Systems and methods for efficient password based public key authentication

1. A method for efficient password based public key authentication between a first user device and a second user device, the method comprising:

receiving a shared password by a first user device;

generating a first hash value of the shared password by the first user device;

generating, at the first user device, a first value, wherein the first value is composed of at least:

a product of the first hash value and a first unique security constant associated with the first user device; and

a first random value generated using data from a generator element;

generating, at the first user device, a first blind public key associated with the first user device, wherein the first blind public key is generated using a first public key; and

concurrently sending the first value and the first blind public key to the second user device for authentication;

receiving the first value and the first blind public key at the second user device;

combining, at the second user device, a second random value and the first public key to generate a second blind public key; and

comparing, at the second user device, the second blind public key and the received first blind public key to verify the identity of the first user device.

2. The method of claim 1 , wherein combining, at the second user device, the second random value and the first public key to generate a second blind public key comprises:

receiving the shared password by the second user device;

generating a second hash value of the shared password by the second user device;

generating, at the second user device, a second value, wherein the second value is composed of at least:

a product of the second hash value and a second unique security constant associated with the second user device; and

a second random value generated using data from the generator element;

generating, at the second user device, a second blind public key associated with the second user device, wherein the second blind public key is generated using a second public key.

3. The method of claim 2 , further comprising:

generating a first shared key at the second user device, wherein the first shared key is generated using the first blind public key, the first value, the first unique security constant, the second hash value and a first plurality of random values.

4. The method of claim 3 , further comprising:

generating at the second user device, a first symmetric key, wherein the first symmetric key is generated using the first value, the second value, and the second hash value; and

encrypting, using the first symmetric key, a first message wherein the first message comprises at least the second public key and a random value used to blind the second public key.

5. The method of claim 4 , further comprising concurrently sending the second value, the second blind public key, and the first message to the first user device.

6. The method of claim 5 , further comprising:

receiving at the first user device, the second value, the second blind public key, and the first message;

generating a second shared key at the first user device, wherein the second shared key is generated using the second blind public key, the second value, the second unique security constant, the first hash value, and a second plurality of random values; and

generating a first decryption key at the first device using the first value, the second value, the first hash value, and the second shared key, wherein the first decryption key is same as the first symmetric key generated at the second user device.

7. The method of claim 6 , further comprising:

decrypting, at the first user device, using the first decryption key, the first message to reveal the first random value and the second public key;

combining the first random value and the second public key to generate a blind public key; and

comparing the generated blind public key and the received second blind public key to verify the identity of a second user.

8. The method of claim 6 , further comprising:

generating at the first user device, a second symmetric key, wherein the second symmetric key is generated using the second value, the first value, and the first hash value;

encrypting, using the second symmetric key, a second message, wherein the second message at least includes the first public key and a second random value used to blind the first public key; and

sending the second message to the second user device.

9. The method of claim 8 , further comprising:

generating a second decryption key at the second user device using the first value, the second value, the second hash value, and the first shared key, wherein the second decryption key is same as the second symmetric key generated at the first user device; and

decrypting, using the second decryption key, the second message to reveal the second random value and the first public key.

10. The method of claim 9 , wherein the second user device sends an acknowledgement to the first user device, wherein the acknowledgement includes the second shared key.

11. A system for efficient password based public key authentication between a first user device and a second user device, the system comprising:

a first device having first control circuitry configured to:

receive a shared password by a first user device;

generate a first hash value of the shared password by the first user device;

generate a first value, wherein the first value is composed of at least:

a product of the first hash value and a first unique security constant associated with the first user device; and

a first random value generated using data from a generator element;

generate a first blind public key associated with the first user device, wherein the first blind public key is generated using a first public key; and

concurrently send the first value and the first blind public key to the second user device for authentication; and

a second device having second control circuitry configured to:

receive the first value and the first blind public key;

combine a second random value and the first public key to generate a second blind public key; and

compare the second blind public key and the received first blind public key to verify the identity of the first user device.

12. The system of claim 11 , wherein the second control circuitry configured to combine the second random value and the first public key to generate a second blind public key is further configured to:

receive the shared password by the second user device;

generate a second hash value of the shared password by the second user device;

generate, at the second user device, a second value, wherein the second value is composed of at least:

a product of the second hash value and a second unique security constant associated with the second user device; and

a second random value generated using data from the generator element;

generate, at the second user device, a second blind public key associated with the second user device, wherein the second blind public key is generated using a second public key.

13. The system of claim 12 , wherein the second control circuitry is further configured to:

generate a first shared key at the second user device, and wherein the first shared key is generated using the first blind public key, the first value, the first unique security constant, the second hash value and a first plurality of random values.

14. The system of claim 13 , wherein the second control circuitry is further configured to:

generate at the second user device, a first symmetric key, wherein the first symmetric key is generated using the first value, the second value, and the second hash value; and

encrypt, using the first symmetric key, a first message wherein the first message comprises at least the second public key and a random value used to blind the second public key.

15. The system of claim 14 , wherein the second control circuitry is further configured to concurrently send the second value, the second blind public key, and the first message to the first user device.

16. The system of claim 15 , wherein the first control circuitry is further configured to:

receive, at the first user device, the second value, the second blind public key, the, and the first message;

generate a second shared key at the first user device, wherein the second shared key is generated using the second blind public key, the second value, the second unique security constant, the first hash value, and a second plurality of random values; and

generate a first decryption key at the first device using the first value, the second value, the first hash value, and the second shared key, wherein the first decryption key is same as the first symmetric key generated at the second user device.

17. The system of claim 16 , wherein the first control circuitry is further configured to:

decrypt, at the first user device, using the first decryption key, the first message to reveal the first random value and the second public key;

combine the first random value and the second public key to generate a blind public key; and

compare the generated blind public key and the received second blind public key to verify the identity of a second user.

18. The system of claim 16 , wherein the first control circuitry is further configured to:

generate at the first user device, a second symmetric key, wherein the second symmetric key is generated using the second value, the first value, and the first hash value;

encrypt, using the second symmetric key, a second message, wherein the second message at least includes the first public key and a second random value used to blind the first public key; and

send the second message to the second user device.

19. The system of claim 18 , wherein the second control circuitry is further configured to:

generate a second decryption key at the second user device using the first value, the second value, the second hash value, and the first shared key, wherein the second decryption key is same as the second symmetric key generated at the first user device;

decrypt, using the second decryption key, the second message to reveal the second random value and the first public key;

combine the second random value and the first public key to generate a blind public key; and

compare the generated blind public key and the received first blind public key to verify the identity of the first user device.

20. The system of claim 19 , wherein the second control circuitry is further configured to send an acknowledgement to the first user device, wherein the acknowledgement includes the second shared key.