User authentication using multi-party computation and public key cryptography

1. A method, comprising:

receiving, by a server system from a client system, a request to authenticate a user to a service;

accessing, by the server system, key-pair information associated with the user, wherein the key-pair information includes, for a server key-pair, a first component of a server private key, and, for a client key-pair, a client public key and a first component of a client private key;

in response to the request, generating, by the server system, challenge information to be sent to the client system;

generating, by the server system, a partial signature value based on the first component, but not an entirety, of the server private key;

sending, by the server system to the client system, an authentication challenge that includes the challenge information and the partial signature value;

receiving, by the server system, an authentication response from the client system; and

determining, by the server system, whether to authenticate the user to the service based on the authentication response.

2. The method of claim 1 , wherein the generating the partial signature value includes:

generating a digest value based on an initial input value; and

calculating the partial signature value based on the digest value and the first component of the server private key.

3. The method of claim 1 , wherein the client system stores a second component of the server private key, and wherein the client system is operable to generate a final signature value using the second component of the server private key and the partial signature value.

4. The method of claim 1 , wherein the generating the challenge information includes:

encrypting an original challenge value using the client public key to generate an encrypted challenge value; and

creating a partially decrypted challenge value based on the encrypted challenge value and the first component of the client private key;

wherein the encrypted challenge value and the partially decrypted challenge value are included in the challenge information sent to the client system.

5. The method of claim 4 , wherein the authentication response indicates a decrypted challenge value generated, by the client system, based on a second component of the client private key.

6. The method of claim 5 , wherein the determining whether to authenticate the user to the service includes comparing the decrypted challenge value to the original challenge value.

7. The method of claim 1 , wherein the server system and the client system are communicating over a secured network connection using the Transport Layer Security (TLS) protocol.

8. A non-transitory, computer-readable medium having instructions stored thereon that are capable of execution by a server system to perform operations comprising:

receiving, from a client system, a request to authenticate a user to a service;

accessing key-pair information associated with the user, wherein the key-pair information includes, for a server key-pair, a first component of a server private key, and, for a client key-pair, a client public key and a first component of a client private key;

in response to the request, generating challenge information to be sent to the client system;

generating a partial signature value based on the first component, but not an entirety, of the server private key;

sending, to the client system, an authentication challenge that includes the challenge information and the partial signature value;

receiving an authentication response from the client system; and

determining whether to authenticate the user to the service based on the authentication response.

9. The non-transitory, computer-readable medium of claim 8 , wherein the generating the partial signature value includes:

generating a digest value based on an initial input value; and

calculating the partial signature value based on the digest value and the first component of the server private key.

10. The non-transitory, computer-readable medium of claim 9 , wherein the initial input value corresponds to a current time at which the digest value is generated.

11. The non-transitory, computer-readable medium of claim 8 , wherein the generating the challenge information includes:

encrypting an original challenge value using the client public key to generate an encrypted challenge value; and

creating a partially decrypted challenge value based on the encrypted challenge value and the first component of the client private key;

wherein the encrypted challenge value and the partially decrypted challenge value are included in the challenge information sent to the client system.

12. The non-transitory, computer-readable medium of claim 11 , wherein the authentication response indicates a decrypted challenge value generated, by the client system, based on a second component of the client private key.

13. The non-transitory, computer-readable medium of claim 12 , wherein the determining whether to authenticate the user to the service includes comparing the decrypted challenge value to the original challenge value.

14. The non-transitory, computer-readable medium of claim 12 , wherein the authentication response includes a first hash value generated, by the client system, based on the decrypted challenge value; and wherein the determining whether to authenticate the user to the service includes:

generating a second hash value based on the original challenge value; and

comparing the first and second hash values.

15. A system, comprising:

at least one processor; and

a non-transitory, computer-readable medium having instructions stored thereon that are capable of execution by the at least one processor to perform operations comprising:

receiving, from a client system, a request to authenticate a user to a service;

accessing key-pair information associated with the user, wherein the key-pair information includes, for a server key-pair, a first component of a server private key, and, for a client key-pair, a client public key and a first component of a client private key;

in response to the request, generating challenge information to be sent to the client system;

generating a partial signature value based on the first component, but not an entirety, of the server private key;

sending, to the client system, an authentication challenge that includes the challenge information and the partial signature value;

receiving an authentication response from the client system; and

determining whether to authenticate the user to the service based on the authentication response.

16. The system of claim 15 , wherein the generating the partial signature value includes:

generating a digest value based on an initial input value; and

calculating the partial signature value based on the digest value and the first component of the server private key.

17. The system of claim 16 , wherein the initial input value is an encrypted challenge value generated based on the client public key.

18. The system of claim 15 , wherein the generating the challenge information includes:

encrypting an original challenge value using the client public key to generate an encrypted challenge value; and

creating a partially decrypted challenge value based on the encrypted challenge value and the first component of the client private key;

wherein the encrypted challenge value and the partially decrypted challenge value are included in the challenge information sent to the client system.

19. The system of claim 18 , wherein the authentication response indicates a decrypted challenge value generated, by the client system, based on a second component of the client private key.

20. The system of claim 19 , wherein the determining whether to authenticate the user to the service includes comparing the decrypted challenge value to the original challenge value.