Systems and methods for cryptographic authentication of contactless cards

1. An authentication system, comprising:

a contactless card including one or more processors and a memory, the memory containing a key and a counter, wherein the contactless card is configured to:

create cryptographic data based on the key and the counter, and

transmit the cryptographic data and a one-time password;

wherein the counter is configured to increment at one or more intervals in a non-monotonic sequence; and

wherein the increment is associated with one or more cryptographic algorithms.

2. The authentication system of claim 1 , wherein the counter is configured to begin at a first value for a first account and a second value for a second account.

3. The authentication system of claim 2 , wherein the one or more cryptographic algorithms are configured to encrypt a starting value to obtain one or more subsequent counter values.

4. The authentication system of claim 1 , wherein the one or more cryptographic algorithms are selected based on a time for entry into an active communication field with a device.

5. The authentication system of claim 1 , wherein the increment is based on one selected from the group of an assigned sequence and a derived sequence.

6. The authentication system of claim 5 , wherein the increment is based on the derived sequence and the derived sequence comprises account information and session information.

7. The authentication system of claim 6 , wherein the account information comprises at least one selected from the group of a unique identifier, a shared secret, a card sequence number, card information, address information, a time of programming of the contactless card, or any combination thereof.

8. The authentication system of claim 6 , wherein the session information comprises one or more random values exchanged during an established session.

9. The authentication system of claim 6 , wherein the account information comprises at least one dynamic parameter.

10. The authentication system of claim 1 , wherein the one-time password is transmitted for authentication.

11. A method for authenticating one-time passwords, comprising:

creating, by one or more processors, cryptographic data based on a key and a counter contained in a memory of a contactless card; and

transmitting, by the one or more processors, the cryptographic data and one or more one-time passwords for authentication;

wherein the counter is configured to decrement at one or more intervals in a non-monotonic sequence; and

wherein the decrement associated with one or more cryptographic algorithms.

12. The method of claim 11 , wherein the counter is configured to begin at a first value for a first account and a second value for a second account.

13. The method of claim 12 , wherein the one or more cryptographic algorithms are configured to encrypt a starting value to obtain one or more subsequent counter values.

14. The method of claim 11 , wherein the one or more cryptographic algorithms are selected based on a time for entry into an active communication field with a device.

15. The method of claim 11 , wherein the decrement is based on an assigned sequence and the assigned sequence is based on a previous counter value.

16. The method of claim 11 , wherein the decrement is based on a derived sequence and the derived sequence comprises account information and session information.

17. The method of claim 16 , wherein the account information comprises at least one selected from the group of a plurality of parameters including a unique identifier, a shared secret, a card sequence number, card information, address information, a time of programming of the contactless card, or any combination thereof.

18. The method of claim 17 , wherein a first parameter of the plurality of parameters is combined with a second parameter of the plurality of parameters to yield the derived sequence.

19. The method of claim 11 , wherein the one or more cryptographic algorithms are selected to avoid wrapping of the counter.

20. A contactless card comprising:

one or more processors and a memory, wherein the memory contains a counter,

wherein the contactless card is configured to:

transmit one or more one-time passwords, and

adjust the counter with generation of each of the one or more one-time passwords;

wherein the counter is configured to increment or decrement in a non-monotonic sequence; and

wherein a value of the increment or decrement is selected based on a time for entry by the contactless card into an active communication field of a device.