Efficient fault countermeasure through polynomial evaluation

A method of detecting faults in a polynomial operation, comprising:

• selecting a plurality of evaluation points;
• evaluating a first polynomial at the plurality of evaluation points to produce first results;
• applying a first function to the first polynomial to produce a second polynomial;
• evaluating the second polynomial at the plurality of evaluation points to produce second results;
• evaluating a second scalar function on the first results to produce third results;
• comparing the second results to the third results;
• and
• performing a polynomial operation using the second polynomial when the second results match the third results.

A data processing system comprising instructions embodied in a non-transitory computer readable medium, the instructions for a fault detection in polynomial operations in a processor, the instructions, comprising:

• selecting a plurality of evaluation points;
• evaluating a first polynomial at the plurality of evaluation points to produce first results;
• decomposing the first polynomial into a second polynomial and a third polynomial wherein the first polynomial equals the second polynomial plus alpha times the third polynomial wherein alpha is an integer;
• evaluating the second polynomial at the plurality of evaluation points to produce second results;
• evaluating the third polynomial at the plurality of evaluation points to produce third results;
• calculating fourth results by adding the second results to alpha times the third results;
• comparing the first results to the fourth results;
• and
• performing a polynomial operation using the second polynomial and third polynomial when the first results match the fourth results.