What is the idea behind binary exponent evaluation? Write pseudocode to compute an using right to left and left to right binary exponentiation algorithm and perform its complexity analysis. Apply the algorithm to compute a55 and calculate the total number of multiplication operations in this case. How many multiplication operations are required if brute force multiplication method is used in this example? Show all the intermediate steps.

Binary exponentiation is an efficient algorithm for calculating exponentials by breaking down the exponent into its binary representation. The idea is to leverage the binary representation of the exponent to reduce the number of multiplications needed. The pseudocode for both right-to-left and left-to-right binary exponentiation algorithms is as follows:

Right-to-Left Binary Exponentiation:
```
function binaryExponentiation(base, exponent):
    result = 1
    while exponent > 0:
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