@inproceedings{c375958ec35a4d65945a224aa084af4c,

title = "Smaller decoding exponents : ball-collision decoding",

abstract = "Very few public-key cryptosystems are known that can encrypt and decrypt in time $ b^{ 2¿+¿o(1) } $with conjectured security level $2^b$ against conventional computers and quantum computers. The oldest of these systems is the classic McEliece code-based cryptosystem. The best attacks known against this system are generic decoding attacks that treat McEliece{\textquoteright}s hidden binary Goppa codes as random linear codes. A standard conjecture is that the best possible w-error-decoding attacks against random linear codes of dimension k and length n take time $ 2^{ (\alpha(R,W)¿+¿o(1))^n } $ if k/n¿¿¿R and w/n¿¿¿W as n¿¿¿8. Before this paper, the best upper bound known on the exponent a(R,W) was the exponent of an attack introduced by Stern in 1989. This paper introduces {"}ball-collision decoding{"} and shows that it has a smaller exponent for each (R,W): the speedup from Stern{\textquoteright}s algorithm to ball-collision decoding is exponential in n.",

author = "D.J. Bernstein and T. Lange and C.P. Peters",

year = "2011",

doi = "10.1007/978-3-642-22792-9_42",

language = "English",

isbn = "978-3-642-22791-2",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "743--760",

editor = "P. Rogaway",

booktitle = "Advances in Cryptology - CRYPTO 2011 (31st Annual International Cryptology Conference, Santa Barbara CA, USA, August 14-18, 2011. Proceedings)",

address = "Germany",

}