Systems and methods for privacy-preserving inventory matching with security against malicious adversaries

A system, comprising:

• a plurality of party electronic devices, each party electronic device associated with one of a plurality of parties;
• and
• a privacy-preserving inventory matching electronic server comprising a computer processor that is configured to:
• receive, from each of the plurality of party electronic devices, an axe submission, each axe submission comprising a direction and a quantity commitment to a quantity integer, wherein the quantity integer is not revealed in the quantity commitment;
• arrange the parties into data structures based on the direction in the party's axe submission;
• for a first party and a second party, the first party and the second party being in different data structures, send each party's quantity commitment to the party electronic device for the other party;
• receive, from the party electronic device for the first party and the party electronic device for the second party, output secret-shares of an arithmetized comparison circuit;
• verify that the output secret-shares of the arithmetized comparison circuit received from the party electronic device for the first party and the party electronic device for the second party match quantity commitments to the output secret-shares sent by the respective opposite party;
• identify a minimal party based on the outputs of the arithmetized comparison circuit;
• generate and send a minimal party identification proof of the minimal party identification to the party electronic device for the minimal party;
• receive a minimal quantity integer from the party electronic device for the minimal party, wherein the minimal quantity integer is the quantity integer for the minimal party;
• reveal the minimal quantity integer to the party electronic device for the first party and the party electronic device for the second party;
• and
• execute a trade for the minimal quantity integer.

A non-transitory computer readable storage medium,

• including instructions stored thereon, which when read and executed by one or more computer processors, cause the one or more computer processors to perform steps comprising:
• submit, to a privacy-preserving inventory matching electronic server, an axe submission comprising a direction and a first party quantity commitment to a first party quantity integer, wherein the first party quantity integer is not revealed in the first party quantity commitment;
• send, via the privacy-preserving inventory matching electronic server, the first party quantity commitment to a second party and receiving a second party quantity commitment to a second party quantity integer from the second party, wherein the second party quantity integer is not revealed in the second party quantity commitment;
• decompose the first party quantity integer into a plurality of bits;
• perform a bit-commitment protocol process on the plurality of bits comprising two first party secret-shares;
• send the second party one of the first party secret-shares;
• receive a second party secret share from the second party;
• execute an arithmetized comparison circuit on the first party secret-share that was not sent to the second party and the second party secret-share received from the second party;
• send outputs of the arithmetized comparison circuit to the privacy-preserving inventory matching electronic server, wherein the privacy-preserving inventory matching electronic server verifies that the outputs received from the first party and outputs received from the second party match commitments to the output secret-shares sent by the second party and the first party, respectively;
• receive, from the privacy-preserving inventory matching electronic server, a minimal party identification proof of that the first party is a minimal party;
• and
• verify the minimal party identification and sending the first party quantity integer to the privacy-preserving inventory matching electronic server, wherein the first party quantity integer is a minimal quantity integer;
• wherein a transaction is executed for the minimal quantity integer.

A non-transitory computer readable storage medium, including instructions stored thereon, which when read and executed by one or more computer processors, cause the one or more computer processors to perform steps comprising:

• submit, to a privacy-preserving inventory matching electronic server, an axe submission comprising a direction and a first party quantity commitment to a first party quantity integer, wherein the first party quantity integer is not revealed in the first party quantity commitment;
• send, via the privacy-preserving inventory matching electronic server, the first party quantity commitment to a second party and receiving a second party quantity commitment to a second party quantity integer from the second party, wherein the second party quantity integer is not revealed in the second party quantity commitment;
• decompose the first party quantity integer into a plurality of bits;
• perform a bit-commitment protocol process on the plurality of bits comprising two first party secret-shares;
• send the second party one of the first party secret-shares;
• receive a second party secret share from the second party;
• execute an arithmetized comparison circuit on the first party secret-share that was not sent to the second party and the second party secret-share received from the second party;
• send outputs of the arithmetized comparison circuit to the privacy-preserving inventory matching electronic server, wherein the privacy-preserving inventory matching electronic server verifies that the outputs received from the first party and outputs received from the second party match commitments to the output secret-shares sent by the second party and the first party, respectively;
• and
• receive, from the privacy-preserving inventory matching electronic server, an identification of a minimal quantity integer, wherein the minimal quantity integer is the second party quantity integer;
• wherein a transaction is executed for the minimal quantity integer.