Quasi-cyclic Moderate Density Parity-check Research Articles

Novel Side-Channel Attacks on Quasi-Cyclic Code-Based Cryptography

Chou suggested a constant-time implementation for quasi-cyclic moderatedensity parity-check (QC-MDPC) code-based cryptography to mitigate timing attacks at CHES 2016. This countermeasure was later found to become vulnerable to a differential power analysis (DPA) in private syndrome computation, as described by Rossi et al. at CHES 2017. The proposed DPA, however, still could not completely recover accurate secret indices, requiring further solving linear equations to obtain entire secret information. In this paper, we propose a multiple-trace attack which enables to completely recover accurate secret indices. We further propose a singletrace attack which can even work when using ephemeral keys or applying Rossi et al.’s DPA countermeasures. Our experiments show that the BIKE and LEDAcrypt may become vulnerable to our proposed attacks. The experiments are conducted using power consumption traces measured from ChipWhisperer-Lite XMEGA (8-bit processor) and ChipWhisperer UFO STM32F3 (32-bit processor) target boards.

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.

A Secure Code-Based Authentication Scheme for RFID Systems

Two essential problems are still posed in terms of Radio Frequency Identification (RFID) systems, including: security and limitation of resources. Recently, Li et al.'s proposed a mutual authentication scheme for RFID systems in 2014, it is based on Quasi CyclicModerate Density Parity Check (QC-MDPC) McEliece cryptosystem. This cryptosystem is designed to reducing the key sizes. In this paper, we found that this scheme does not provide untraceability and forward secrecy properties. Furthermore, we propose an improved version of this scheme to eliminate existing vulnerabilities of studied scheme. It is based on the QC-MDPC McEliece cryptosystem with padding the plaintext by a random bitstring. Our work also includes a security comparison between our improved scheme and different code-based RFID authentication schemes. We prove secrecy and mutual authentication properties by AVISPA (Automated Validation of Internet Security Protocols and Applications) tools. Concerning the performance, our scheme is suitable for low-cost tags with resource limitation.

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.