In 2000, a paper by Kohno et al. presents a meet-in-the-middle attack against 6 of 32 rounds of Serpent and an amplified boomerang attack against 9 of 32 rounds in Serpent.[3]A 2001 attack by Eli Biham, Orr Dunkelman and Nathan Keller presents a linear cryptanalysis attack that breaks 10 of 32 rounds of Serpent-128 with 2118 known plaintexts and 289 time, and 11 rounds of Serpent-192/256 with 2118 known plaintexts and 2187 time.[4]
A 2011 attack by Hongjun Wu, Huaxiong Wang and Phuong Ha Nguyen, also using linear cryptanalysis, breaks 11 rounds of Serpent-128 with 2116 known plaintexts, 2107.5 time and 2104 memory.[1]
The same paper also describes two attacks which break 12 rounds of Serpent-256. The first requires 2118 known plaintexts, 2228.8 time and 2228 memory. The other attack requires 2116 known plaintexts and 2121 memory but also requires 2237.5 time.