USC-SIPI and 50 standard images from BOSS-BASE are 2.228 and 2.323 bpp, respectively.

Securing an Internet of Things from Distributed Denial of Service and Mirai Botnet Attacks Using a Novel Hybrid Detection and Mitigation Mechanism

Internet of Things (IoT) has become more familiar in all applications and industrial fields such as medical, military, transportation, etc. It has some limitations because of the attack model in the transmission or communication channel. Moreover, one of the deadliest attacks is known as a Distributed Denial of Service Attack (DDoS). The Presence of DDoS in network layer cause huge damage in data transmission channel that ends in data loss or collapse. To address this issue the current research focused on an innovative detection and mitigation of Mirai and DDoS attack in IoT environment. Initially, number of IoT devices is arranged with the help of a novel Hybrid Strawberry and African Buffalo Optimization (HSBABO). Consequently, the types of DDoS attacks are launched in the developed IoT network. Moreover, the presence of strawberry and African Buffalo fitness is utilized to detect and specify the attack types. Subsequently a novel MCELIECE encryption with Cloud Shield scheme is developed to prevent the low and high rate DDoS attack in the Internet of Things. Finally, the proposed model attained 94% of attack detection accuracy, 3% of false negative rate and 5.5% of false positive rate.

Provably Secure Group Signature Schemes From Code-Based Assumptions

We solve an open question in code-based cryptography by introducing two provably secure group signature schemes from code-based assumptions. Our basic scheme satisfies the CPA-anonymity and traceability requirements in the random oracle model, assuming the hardness of the McEliece problem, the Learning Parity with Noise problem, and a variant of the Syndrome Decoding problem. The construction produces smaller key and signature sizes than the previous group signature schemes from lattices, as long as the cardinality of the underlying group does not exceed $2^{24}$, which is roughly comparable to the current population of the Netherlands. We develop the basic scheme further to achieve the strongest anonymity notion, i.e., CCA-anonymity, with a small overhead in terms of efficiency. The feasibility of two proposed schemes is supported by implementation results. Our two schemes are the first in their respective classes of provably secure groups signature schemes. Additionally, the techniques introduced in this work might be of independent interest. These are a new verifiable encryption protocol for the randomized McEliece encryption and a novel approach to design formal security reductions from the Syndrome Decoding problem.

Amount of Key Information Contained in Plain and Encrypted Text Sets of the Symmetric Randomized McEliece Cryptosystem

A symmetric code cryptosystem, which is similar to the randomized (asymmetric) McEliece encryption scheme, is considered. An expression for the amount of information on the private key, which can be extracted from public and respective encrypted messages of the cryptosystem, is obtained. It is shown that with this information, the security of the symmetric cryptosystem against attacks based on the known ciphertext coincides with the security of its asymmetric counterpart.

A Cryptographic System Based on a New Class of Binary Error-Correcting Codes

Abstract In this paper we introduce a new cryptographic system which is based on the idea of encryption due to [McEliece, R. J. A public-key cryptosystem based on algebraic coding theory, DSN Progress Report. 44, 1978, 114–116]. We use the McEliece encryption system with a new linear error-correcting code, which was constructed in [Hannusch, C.—Lakatos, P.: Construction of self-dual binary 22 k, 22 k−1, 2 k-codes, Algebra and Discrete Math. 21 (2016), no. 1, 59–68]. We show how encryption and decryption work within this cryptosystem and we give the parameters for key generation. Further, we explain why this cryptosystem is a promising post-quantum candidate.

A toolbox for software optimization of QC-MDPC code-based cryptosystems

The anticipated emergence of quantum computers in the foreseeable future drives the cryptographic community to start considering cryptosystems, which are based on problems that remain intractable even with large-scale quantum computers. One example is the family of code-based cryptosystems that relies on the syndrome decoding problem. Recent work by Misoczki et al. (in: 2013 IEEE international symposium on information theory, pp 2069–2073, 2013. https://doi.org/10.1109/ISIT.2013.6620590 ) showed a variant of McEliece encryption which is based on quasi cyclic moderate density parity check (QC-MDPC) codes and has significantly smaller keys than the original McEliece encryption. It was followed by the newly proposed QC-MDPC-based cryptosystems CAKE (Barreto et al. in: IMA international conference on cryptography and coding, Springer, Berlin, pp 207–226, 2017) and Ouroboros (Deneuville et al. in Ouroboros: a simple, secure and efficient key exchange protocol based on coding theory, Springer, Cham, pp 18–34, 2017. https://doi.org/10.1007/978-3-319-59879-6_2 ). These motivate dedicated new software optimizations. This paper lists the cryptographic primitives that QC-MDPC cryptosystems commonly employ, studies their software optimizations on modern processors, and reports the achieved speedups. It also assesses methods for side channel protection of the implementations and their performance costs. These optimized primitives offer a useful toolbox that can be used, in various ways, by designers and implementers of QC-MDPC cryptosystems. Indeed, we applied our methods to generate a platform-specific additional implementation of “BIKE”—a QC-MDPC key encapsulation mechanism (KEM) proposal submitted to the NIST Post-Quantum Project (NIST:Post-Quantum Cryptography—call for proposals, https://csrc.nist.gov/Projects/Post-Quantum-Cryptography , 2017). This gave a $$5\times $$ speedup compared to the reference implementation.

Polynomial-time key recovery attack on the Faure–Loidreau scheme based on Gabidulin codes

Encryption schemes based on the rank metric lead to small public key sizes of order of few thousands bytes which represents a very attractive feature compared to Hamming metric-based encryption schemes where public key sizes are of order of hundreds of thousands bytes even with additional structures like the cyclicity. The main tool for building public key encryption schemes in rank metric is the McEliece encryption setting used with the family of Gabidulin codes. Since the original scheme proposed in 1991 by Gabidulin, Paramonov and Tretjakov, many systems have been proposed based on different masking techniques for Gabidulin codes. Nevertheless, over the years most of these systems were attacked essentially by the use of an attack proposed by Overbeck. In 2005 Faure and Loidreau designed a rank-metric encryption scheme which was not in the McEliece setting. The scheme is very efficient, with small public keys of size a few kiloBytes and with security closely related to the linearized polynomial reconstruction problem which corresponds to the decoding problem of Gabidulin codes. The structure of the scheme differs considerably from the classical McEliece setting and until our work, the scheme had never been attacked. We show in this article that for a range of parameters, this scheme is also vulnerable to a polynomial-time attack that recovers the private key by applying Overbeck’s attack on an appropriate public code. As an example we break in a few seconds parameters with 80-bit security claim. Our work also shows that some parameters are not affected by our attack but at the cost of a lost of efficiency for the underlying schemes.

Implementing QC-MDPC McEliece Encryption

With respect to performance, asymmetric code-based cryptography based on binary Goppa codes has been reported as a highly interesting alternative to RSA and ECC. A major drawback is still the large keys in the range between 50 and 100KB that prevented real-world applications of code-based cryptosystems so far. A recent proposal by Misoczki et al. showed that quasi-cyclic moderate-density parity-check (QC-MDPC) codes can be used in McEliece encryption, reducing the public key to just 0.6KB to achieve an 80-bit security level. In this article, we provide optimized decoding techniques for MDPC codes and survey several efficient implementations of the QC-MDPC McEliece cryptosystem. This includes high-speed and lightweight architectures for reconfigurable hardware, efficient coding styles for ARM’s Cortex-M4 microcontroller, and novel high-performance software implementations that fully employ vector instructions. Finally, we conclude that McEliece encryption in combination with QC-MDPC codes not only enables high-performance implementations but also allows for lightweight designs on a wide range of different platforms.