Theses in Progress
Ideal LRPC Codes: Decoding and Syndrome Space Expansion
Rank-metric Codes, Coding Theory, LRPC Codes
LRPC (Low Rank Parity Check) codes are the rank-metric analog to the well-studied LDPC codes in the Hamming metric. They are a relatively new family of codes which is well suited to cryptographic applications due to their weak algebraic structure. There exists an efficient decoding algorithm for LRPC codes which was recently improved by the use of ideal codes (changing the structure of the parity-check matrix such that keys are smaller) and the syndrome space expansion algorithm (Increasing the number of syndromes that can be decoded).
During the seminar the student should understand and summarize the content of paper, especially:
-The concept of LRPC codes and their basic decoding,
-The extension to ideal/double circulant LRPC codes ( -> reduce keysize),
-The syndrome space expansion algorithm ( -> improve the number of decodable syndromes).
recommended reading on LRPC codes:
for some application:
Proficiency in linear algebra
Basics of coding theory, not necessarily in the rank metric
Knowledge of LDPC/LRPC codes is a plus