System to generate a signature key and method of operating the same

1. A method for utilizing a plurality of physical unclonable function (PUF) cells to generate a signature key with a desired bit length, the method comprising:

setting a state of each of the plurality of PUF cells to a uniform level at a predetermined time point, wherein each of the plurality of PUF cells has retention time, wherein the retention time of each PUF cell is between the predetermined time point and a time point when a state of each of the plurality of PUF cells changes, and the retention times of the plurality of PUF cells are all different from each other;

periodically sampling states of the plurality of PUF cells until states of at least a portion of the plurality of PUF cells change, and states of the other PUF cells are unchanged to obtain an order of change in the state of at least the portion of the plurality of PUF cells, including:

at a first time, determining only a state of a PUF cell of the plurality of PUF cells is changed, and states of the other PUF cells of the plurality of PUF cells is unchanged, and generating a first state changing information according to position of the first changed PUF cell among the plurality of PUF cells;

generating a first address according to the first state changing information accordingly;

at a second time after the first time, determining only a state of another PUF cell of the plurality of PUF cells is changed except the first changed PUF cell, and states of the other PUF cells of the plurality of PUF cells is unchanged, and generating a second state changing information according to position of the second changed PUF cell among the plurality of PUF cells; and

generating a second address according to the second state changing information accordingly; and

generating the signature key at least based on the first address and the second address.

2. The method as claimed in claim 1 , wherein the obtaining the order of change in the state of at least the portion of the plurality of PUF cells comprises:

determining the number of the portion of the plurality of PUF cells according to the desired bit length.

3. The method as claimed in claim 2 , wherein the signature key includes information of addresses of the portion of the plurality of PUF cells.

4. The method as claimed in claim 3 , wherein the generation of the signature key comprises:

collecting the addresses of the portion of the plurality of PUF cells by using a plurality of registers.

5. The method as claimed in claim 2 , wherein the number of the portion of the plurality of PUF cells is less than the desired bit length.

6. The method as claimed in claim 1 , wherein the periodically sampling states of the plurality of PUF cells comprises:

periodically sampling states of the plurality of PUF cells by using a sampling rate, wherein a sampling period corresponding to the sampling rate is shorter than a minimum time difference between two consecutive changes of the state of two of the plurality of PUF cells.

7. The method as claimed in claim 6 , wherein the plurality of state changing information individually corresponds to one of the portion of the plurality of PUF cells.

8. The method as claimed in claim 7 , further comprising:

generating a lookup table; and

individually converting the plurality of state changing information into one of a plurality of addresses based on the lookup table.

9. The method as claimed in claim 8 , wherein each of the plurality of addresses includes a plurality of bits, and logic levels of a half of the plurality of bits are at a high logical level, and logic levels of the other half of the plurality of bits are at a low logical level opposite to the high logical level.

10. A method for utilizing a plurality of physical unclonable function (PUF) cells to generate a signature key with a desired bit length, the method comprising:

setting a state of each of the plurality of PUF cells to a uniform level at a predetermined time point, wherein each of the plurality of PUF cells has retention time, wherein the retention time of each PUF cell is between the predetermined time point and a time point when a state of each of the plurality of PUF cells changes, and the retention times of the plurality of PUF cells are all different from each other;

periodically sampling states of the plurality of PUF cells until states of a portion of the plurality of PUF cells change, and states of the other PUF cells are unchanged to obtain a plurality of state changing information, the plurality of state changing information corresponding to the portion of the plurality of PUF cells, wherein the number of the plurality of state changing information is less than the number of the plurality of PUF cells; and

generating the signature key based on the plurality of state changing information, wherein the desired bit length of the signature key is greater than the number of the plurality of state changing information.

11. The method as claimed in claim 10 , wherein relationship between the portion of the plurality of PUF cells and the plurality of PUF cells is expressed by P n m , wherein n represents the number of the portion of the plurality of PUF cells, and m represents the number of the plurality of PUF cells.

12. The method as claimed in claim 11 , wherein the number of the plurality of PUF cells is greater than the desired bit length.

13. The method as claimed in claim 12 , further comprising:

determining the number of the portion of the plurality of PUF cells according to a relationship between P n m and C k/2 k , wherein k represents the desired bit length.

14. The method as claimed in claim 13 , wherein the relationship between the P n m and the C k/2 k is expressed as follows:

P n m >C k/2 k .

15. A system to generate a signature key, comprising:

a plurality of physical unclonable function (PUF) cells;

a controller, arranged for setting a state of each of the plurality of PUF cells to a uniform level at a predetermined time point, wherein each of the plurality of PUF cells has retention time, wherein the retention time of each PUF cell is between the predetermined time point and a time point when a state of each of the plurality of PUF cells changes, and the retention times of the plurality of PUF cells are all different from each other;

a state determination device, arranged for periodically sampling states of the plurality of PUF cells until states of at least a portion of the plurality of PUF cells change, and states of the other PUF cells are unchanged to obtain an order of change in the state of at least the portion of the plurality of PUF cells; and

an encoder arranged for generating a signature key at least based on the order.

16. The system as claimed in claim 15 , further comprising:

a plurality of registers, arranged for sampling the state of a portion of the plurality of PUF cells to obtain a plurality of state changing information, the plurality of state changing information corresponding to the portion of the plurality of PUF cells.

17. The system as claimed in claim 16 , wherein the plurality of state changing information individually corresponds to one of the portion of the plurality of PUF cells respectively.

18. The system as claimed in claim 16 , further comprising:

a lookup table, arranged for converting the plurality of state changing information into a plurality of addresses respectively based on the lookup table.

19. The system as claimed in claim 15 , wherein the controller is further configured to determining the number of the portion of the plurality of PUF cells according to a desired bit length of the signature key.

20. The method as claimed in claim 19 , wherein the signature key includes information of addresses of the portion of the plurality of PUF cells.