PUF with dissolvable conductive paths
The generation of “fingerprints”, also called challenge-response pairs (CRPs) of Physically Unclonable Functions (PUFs), can often stress electronic components, leaving behind traces that can be exploited by crypto-analysts. A non-intrusive method to generate CRPs based on Resistive RAMs may instead be used, which does not disturb the memory cells. The injection of small electric currents (magnitude of nanoAmperes) in each cell causes the resistance of each cell to drop abruptly by several orders of magnitudes through the formation of temporary conductive paths in each cell. A repeated injection of currents into the same cell, results in an almost identical effect in resistance drop for a single cell. However, due to the small physical variations which occur during manufacturing, the cells are significantly different from each other, in such a way that a group of cells can be used as a basis for PUF authentication.
1. A method of generating a physically unclonable function response, the method comprising:
exposing each cell of a random access memory array to an electric field to form temporary dissolvable conductive paths in dielectric material between electrodes of each of a plurality of resistive random access memory cells in the random access memory array;
measuring the resistances of each of the plurality of resistive random access memory cells along the temporary conductive paths;
assigning a parameter value of zero to resistive random access memory cells with resistance measurements within a first predefined resistance threshold range;
assigning a parameter value of one to resistive random access memory cells with resistance measurements within a second predefined resistance threshold range that is higher than the first predefined resistance threshold range; and
generating a data stream of parameter values, each parameter value representing one of the plurality of resistive random access memory cells, the data stream being used to generate a physically unclonable function response that uniquely identifies the random access memory array,
wherein, for a given resistive random access memory cell of the plurality of resistive random access memory cells, the electric field is generated by applying a gradually increasing electric current to at least one of the electrodes of the given resistive random access memory cell.
2. The method of claim 1 , further comprising:
assigning an arbitrary parameter value to resistive random access memory cells with resistance measurements within a third predefined resistance threshold range that is between the first and second predefined resistance threshold ranges; and
assigning the arbitrary parameter value to resistive random access memory cells with resistance measurements above a predefined upper resistance threshold range that is above the second predefined resistance threshold range, wherein the data stream is a ternary data stream.
3. The method of claim 1 , wherein the resistance of the given resistive random access memory cell along a temporary conductive path of the temporary conductive paths for the given resistive random access memory cell is related to the electric current applied to the given resistive random access memory cell.
4. The method of claim 1 , further comprising:
forming, in each of the plurality of resistive random access memory cells, permanent filaments by applying a forming voltage to each resistive random access memory cell of the plurality of resistive random access memory cells, wherein the temporary conductive paths are formed extending from the permanent filaments.
5. The method of claim 1 , wherein the random access memory array is selected from a group consisting of: a conductive bridge random access memory array, a memristor memory array, and a phase change memory array.
6. The method of claim 1 , wherein a temporary conductive path of the temporary conductive paths for a given resistive random access memory cell of the plurality of resistive random access memory cells is formed between a top electrode and a bottom electrode of the given resistive random access memory cell, the temporary conductive being a path formed from a material selected from at least one of: metallic positive ions such as copper or silver, elements with oxygen vacancies, crystallographic defects or doping elements, and a dielectric material manufactured with chalcogenide, tantalum oxide, silicon dioxide, hafnium oxide, and other solid electrolyte material.
7. A system comprising:
a secure server;
an electronic device communicatively coupled to the secure server, the electronic device comprising:
an array comprising resistive random access memory cells;
a secure processor coupled to the array, the secure processor configured to execute instructions for:
causing a gradually increasing current to be applied to each of the resistive random access memory cells to form temporary dissolvable conductive paths in dielectric material between electrodes of each of the resistive random access memory cells;
measuring the resistances between the electrodes of each of the resistive random access memory cells;
assigning a parameter value of zero to resistive random access memory cells with resistance measurements within a first predefined resistance threshold range;
assigning a parameter value of one to resistive random access memory cells with resistance measurements within a second predefined resistance threshold range that is higher than the first predefined resistance threshold range; and
generating a physically unclonable function response comprising parameter values, each of the parameter values representing one of the resistive random access memory cells, the physically unclonable function response uniquely identifying the electronic device.
