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Design and Application of Codes for Post-Quantum Cryptography

Subject Area Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
Term from 2019 to 2023
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 415543807
 
Final Report Year 2023

Final Report Abstract

This project aimed at improving code- and lattice-based public-key cryptography (PKC) with the goal of obtaining efficient and secure post-quantum systems. It is based on the development of new coding theory suitable for these two types of post-quantum cryptosystems. Our goals were hereby: i) improving the key, ciphertext, and signature sizes; ii) enhancing the reliability of the decryption process; and iii) providing resistance to algorithmic, side-channel, and fault attacks. The significantly larger key, ciphertext, and signature sizes are the most severe drawback of code- and lattice-based post-quantum secure systems compared to traditional cryptography. To turn post-quantum systems practical, these numbers must be decreased while meeting the security levels specified by the National Institute of Standards and Technology (NIST). This project focused on algebraic codes and LWE/Ring-LWE lattices. We estimate the quality of the result by metrics such as key, ciphertext, signature sizes, code rates, security level, and resistance to implementation attacks. We explored potential codes and developed new code constructions that are suitable for both code- and latticebased post-quantum cryptography requirements. Central to this project is to approach post-quantum cryptography from theory and implementation points of view. The theory provided new systems and theoretical attack approaches while the implementation developed methods, architectures, and tools to efficiently implement code- and lattice-based protected cryptosystems able to resist side-channel and fault attacks. The primary tool of this project was error-correcting codes, as they play a crucial role in the design of code-based and lattice-based cryptosystems. Among our results of this project is a power side-channel attack on a NIST finalist, HQC; an analysis of how information leakage can be incorporated into information set decoding attacks; an analysis of RLWE-based cryptosystems as a communication channel, which resulted in improving the parameters of such systems; and the development and implementation of two code-based signature schemes that were submitted to the recent NIST signature competition. The collaboration between the two groups was highly successful since they were complementary in their expertise (coding theory expertise vs. practical attack expertise).

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