Shared secret data production system

A system effective to produce shared secret data, the system comprising:

• a first device including a first memory;
• and
• a second device including a second memory;
• the first device being configured to:
• receive key generation data from a third device, wherein the key generation data is effective to indicate a braid group, a first set of conjugates included in the braid group, a non-singular matrix, and a set of invertible elements among a finite field;
• store the key generation data in the first memory;
• the second device being configured to:
• receive a first secret element from the third device;
• receive a public key from the third device, wherein the public key is based on the first secret element, a first monoid element, and a first permutation associated with a first expression in a second set of conjugates included in the braid group, wherein the second set of conjugates commutes with the first set of conjugates;
• store the first secret element in the second memory of the second device;
• and
• send the public key to the first device;
• the first device being further configured to:
• generate a first ephemeral private key based on:
• a second secret element,
• a second expression in the first set of conjugates, and
• a second permutation associated with the second expression in the first set of conjugates, wherein the first ephemeral private key is based on the second secret element, a second monoid element, and the second permutation;
• generate a second ephemeral private key based on:
• a third secret element,
• a third expression in the first set of conjugates, and
• the second permutation associated with the third expression in the first set of conjugates, wherein the second ephemeral private key is based on the third secret element, a third monoid element, and the second permutation;
• store the first ephemeral private key in the first memory of the first device;
• store the second ephemeral private key in the first memory of the first device;
• generate a first element based on the public key received from the second device, and based on the first ephemeral private key;
• generate a second element based on the public key received from the second device, and based on the second ephemeral private key, wherein the second element relates to the shared secret data;
• and
• generate a session public key based on the first element, the second secret element, the third secret element, the second monoid element, and the third monoid element, wherein the session public key is specified for one or more communication sessions between the first device and the second device;
• and
• send the session public key to the second device;
• the second device being further configured to:
• receive the session public key from the first device;
• determine the second element based on the first secret element and the session public key to produce the shared secret data.

A first device effective to produce shared secret data, the device comprising:

• a memory;
• a receiver configured to be in communication with the memory;
• an algebraic eraser module configured to be in communication with the memory and the receiver;
• a session key generator configured to be in communication with the memory, the receiver, and the algebraic eraser module;
• and
• the receiver being configured to:
• receive key generation data from a third device;
• store the key generation data in the memory, wherein the key generation data is effective to indicate a braid group, a first set of conjugates included in the braid group, a non-singular matrix, and a set of invertible elements among a finite field;
• receive a public key from a second device, wherein the public key is based on a first secret element, a first monoid element, and a first permutation associated with a first expression in a second set of conjugates included in the braid group, wherein the second set of conjugates commutes with the first set of conjugates;
• send the received public key to the algebraic eraser module;
• the algebraic eraser module being configured to:
• retrieve a first portion of the key generation data stored in the memory, wherein the first portion of the key generation data indicates a second expression in the first set of conjugates;
• generate a first ephemeral private key based on:
• a second secret element,
• the second expression in the first set of conjugates, and
• a second permutation associated with the second expression in the first set of conjugates, wherein the first ephemeral private key is based on the second secret element, a second monoid element, and the second permutation;
• retrieve a second portion of the key generation data stored in the memory, wherein the second portion of the key generation data indicates a third expression in the first set of conjugates;
• generate a second ephemeral private key based on:
• a third secret element,
• the third expression in the first set of conjugates, and
• the second permutation associated with the third expression in the first set of conjugates, wherein the second ephemeral private key is based on the third secret element, a third monoid element, and the second permutation;
• store the first ephemeral private key in the memory of the first device;
• store the second ephemeral private key in the memory of the first device;
• send the first ephemeral private key to the session key generator;
• send the second ephemeral private key to the session key generator;
• the session key generator being configured to:
• generate a first element based on the public key received from the second device, and based on the first ephemeral private key;
• generate a second element based on the public key received from the second device, and based on the second ephemeral private key, wherein the second element relates to the shared secret data;
• and
• generate a session public key based on the first element, the second secret element, the third secret element, the second monoid element, and the third monoid element, wherein the shared secret data is derivable from the session public key.