8. The system of claim 7 , wherein the secure processor is further configured to execute instructions for:
retrieving a physically unclonable function key from the secure server; and
comparing the physically unclonable function key to the physically unclonable function response to determine a correlation between the physically unclonable function key and the physically unclonable function response.
9. The system of claim 8 , wherein the secure processor is further configured to execute instructions for:
determining that the correlation between the physically unclonable function key and the physically unclonable function response exceeds a predefined threshold; and
authenticating the electronic device.
10. The system of claim 7 , wherein the secure processor is further configured to execute instructions for:
assigning an arbitrary parameter value to resistive random access memory cells with resistance measurements within a third predefined resistance threshold range that is between the first and second predefined resistance threshold ranges; and
assigning the arbitrary parameter value to resistive random access memory cells with resistance measurements above a predefined upper resistance threshold range that is above the second predefined resistance threshold range.
11. The system of claim 7 , wherein each of the resistive random access memory cells comprises a permanent conductive filament interposed between the electrodes of each of the resistive random access memory cells, and wherein, for a given resistive random access memory cell of the resistive access memory cells, a temporary conductive path of the temporary conductive paths extends between the permanent conductive filament and a bottom electrode of the electrodes corresponding to the given resistive random access memory cell.
12. The system of claim 7 , wherein the array is selected from a group consisting of: a conductive bridge random access memory array, a memristor memory array, and a phase change memory array.
13. The system of claim 7 , wherein a temporary conductive path of the temporary conductive paths for a given resistive random access memory cell of the resistive random access memory cells is formed between a top electrode and a bottom electrode of the given resistive random access memory cell, the temporary conductive being path formed from a material selected from at least one of: metallic positive ions such as copper or silver, elements with oxygen vacancies, crystallographic defects or doping elements, and a dielectric material manufactured with chalcogenide, tantalum oxide, silicon dioxide, hafnium oxide, and other solid electrolyte material.
14. A method of generating a physically unclonable function key, the method comprising:
exposing each cell of a random access memory array to an electric field to form temporary dissolvable conductive paths in dielectric material between electrodes of each of a plurality of resistive random access memory cells in the random access memory array;
measuring, by a processor, the resistances of each of the plurality of resistive random access memory cells along the temporary conductive paths;
assigning, by the processor, a parameter value of zero to resistive random access memory cells with resistance measurements within a first predefined resistance threshold range;
assigning, by the processor, a parameter value of one to resistive random access memory cells with resistance measurements within a second predefined resistance threshold range that is higher than the first predefined resistance threshold range;
generating, by the processor, a physically unclonable function key comprising parameter values, each of the parameter values representing one of the plurality of resistive random access memory cells, the physically unclonable function key uniquely identifying the random access memory array; and
sending, by the processor, the physically unclonable function key to a secure server to be stored,
wherein, for a given resistive random access memory cell of the plurality of resistive random access memory cells, the electric field is generated by applying a gradually increasing electric current to at least one of the electrodes of the given resistive random access memory cell.
15. The method of claim 14 , further comprising:
assigning an arbitrary parameter value to resistive random access memory cells with resistance measurements within a third predefined resistance threshold range that is between the first and second predefined resistance threshold ranges; and
assigning the arbitrary parameter value to resistive random access memory cells with resistance measurements above a predefined upper resistance threshold range that is above the second predefined resistance threshold range, wherein the data stream is a ternary data stream.
16. The method of claim 14 , wherein the resistance of the given resistive random access memory cell along a temporary conductive path of the temporary conductive paths for the given resistive random access memory cell is related to the electric current applied to the given resistive random access memory cell.
17. The method of claim 14 , further comprising:
forming, in each of the plurality of resistive random access memory cells, permanent filaments by applying a forming voltage to each resistive random access memory cell of the plurality of resistive random access memory cells, wherein the temporary conductive paths are formed in combination with the permanent filaments.
18. The method of claim 14 , wherein a temporary conductive path of the temporary conductive paths for a given resistive random access memory cell of the plurality of resistive random access memory cells is formed between a top electrode and a bottom electrode of the given resistive random access memory cell, the temporary conductive being path formed from a material selected from at least one of: metallic positive ions such as copper or silver, elements with oxygen vacancies, crystallographic defects or doping elements, and a dielectric material manufactured with chalcogenide, tantalum oxide, silicon dioxide, hafnium oxide, and other solid electrolyte material.