Authenticating communications

A system comprising:

• data processing hardware;
• and
• memory hardware in communication with the data processing hardware, the memory hardware storing instructions that when executed on the data processing hardware cause the data processing hardware to perform operations comprising:
• dividing an operation period into a plurality of time intervals each spanning an equal length of time, the operation period starting at an initial time and ending at a final time, and the plurality of time intervals including a first time interval beginning at the initial time and a last time interval ending at the final time;
• populating each of the plurality of time intervals sequentially from the last time interval to the first time interval with an associated authentication value, each authentication value based on a hash function applied to the authentication value associated with a sequentially subsequent time interval of the plurality of time intervals;
• executing a clock for the operation period;
• receiving a communication from a remote device at a communication time corresponding to a time interval of the plurality of time intervals, the communication comprising a commitment value;
• determining whether the commitment value matches the authentication value associated with the time interval corresponding to the communication time;
• and
• processing the communication when the commitment value matches the authentication value associated with the time interval corresponding to the communication time,
• wherein the authentication value associated with the time interval corresponding to the communication time comprises hash digest of the hash function applied to the authentication value associated with the sequentially subsequent time interval of the plurality of time intervals.

A method comprising:

• dividing, by data processing hardware, an operation period into a plurality of time intervals each spanning an equal length of time, the operation period starting at an initial time and ending at a final time, and the plurality of time intervals including a first time interval beginning at the initial time and a last time interval ending at the final time;
• receiving, at the data processing hardware, a seed value;
• populating, by the data processing hardware, each of the plurality of time intervals sequentially from the last time interval to the first time interval with an associated authentication value by:
• applying a hash function to the seed value to determine a last authentication value for the last time interval of the plurality of time intervals;
• and
• for each sequentially preceding time interval, applying the hash function to a subsequent authentication value associated with a sequentially subsequent time interval to determine a preceding authentication value for the sequentially preceding time interval;
• determining, by the data processing hardware, a current time interval of the plurality of time intervals corresponding to a current time;
• and
• sending, from the data processing hardware to a remote device, a communication comprising a current authentication value associated with the current time interval.

A system comprising:

• data processing hardware;
• and
• memory hardware in communication with the data processing hardware, the memory hardware storing instructions that when executed on the data processing hardware cause the data processing hardware to perform operations comprising:
• dividing an operation period into a plurality of time intervals each spanning an equal length of time, the operation period starting at an initial time and ending at a final time, and the plurality of time intervals including a first time interval beginning at the initial time and a last time interval ending at the final time;
• receiving a seed value;
• populating each of the plurality of time intervals sequentially from the last time interval to the first time interval with an associated authentication value by:
• applying a hash function to the seed value to determine a last authentication value for the last time interval of the plurality of time intervals;
• and
• for each sequentially preceding time interval, applying the hash function to a subsequent authentication value associated with a sequentially subsequent time interval to determine a preceding authentication value for the sequentially preceding time interval;
• determining a current time interval of the plurality of time intervals corresponding to a current time;
• and
• sending, to a remote device, a communication comprising a current authentication value associated with the current time interval.