Adaptive attack resistant distributed symmetric encryption

A method comprising performing, by a computer system:

• receiving a payload comprising a ciphertext, a first commitment, and a second commitment;
• transmitting a request including the first commitment and the second commitment to each of a plurality of cryptographic devices, the plurality of cryptographic devices storing a first plurality of secret shares that are generated from a first secret value and a second plurality of secret shares that are generated from a second secret value;
• receiving, from the plurality of cryptographic devices, a plurality of partial computations, wherein each partial computation of the plurality of partial computations was generated by a respective one of the plurality of cryptographic devices using a respective first partial computation and a respective second partial computation, wherein the respective first partial computation is generated using a respective first secret share and the first commitment, and wherein the respective second partial computation is generated using a respective second secret share and the second commitment;
• generating a cryptographic key based on the plurality of partial computations;
• and
• decrypting the ciphertext using the cryptographic key to produce a message.

A method comprising performing, by a cryptographic device:

• receiving, from a client computer, a request including a first commitment generating using a message and a first hash function, and a second commitment generated using the message and a second hash function;
• generating a first partial computation based on a first secret share and the first commitment;
• generating a second partial computation based on a second secret share and the second commitment;
• generating a partial computation by combining the first partial computation and the second partial computation;
• and
• transmitting the partial computation to the client computer, thereby enabling the client computer to:
• (1) generate a cryptographic key using the partial computation, (2) encrypt the message using the cryptographic key, thereby generating a ciphertext, and (3) generate a payload comprising the ciphertext, the first commitment, and the second commitment.