SPA resistant RSA trace I am trying to perform simple power analysis on RSA. In particular focusing the 
modular exponentiation module and for this I have implemented left-to-right variant of binary exponentiation.

pseudo code of the implemented algorithm is as follows:

Result = a^b mod N
k = length(b);

Result = 1;
for i = k-1 to 0 do
  Result = (Result X Result) mod N;   // SQUARING

  if b[i] == 1
    Result = (Result X a) mod N;     // MULTIPLICATION
  end if

end for


From the acquired power trace, I cannot differentiate between square and multiplication samples just by looking at the trace.

I also tried by performing a correlation test between the first operation(i.e. square) and all the other operations but i get the same level of correlation peaks for all the operations.

So from these observations can I conclude that my implementation is SPA resistant at least with respect to the regularity between the patterns of both operations.

My second question is, if it is SPA resistant then why in some of the cases which I read on internet have different pattern for both operations. Even though in practice they also use same multiplication algorithm for both squaring and multiplication as I did.
Clearly, your code is not SPA safe. 
The if condition over a sensitive bit will certainly leak in timing. The time taken by a square is slower that a multiplication due to this if condition.
Exemple: bit 000 will induce a Square Square Square in term of cpu instruction will have less than a bit 100 where you will perform Square Multiply Square ... 
Try to compare couple of operations instead of individual.

Regarding, the difference between a square and a multiply it depends on the chip you are working on, does modular operation are provided by a crypto processor? In this case, some countermeasures might have been implemented to avoid differences between a multiplication and a square.

You can share your traces if you like.

edit

Here is two SPA safe algorithm

Atomic The most elegant SPA safe algorithm, imo http://bcm.crypto.free.fr/pdf/CCJ04.pdf Fig2

The Montgomery Powering Ladder  Less efficient as it is a square and multiply always (trash multiply for square) https://www.iacr.org/workshops/ches/ches2002/presentations/Joye.pdf