@misc{cryptoeprint:2011:040, author = {Hoon Hong, Eunjeong Lee, Hyang-Sook Lee and Cheol-Min Park}, title = {Simple and Exact Formula for Minimum Loop Length in Ate_i Pairing based on Brezing-Weng Curves}, howpublished = {Cryptology ePrint Archive, Report 2011/040}, year = {2011}, url = {http://eprint.iacr.org/2011/040}, }