Anonymous message board server verification

One or more non-transitory computer-readable media having instructions stored thereon that, in response to being executed by one or more processors, cause a system to perform operations, the operations comprising:

• receiving, by a server si of a group of servers that manages the anonymous message board and that includes n number of servers, a group of message shares that includes m number of message shares, each respective message share bi,j corresponding to a portion of a message provided by a respective client device of a plurality of client devices, “i” being an integer between “2” and n and “j” being an integer between “2” and m;
• generating, by the server si, an aggregate hash share signi of the message shares;
• receiving, by the server si, a verification vector iteration vi-1 from a server si-1 of the servers;
• generating, by the server si, a verification vector iteration vi based on:
• the verification vector iteration vi-1;
• a permutation pi that corresponds to the server si and that indicates a particular arrangement order of elements of an m-element set;
• and
• a masking vector ui that corresponds to the server si;
• obtaining a verification hash sign′ that is based on the verification vector iteration vi;
• participating, with one or more other servers of the servers, in a multiparty computation to determine an aggregate hash sign, the aggregate hash sign being determined based on the aggregate hash share signi;
• determining, as part of the multiparty computation, whether one or more of the servers of the group of servers is operating in an adverse manner based on whether the verification hash sign′ is equal to the aggregate hash sign;
• and
• removing a particular server from group of servers in response to determining that the particular server is operating in an adverse manner.

A system comprising:

• one or more processors;
• and
• one or more non-transitory computer-readable media having instructions stored thereon that, in response to being executed by one or more processors, cause a system to perform operations, the operations comprising:
• receiving, by a server fi of a group of servers that manages the anonymous message board and that includes n number of servers, a group of message shares that includes m number of message shares, each respective message share bi,j corresponding to a portion of a message provided by a respective client device of a plurality of client devices, “i” being an integer between “2” and n and “j” being an integer between “2” and m;
• generating, by the server si, an aggregate hash share signi of the message shares;
• receiving, by the server si, a verification vector iteration vi-1 from a server si-1 of the servers;
• generating, by the server si, a verification vector iteration vi based on:
• the verification vector iteration vi-1;
• a permutation pi that corresponds to the server si and that indicates a particular arrangement order of elements of an m-element set;
• and
• a masking vector ui that corresponds to the server si;
• obtaining a verification hash sign′ that is based on the verification vector iteration vi;
• participating, with one or more other servers of the servers, in a multiparty computation to determine an aggregate hash sign, the aggregate hash sign being determined based on the aggregate hash share signi;
• determining, as part of the multiparty computation, whether one or more of the servers of the group of servers is operating in an adverse manner based on whether the verification hash sign′ is equal to the aggregate hash sign;
• and
• removing a particular server from group of servers in response to determining that the particular server is operating in an adverse manner.