Methods and systems for determining the authenticity of a component using elliptic-curve cryptography

1 . A method of determining the authenticity of a replaceable toner cartridge in a printing device using an elliptic curve E defined over a finite field F q , where q is an integer, the method comprising:

the printing device generating a random integer j, where the random integer j is in the interval of one to the integer q;

the printing device calculating a point T=j·S, where point S is a point on elliptic curve E(F q );

the printing device calculating a binary value k which is equal to the binary random integer j with a bitmask m applied thereto;

the printing device sending point T and binary value k to the replaceable toner cartridge; and

the replaceable toner cartridge iteratively calculating point U=n·S for different values of integer n, where for each iterative calculation integer n takes different values, wherein for each iteration:

the bits of binary integer n corresponding to the unmasked bits of bitmask m are the same as the corresponding bits of binary random integer j; and

the bits of binary integer n corresponding to the masked bits of bitmask m are varied in each iteration,

and wherein the bits of binary value k corresponding to the unmasked bits of bitmask m are the same as the corresponding bits of binary random integer j, and wherein the bits of binary value k corresponding to the masked bits of bitmask m are masked bits.

2 . The method of claim 1 , further comprising:

the printing device requesting a response from the replaceable toner cartridge;

the replaceable toner cartridge responding by returning at least part of the current value of the integer n to the printing device;

the printing device comparing the at least part of the integer n received from the replaceable toner cartridge with the corresponding part of random integer j.

3 . The method of claim 2 , wherein upon a determination that the at least part of the integer n received from the replaceable toner cartridge is the same as the corresponding part of random integer j, the replaceable toner cartridge is identified as an authentic component, and wherein upon a determination that the at least part of the integer n received from the replaceable toner cartridge is different from the corresponding part of random integer j, the replaceable toner cartridge is identified as a non-authentic component.

4 . A method of determining the authenticity of a supply item in a printing device using an elliptic curve E defined over a finite field F q , where q is an integer, the method comprising:

the printing device generating a random integer j, where the random integer j is in the interval of one to the integer q;

the printing device calculating a point T=j·S, where point S is a point on elliptic curve E(F q );

the printing device calculating a binary value k which is equal to the binary random integer j with a bitmask m applied thereto;

the printing device sending point T and binary value k to the supply item; and

the supply item iteratively calculating point U=n·S for different values of integer n, where for each iterative calculation integer n takes different values, wherein for each iteration:

the bits of binary integer n corresponding to the unmasked bits of bitmask m are the same as the corresponding bits of binary random integer j; and

the bits of binary integer n corresponding to the masked bits of bitmask m are varied in each iteration.

5 . The method of claim 4 , further comprising:

the printing device requesting a response from the supply item;

the supply item responding by returning at least part of the current value of the integer n to the printing device;

the printing device comparing the at least part of the integer n received from the supply item with the corresponding part of random integer j.

6 . The method of claim 5 , wherein upon a determination that the at least part of the integer n received from the supply item is the same as the corresponding part of random integer j, the supply item is identified as an authentic component, and wherein upon a determination that the at least part of the integer n received from the supply item is different from the corresponding part of random integer j, the supply item is identified as a non-authentic component.

7 . The method of claim 5 , wherein the printing device requests the response from the supply item after a predetermined time has elapsed.

8 . The method of claim 4 , wherein the iterative calculation by the supply item stops when U=T.

9 . The method of claim 4 , wherein the bits of binary value k corresponding to the unmasked bits of bitmask m are the same as the corresponding bits of binary random integer j, and wherein the bits of binary value k corresponding to the masked bits of bitmask m are masked bits.

10 . The method of claim 4 , wherein in the step of calculating the binary value k the bitmask m masks one or more of the least significant bits of the binary random integer j to give binary value k.

11 . The method of claim 10 , wherein in the step of calculating the binary value k the bitmask m masks sixteen of the least significant bits of the binary random integer j to give binary value k.

12 . The method of claim 10 , wherein for iteratively calculating point U comprises adding point S to the point U of the previous iteration.

13 . The method of claim 4 , wherein bits in the bitmask m with a value of zero are masked bits of bitmask m and bits in the bitmask m with a value of one are unmasked bits of bitmask m, and wherein binary value k=binary random integer j AND bitmask m.

14 . The method of claim 13 , wherein for each iterative calculation performed by the supply item the binary integer n=binary value k OR binary value o, where binary value o AND bitmask m=0.

15 . The method of claim 4 , wherein bits in the bitmask m with a value of one are masked bits of bitmask m and bits in the bitmask m with a value of zero are unmasked bits of bitmask m, and wherein binary value k=binary random integer j OR bitmask m.

16 . The method of claim 15 , wherein for each iterative calculation performed by the supply item the binary integer n=binary value k AND binary value o, where binary value o OR bitmask m=binary 1111 . . . 1.

17 . The method of claim 4 , comprising the printing device saving at least part of random integer j to memory of the printing device.

18 . A printing system comprising:

a printing device; and

a supply item communicatively connectable to the printing device,

wherein the printing device is configured to determine the authenticity of the supply item using an elliptic curve E defined over a finite field F q , where q is an integer, by:

generating a random integer j, where the random integer j is in the interval of one to the integer q;

calculating a point T=j·S, where point S is a point on elliptic curve E(F q );

calculating a binary value k which is equal to the binary random integer j with a bitmask m applied thereto; and

sending point T and binary value k to the supply item,

and wherein the supply item is configured to:

iteratively calculate point U=n·S for different values of integer n, where for each iterative calculation integer n takes different values, wherein for each iteration:

the bits of binary integer n corresponding to the unmasked bits of bitmask m are the same as the corresponding bits of binary random integer j; and

the bits of binary integer n corresponding to the masked bits of bitmask m are varied in each iteration.

19 . The printing system of claim 18 , wherein the printing device is configured to request a response from the supply item, wherein the supply item is configured to respond by returning at least part of the current value of the integer n to the printing device, and wherein the printing device is configured to compare the at least part of the integer n received from the supply item with the corresponding part of random integer j.

20 . The printing system of claim 19 , wherein upon a determination that the at least part of the integer n received from the supply item is the same as the corresponding part of random integer j, the supply item is identified as an authentic component, and wherein upon a determination that the at least part of the integer n received from the supply item is different from the corresponding part of random integer j, the supply item is identified as a non-authentic component.