Improved security and efficiency for multi-party computation wallets

A classical computing system comprising one or more computers and one or more storage devices storing instructions that are operable, when executed by the one or more computers, to cause the one or more computers to perform operations comprising:

• generating, by a first party in possession of a first secret value, a graded encoding for the first secret value using a first learning with errors (LWE) instance that comprises the first secret value;
• receiving, by the first party and from a second party in possession of a second secret value, a graded encoding for the second secret value, wherein the secret is equal to a product of the first secret value and the second secret value;
• computing, by the first party, a product of:
• the graded encoding for the second secret value, the graded encoding for the first secret value, and a first public matrix generated by or assigned to the first party, wherein the product comprises a second additive secret value and forms a second LWE instance;
• computing, by inverting the second LWE instance, a first additive secret value, wherein the secret is equal to a sum of the first additive secret value and the second additive secret value;
• and
• performing, by the first party, a cryptographic operation in an MPC wallet protocol using the first additive secret value.

A computer-readable storage medium comprising instructions stored thereon that are executable by a classical processing device and upon such execution cause the processing device to perform operations comprising:

• generating, by a first party in possession of a first secret value, a graded encoding for the first secret value using a first learning with errors (LWE) instance that comprises the first secret value;
• receiving, by the first party and from a second party in possession of a second secret value, a graded encoding for the second secret value, wherein the secret is equal to a product of the first secret value and the second secret value;
• computing, by the first party, a product of:
• the graded encoding for the second secret value, the graded encoding for the first secret value, and a first public matrix generated by or assigned to the first party, wherein the product comprises a second additive secret value and forms a second LWE instance;
• computing, by inverting the second LWE instance, a first additive secret value, wherein the secret is equal to a sum of the first additive secret value and the second additive secret value;
• and
• performing, by the first party, a cryptographic operation in an MPC wallet protocol using the first additive secret value.