Encryption function and authentication of a replaceable printer component

1. A method, comprising:

protecting, using four words, each word representing codes in base 7, an electronic circuit during execution of a cryptographic operation by the electronic circuit, wherein the cryptographic operation comprises authentication of a replaceable printer component by a printer, the protecting including:

multiplying, code by code, a third word of the four words by a fourth word of the four words;

adding, code by code, a result of the multiplying to a first word of the four words;

adding, code by code, the result of the multiplying to a second word of the four words;

subtracting, code by code, a result of the addition to the second word from a result of the addition to the first word;

adding, code by code, a result of the subtraction to the third word;

adding the result of the subtraction to the fourth word;

combining, code by code, with a round constant, a result of the adding the third word to the result of the subtraction;

multiplying by two, code by code, a result of said combination;

circularly shifting codes of a result of the adding the fourth word to the result of the subtraction;

circularly shifting codes of the result of adding the second word to the result of the multiplication; and

circularly shifting codes of the result of adding the first word to the result of the multiplication, wherein the protecting is performed by one of the replaceable printer component or the printer.

2. The method of claim 1 wherein each word comprises thirty-two codes.

3. The method of claim 1 wherein the circular shifts are respectively by one, five, and fourteen positions.

4. The method of claim 1 wherein each code in base 7 is represented as a triplet of binary states.

5. The method of claim 1 wherein the protecting is an iterative process, a last state of an iteration forming an initial state of a next iteration.

6. The method of claim 1 wherein the cryptographic operation comprises a hashing function.

7. The method of claim 6 , comprising converting a message to base 7.

8. The method of claim 6 wherein the protecting is an iterative process applied a plurality of times.

9. The method of claim 1 wherein the protecting comprises protecting information manipulated by the electronic circuit.

10. The method of claim 4 wherein an occurrence of a determined triplet identifies an error.

11. The method of claim 1 wherein the electronic circuit is included in the printer.

12. The method of claim 1 wherein the electronic circuit is included in the replaceable printer component.

13. The method of claim 12 wherein the replaceable printer component performs the protecting.

14. A device, comprising:

one or more memories; and

digital signal processing circuitry coupled to the one or more memories, which, in operation, protects, using four words, each word representing codes in base 7, a cryptographic operation to authenticate a replaceable printer component by a printer, the protecting including:

multiplying, code by code, a third word of the four words by a fourth word of the four words;

adding, code by code, a result of the multiplying to a first word of the four words;

adding, code by code, the result of the multiplying to a second word of the four words;

subtracting, code by code, a result of the addition to the second word from a result of the addition to the first word;

adding, code by code, a result of the subtraction to the third word;

adding the result of the subtraction to the fourth word;

combining, code by code, with a round constant, a result of the adding the third word to the result of the subtraction;

multiplying by two, code by code, a result of said combination;

circularly shifting codes of a result of the adding the fourth word to the result of the subtraction;

circularly shifting codes of the result of adding the second word to the result of the multiplication; and

circularly shifting codes of the result of adding the first word to the result of the multiplication, wherein the protecting is performed by one of the replaceable printer component or the printer.

15. The device of claim 14 wherein each word comprises thirty-two codes.

16. The device of claim 14 wherein the circular shifts are respectively by one, five, and fourteen positions.

17. The device of claim 14 wherein each code in base 7 is represented as a triplet of binary states.

18. The device of claim 14 wherein the protecting is an iterative process, a last state of an iteration forming an initial state of a next iteration.

19. The device of claim 14 wherein the cryptographic operation comprises a hashing function.

20. The device of claim 14 wherein the protecting comprises generating the four words.

21. The device of claim 14 wherein the protecting comprises protecting information manipulated by the cryptographic operation.

22. The device of claim 14 wherein an occurrence of a determined triplet identifies an error in the cryptographic operation.

23. The device of claim 14 wherein the device is a included in the printer.

24. The device of claim 14 wherein the device is a included in the replaceable printer component.

25. The device of claim 24 wherein the replaceable printer component performs the protecting.

26. A system, comprising:

one or more functional circuits; and

digital signal processing circuitry coupled to the one or more functional circuits, which, in operation, protects, using four words, each word representing codes in base 7, execution of a cryptographic operation to authenticate a replaceable printer component by a printer, the protecting including:

multiplying, code by code, a third word of the four words by a fourth word of the four words;

adding, code by code, a result of the multiplying to a first word of the four words;

adding, code by code, the result of the multiplying to a second word of the four words;

subtracting, code by code, a result of the addition to the second word from a result of the addition to the first word;

adding, code by code, a result of the subtraction to the third word;

adding the result of the subtraction to the fourth word;

combining, code by code, with a round constant, a result of the adding the third word to the result of the subtraction;

multiplying by two, code by code, a result of said combination;

circularly shifting codes of a result of the adding the fourth word to the result of the subtraction;

circularly shifting codes of the result of adding the second word to the result of the multiplication; and

circularly shifting codes of the result of adding the first word to the result of the multiplication, wherein the protecting is performed by one of the replaceable printer component or the printer.

27. The system of claim 26 wherein a result of the cryptographic operation is related to a function of the functional circuitry.

28. The system of claim 26 wherein each code in base 7 is represented as a triplet of binary states.

29. The system of claim 26 wherein the protecting includes detecting an error during execution of the cryptographic operation.

