To compute a19 mod N, the modular exponential algorithms that we studied would do 8 modular multiplications (5 squarings and 3 multiplications by a). What is the minimum number of modular multiplications needed to compute a19 mod N if you are free to use any sequence of modular multiplications.)

Answer for the question:

To compute a19 mod N, the modular exponential algorithms that we studied would do 8 modular multiplications (5 squarings and 3 multiplications by a). What is the minimum number of modular multiplications needed to compute a19 mod N if you are free to use any sequence of modular multiplications.)

is given in the attachment.

Step-by-step explanation:

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2