Private and mutually authenticated key exchange

1. A system for private and mutual authenticated key exchange, comprising:

one or more processors configured to:

transmit a first message including a public key from a first device to a second device;

receive, at a first device, a second message transmitted from the second device and including a hierarchical inner-product encryption (HIPE) ciphertext;

decrypt, at the first device, the HIPE ciphertext to generate a first authenticated encryption (AE) ciphertext;

decrypt, at the first device, the first AE ciphertext;

determine, at the first device, a signature and one or more attributes of the second device based on the decrypted first AE ciphertext;

generate, at the first device, a second AE ciphertext including a signature and one or more attributes of the first device; and

transmit a third message including the second AE ciphertext from the first device to the second device.

2. The system of claim 1 , the one or more processors further configured to generate, at the first device, a secret decryption key for the first device based on verification, via a trusted third party (TTP), of one or more attributes of the first device.

3. The system of claim 2 , wherein the one or more processors are configured to decrypt, at the first device, the HIPE ciphertext based on a master public key associated with the HIPE and the secret decryption key.

4. The system of claim 2 , wherein the TTP comprises one of the first device and an organization.

5. The system of claim 1 , the one or more processors further configured to:

generate a session key for the first device based on the second message; and

generate an AE key based on the session key.

6. The system of claim 1 , the one or more processors further configured to generate, at the first device, a signature of the first device based on at least one of the one or more attributes of the first device, the first message, and the second message.

7. The system of claim 1 , wherein the HIPE comprises a lattice-based HIPE.

8. A method of private mutually authenticated key exchange, comprising:

transmitting a first message including a public key from a first device to a second device;

receiving, at the first device, a second message transmitted from a second device and including a hierarchical inner-product encryption (HIPE) ciphertext;

decrypting, at the first device, the HIPE ciphertext to generate a first authenticated encryption (AE) ciphertext;

decrypting, at the first device, the first AE ciphertext;

determining, at the first device, a signature and one or more attributes of the second device based on the decrypted first AE ciphertext;

generating, at the first device, a second AE ciphertext including a signature and one or more attributes of the first device; and

transmitting a third message including the second AE ciphertext from the first device to the second device.

9. The method of claim 8 , further comprising:

generating, at the first device, a session key based on the second message received from the second device; and

generating, at the first device, an AE key based on the session key.

10. The method of claim 8 , further comprising verifying, at the first device, if the signature of the second device is a valid signature.

11. The method of claim 8 , further comprising:

requesting a secret decryption key from a trusted third party (TTP); and

receiving, at the first device, the secret decryption key.

12. The method of claim 11 , wherein the decrypting the HIPE ciphertext comprises decrypting the HIPE ciphertext based on a master public key associated with the HIPE ciphertext and the secret decryption key.

13. The method of claim 11 , wherein the requesting the secret decryption key comprises requesting the secret decryption key from one of the first device and a third device.

14. The method of claim 8 , further comprising generating, at the first device, a signature of the first device based on at least one of the one or more attributes of the first device, the first message, and the second message.

15. A non-transitory computer-readable medium having computer instructions stored thereon that are executable by a processing device to perform or control performance of operations comprising:

transmitting a first message including a public key from a first device to a second device;

receiving, at the first device, a second message from the second device including a hierarchical inner-product encryption (HIPE) ciphertext;

decrypting, at the first device, the HIPE ciphertext to generate a first authenticated encryption (AE) ciphertext;

decrypting, at the first device, the first AE ciphertext;

determining, at the first device, a signature and one or more attributes of the second device based on the decrypted first AE ciphertext;

generating, at the first device, a second AE ciphertext including a signature and one or more attributes of the first device; and

transmitting a third message including the second AE ciphertext from the first device to the second device.

16. The non-transitory computer-readable medium of claim 15 , the operations further comprising:

requesting a secret decryption key from a trusted third party (TTP); and

receiving, at the first device, the secret decryption key.

17. The non-transitory computer-readable medium of claim 16 , wherein the decrypting the HIPE ciphertext comprises decrypting the HIPE ciphertext based on a master public key associated with the HIPE and the secret decryption key.

18. The non-transitory computer-readable medium of claim 15 , the operations further comprising verifying, at the first device, if the signature of the second device is a valid signature.

19. The non-transitory computer-readable medium of claim 15 , the operations further comprising generating, at the first device, a signature of the first device based on at least one of the one or more attributes of the first device, the first message, and the second message.

20. The non-transitory computer-readable medium of claim 15 , wherein the decrypting the first AE ciphertext comprises decrypting the first AE ciphertext based on an AE key generated based on the second message.