30. The system of claim 29 wherein the error is a fault injection error.

31. A non-transitory computer-readable medium having contents which configure digital signal processing circuitry to perform a method, the method comprising:

protecting, using four words, each word representing codes in base 7, a cryptographic operation executed by the digital signal processing circuitry, wherein the cryptographic operation comprises authentication of a replaceable printer component by a printer, the protecting including:

multiplying, code by code, a third word of the four words by a fourth word of the four words;

adding, code by code, a result of the multiplying to a first word of the four words;

adding, code by code, the result of the multiplying to a second word of the four words;

subtracting, code by code, a result of the addition to the second word from a result of the addition to the first word;

adding, code by code, a result of the subtraction to the third word;

adding the result of the subtraction to the fourth word;

combining, code by code, with a round constant, a result of the adding the third word to the result of the subtraction;

multiplying by two, code by code, a result of said combination;

circularly shifting codes of a result of the adding the fourth word to the result of the subtraction;

circularly shifting codes of the result of adding the second word to the result of the multiplication; and

circularly shifting codes of the result of adding the first word to the result of the multiplication, wherein the protecting is performed by one of the replaceable printer component or the printer.

32. The computer-readable medium of claim 31 wherein each word comprises thirty-two codes.

33. The computer-readable medium of claim 31 wherein the contents comprise instructions executed by the digital signal processing circuitry.

34. The computer-readable medium of claim 31 wherein the contents comprise a set of results representative of the application of the method to a set of numbers.

35. The computer-readable medium of claim 31 wherein the digital signal processing circuitry comprises circuitry of the replaceable printer component.

36. A non-transitory computer-readable medium having contents which configure digital signal processing circuitry to perform a method, the method comprising:

receiving a number;

generating an output based on the number; and

protecting a cryptographic operation using the output, wherein the cryptographic operation comprises authentication of a replaceable printer component by a printer and the protecting is performed by one of the replaceable printer component or the printer, wherein the output corresponds to:

representing the number as four words, each word representing codes in base 7;

multiplying, code by code, a third word of the four words by a fourth word of the four words;

adding, code by code, a result of the multiplying to a first word of the four words;

adding, code by code, the result of the multiplying to a second word of the four words;

subtracting, code by code, a result of the addition to the second word from a result of the addition to the first word;

adding, code by code, a result of the subtraction to the third word;

adding the result of the subtraction to the fourth word;

combining, code by code, with a round constant, a result of the adding the third word to the result of the subtraction;

multiplying by two, code by code, a result of said combination;

circularly shifting codes of a result of the adding the fourth word to the result of the subtraction;

circularly shifting codes of the result of adding the second word to the result of the multiplication; and

circularly shifting codes of the result of adding the first word to the result of the multiplication.

37. The computer-readable medium of claim 36 wherein the contents comprise a look-up table to convert numbers to corresponding outputs.

38. The computer-readable medium of claim 36 wherein the digital signal processing circuitry comprises processing circuitry of the replaceable printer component.

39. A method, comprising:

receiving a number;

generating an output based on the number; and

protecting a cryptographic operation using the output, wherein the cryptographic operation comprises authentication of a replaceable printer component by a printer and the protecting is performed by one of the replaceable printer component or the printer, wherein the output corresponds to:

representing the number as four words, each word representing codes in base 7;

multiplying, code by code, a third word of the four words by a fourth word of the four words;

adding, code by code, a result of the multiplying to a first word of the four words;

adding, code by code, the result of the multiplying to a second word of the four words;

subtracting, code by code, a result of the addition to the second word from a result of the addition to the first word;

adding, code by code, a result of the subtraction to the third word;

adding the result of the subtraction to the fourth word;

combining, code by code, with a round constant, a result of the adding the third word to the result of the subtraction;

multiplying by two, code by code, a result of said combination;

circularly shifting codes of a result of the adding the fourth word to the result of the subtraction;

circularly shifting codes of the result of adding the second word to the result of the multiplication; and

circularly shifting codes of the result of adding the first word to the result of the multiplication.

40. The method of claim 39 wherein the generating the output comprises retrieving the output from a look-up table.

41. The method of claim 39 wherein the cryptographic operation is performed by processing circuitry of a the replaceable printer component.

42. A device, comprising:

one or more memories; and

processing circuitry coupled to the one or more memories, wherein the processing circuitry, in operation:

generates an output based on a number; and

protecting protects a cryptographic operation using the output, wherein the cryptographic operation comprises authentication of a replaceable printer component by a printer and the protecting is performed by one of the replaceable printer component or the printer, wherein the output corresponds to:

representing the number as four words, each word representing codes in base 7;

multiplying, code by code, a third word of the four words by a fourth word of the four words;

adding, code by code, a result of the multiplying to a first word of the four words;

adding, code by code, the result of the multiplying to a second word of the four words;

subtracting, code by code, a result of the addition to the second word from a result of the addition to the first word;

adding, code by code, a result of the subtraction to the third word;

adding the result of the subtraction to the fourth word;

combining, code by code, with a round constant, a result of the adding the third word to the result of the subtraction;

multiplying by two, code by code, a result of said combination;

circularly shifting codes of a result of the adding the fourth word to the result of the subtraction;

circularly shifting codes of the result of adding the second word to the result of the multiplication; and

circularly shifting codes of the result of adding the first word to the result of the multiplication.

43. The device of claim 42 wherein the generating the output comprises retrieving the output from a look-up table.

44. The device of claim 42 wherein the device comprises a is included in the replaceable printer component.