Multiparty Key Exchange

An information system comprising:

• a first party generating, by a system, one or more private keys, wherein the one or more private keys of the first party include a machine-generated random sequence of characters of the first party that is generated automatically, by the system;
• the first party computing, by the system, one or more public keys by applying mathematical operations to the one or more private keys;
• the first party sending, by the system, one or more of its public keys to a second party;
• a the second party generating, by the system, one or more private keys;
• the second party computing, by the system, one or more public keys by applying mathematical operations to the second party's one or more private keys;
• the second party sending, by the system, one or more of its the second party's public keys to the first party;
• the first party receiving, by the system, the second party's one or more public keys;
• the first party applying, by the system, mathematical operations between the first party's one or more private keys and the second party's one or more public keys;
• the mathematical operations resulting in a shared secret for the first party;
• the second party receiving, by the system, the first party's one or more public keys;
• the second party applying, by the system, mathematical operations between the second party's one or more private keys and the first party's one or more public keys;
• the mathematical operations resulting in a shared secret for the second party;
• the first party transforming, by the system, the shared secret for the first party to one or more multiparty private keys that are distinct from the first party's private keys and distinct from the second party's private keys;
• the first party computing, by the system, one or more multiparty public keys by applying mathematical operations to information that includes at least the one or more multiparty private keys, the mathematical operations only including operations upon information that is available to the second party;
• the first party sending, by the system, the one or more multiparty public keys to a third party that is distinct from the first party and distinct from the second party;
• wherein the computing of the one or more public keys by the first party is performed by a first machine of the system, the first machine having a first processor system and a first memory system, the first processor system including a first set of one or more processors;
• and wherein the computing of the one or more public keys by the second party is performed by a second machine of the system, second machine having a processor system and a second memory system, the second processor system including a second set of one or more processors;
• wherein each of the one or more multiparty public keys has a size, and the size does not increase faster than linearly as a function of the number of participants that share the one or more multiparty public keys.

A machine-implemented method comprising:

• a first party generating one or more private keys, wherein the one or more private keys of the first party include a machine-generated random sequence of characters of the first party that is generated automatically, by the machine;
• the first party computing, by the machine, one or more public keys by applying mathematical operations to the one or more private keys;
• the first party sending, by the machine, one or more of its public keys to a second party;
• a the second party generating, by the machine, one or more private keys;
• the second party computing, by the machine, one or more public keys by applying mathematical operations to the second party's one or more private keys;
• the second party sending, by the machine, one or more of its the second party's public keys to the first party;
• the first party receiving, by the machine, the second party's one or more public keys;
• the first party applying, by the machine, mathematical operations between the first party's one or more private keys and the second party's one or more public keys;
• the mathematical operations resulting in a shared secret for the first party;
• the second party receiving, by the machine, the first party's one or more public keys;
• the second party applying, by the machine, mathematical operations between the second party's one or more private keys and the first party's one or more public keys;
• the mathematical operations resulting in a shared secret for the second party;
• the first party transforming, by the machine, the shared secret for the first party to one or more multiparty private keys that are distinct from the first party's private keys and distinct from the second party's private keys;
• the first party computing, by the machine, one or more multiparty public keys by applying mathematical operations to information that includes at least the one or more multiparty private keys, the mathematical operations only including operations upon information that is available to the second party;
• the first party sending, by the machine, the one or more multiparty public keys to a third party that is distinct from the first party and distinct from the second party;
• wherein the computing of the one or more public keys by the first party is performed by a first machine, the first machine having a first processor system and a first memory, the first processor system including a first set of one or more processors;
• and wherein the computing of the one or more public keys by the second party is performed by a second machine, second machine having a second processor system and a second memory system, the second processor system including a second set of one or more processors;
• wherein each of the one or more multiparty public keys has a size, and the size does not increase faster than linearly as a function of the number of participants that share the one or more multiparty public keys.