A New Algorithm for Finding Minimum-Weight Words in Large Linear Codes

An algorithm for finding small-weight words in large linear codes is developed and a precise analysis of its complexity is given. It is in particular able to decode random [512,256,57J-linear binary codes in 9 hours on a DEC alpha computer. We improve with it the previously best known attacks on some public-key cryptosystems and identification schemes based on error-correcting codes: for example we reduce the work factor involved in breaking McEliece's cryptosystem, since our algorithm requires 264 elementary operations that is 128 times less than Lee-Brickell's attack. 1 Presentation of the Algorithm Let C be an [n, k]-linear code over GF(2). We present a probabilistic algorithm for finding a codeword of weight w, where w is small. This algorithm was elaborated with Florent Chabaud [2].

• Type: Conference
• Year: 1995
• Where: IMA
• Authors: Anne Canteaut
• Keywords: 512, Algorithm, Cryptology, IMA 1995, Large Linear Codes