Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An O(n)-depth polynomial-size combinational circuit algorithm is proposed for n-bit modular exponentiation, i.e., for the computation of x/sup v/ mod m for arbitrary integers x, y, and m represented as n-bit binary integers, within bounds 2/sup n-1//spl les/m<2/sup n/ and 0/spl les/Ix, y<m. The algorithm is a generalization of the square-and-multiply method. The terms (x(2/sup l/)mod m)s for all is /spl epsiv/{0, n-1} are computed in ~n-1/~/spl alpha/logn\\ parallel rounds, each of which computes ~/spl alpha/logn\ consecutive terms, where /spl alpha//spl ges/1/logn. The circuit implementing a round has depth O((1+/spl alpha/)logn) and size O(n/sup 2(1+/spl alpha/)/) yielding a circuit for modular exponentiation of depth O(1+/spl alpha///spl alpha/n) and size O(n/sup 3+2/spl alpha////spl alpha/logn).
['Takafumi Hamano', 'Naofumi Takagi', 'Shuzo Yajima', 'Franco P. Preparata']
I am writing a research paper on a idea O(n)-depth modular exponentiation circuit algorithm
[{"from": "human", "value": "I am writing a research paper on a idea O(n)-depth modular exponentiation circuit algorithm"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An O(n)-depth polynomial-size combinational circuit algorithm is proposed for n-bit modular exponentiation, i.e., for the computation of x/sup v/ mod m for arbitrary integers x, y, and m represented as n-bit binary integers, within bounds 2/sup n-1//spl les/m<2/sup n/ and 0/spl les/Ix, y<m. The algorithm is a generalization of the square-and-multiply method. The terms (x(2/sup l/)mod m)s for all is /spl epsiv/{0, n-1} are computed in ~n-1/~/spl alpha/logn\\\\ parallel rounds, each of which computes ~/spl alpha/logn\\ consecutive terms, where /spl alpha//spl ges/1/logn. The circuit implementing a round has depth O((1+/spl alpha/)logn) and size O(n/sup 2(1+/spl alpha/)/) yielding a circuit for modular exponentiation of depth O(1+/spl alpha///spl alpha/n) and size O(n/sup 3+2/spl alpha////spl alpha/logn)."}]