Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  describe a new technique for evaluating polynomials over binary finite fields. This is useful in the context of anti-DPA countermeasures when an S-box is expressed as a polynomial over a binary finite field. For n-bit S-boxes our new technique has heuristic complexity    ${\cal O}2^{n/2}/\sqrt{n}$    instead of    ${\cal O}2^{n/2}$    proven complexity for the Parity-Split method.  also prove a lor bound of    ${\Omega}2^{n/2}/\sqrt{n}$    on the complexity of any method to evaluate n-bit S-boxes; this shows that our method is asymptotically optimal. Here, complexity refers to the number of non-linear multiplications required to evaluate the polynomial corresponding to an S-box.#R##N##R##N#In practice  can evaluate any 8-bit S-box in 10 non-linear multiplications instead of 16 in the Roy-Vivek paper from CHES 2013, and the DES S-boxes in 4 non-linear multiplications instead of 7.  also evaluate any 4-bit S-box in 2 non-linear multiplications instead of 3. Hence our method achieves optimal complexity for the PRESENT S-box.
['Jean-Sébastien Coron', 'Arnab Roy', 'Srinivas Vivek']
I am writing a research paper on a idea Fast Evaluation of Polynomials over Binary Finite Fields and Application to Side-Channel Countermeasures
[{"from": "human", "value": "I am writing a research paper on a idea Fast Evaluation of Polynomials over Binary Finite Fields and Application to Side-Channel Countermeasures"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  describe a new technique for evaluating polynomials over binary finite fields. This is useful in the context of anti-DPA countermeasures when an S-box is expressed as a polynomial over a binary finite field. For n-bit S-boxes our new technique has heuristic complexity    ${\\cal O}2^{n/2}/\\sqrt{n}$    instead of    ${\\cal O}2^{n/2}$    proven complexity for the Parity-Split method.  also prove a lor bound of    ${\\Omega}2^{n/2}/\\sqrt{n}$    on the complexity of any method to evaluate n-bit S-boxes; this shows that our method is asymptotically optimal. Here, complexity refers to the number of non-linear multiplications required to evaluate the polynomial corresponding to an S-box.#R##N##R##N#In practice  can evaluate any 8-bit S-box in 10 non-linear multiplications instead of 16 in the Roy-Vivek paper from CHES 2013, and the DES S-boxes in 4 non-linear multiplications instead of 7.  also evaluate any 4-bit S-box in 2 non-linear multiplications instead of 3. Hence our method achieves optimal complexity for the PRESENT S-box."}]