Patent ID: 8239331

Claim:
A method, comprising: receiving, by a data processing apparatus and for each of a plurality of bidders, a sealed bid that has been encrypted with an encryption key, a bid seed value, and an encryption seed value; generating, by a data processing apparatus, commitment data based on the sealed bid for each of the plurality of bidders, the generation of the commitment data comprising: creating a concatenated vector that includes a concatenation of every sealed bid received from the plurality of bidders; and computing, as the commitment data, a hash of the concatenated vector; providing the commitment data to the plurality of bidders; decrypting the sealed bid for each of the plurality of bidders, conducting an auction based on the decrypted bids; for each received sealed bid: generating a plurality of bid representations for the sealed bid, the generation of each bid representation comprising: generating a first coordinate of the bid representation using a first random number generating function and the bid seed value for the sealed bid; and generating a second coordinate of the bid representation based on a modular difference between a value of the sealed bid and the first coordinate; generating a set of different encryption keys for each of the first coordinate and the second coordinate, each set of different encryption keys being generated using a second random number generating function and the encryption seed value for the sealed bid; encrypting the first coordinate with a first of the encryption keys; encrypting the second coordinate with a second of the encryption keys; providing, to a secure processor, a set of decryption keys that reveals only one of the encrypted first coordinate or the encrypted second coordinate; and providing, to the secure processor, at least a portion of the bid representations that were generated for the sealed bid and a verification factor that demonstrates value consistency among the provided bid representations independent of revealing an actual value of the sealed bid.