@article{oai:ipsj.ixsq.nii.ac.jp:00011496,
 author = {Kazumasa, Omote and Atsuko, Miyaji and Kazumasa, Omote and Atsuko, Miyaji},
 issue = {8},
 journal = {情報処理学会論文誌},
 month = {Aug},
 note = {A second-price sealed-bid auction is that wherea bidder who offers the highest price gets a good in the second highest price.This style of auction solves the problems of both an English auction and a first-price sealed-bid auction.An electronic first-price sealed-bid auction cannot directly be applied to a second-price sealed-bid auction which keeps the highest bid secret.We propose the verifiable discriminant function of the p0-th root. Our auction scheme satisfies public verifiability of auction results  and also does not have a single entity who knows the highest bid value even after an auction. Furthermore the bidding cost of our scheme is lower than that of the previous one., A second-price sealed-bid auction is that wherea bidder who offers the highest price gets a good in the second highest price.This style of auction solves the problems of both an English auction and a first-price sealed-bid auction.An electronic first-price sealed-bid auction cannot directly be applied to a second-price sealed-bid auction which keeps the highest bid secret.We propose the verifiable discriminant function of the p0-th root. Our auction scheme satisfies public verifiability of auction results, and also does not have a single entity who knows the highest bid value even after an auction. Furthermore the bidding cost of our scheme is lower than that of the previous one.},
 pages = {1405--2413},
 title = {A Second-price Sealed-bid Auction with Public Verifiability},
 volume = {43},
 year = {2002}
}