I want to calculate the time complexity of two encryption and decryption algorithms.

The first one (RSA-like) has the encryption $$ C := M^e \bmod N $$ and decryption $$ M_P := C^d \bmod N. $$

Assuming $n = \log N$, $m = \log e$ and $k = \log d$, I think they have time complexities $O(n^2 · m)$ and $O(n^2 · k)$, respectively.

Are these two complexities same?

I also have another pair of algorithms, with $$ C := M · k \bmod N $$ and $$ M_P := C · k^{-1} \bmod N.$$

How does the calculation of the modular inverse $k^{-1}$ contribute to the complexity calculation?

I want to calculate the time complexity of two encryption and decryption algorithms.

The first one (RSA-like) has the encryption $$ C := M^e \bmod N $$ and decryption $$ M_P := C^d \bmod N. $$

Assuming $n = \log N$, $m = \log e$ and $k = \log d$, I think they have time complexities $O(n^2 · m)$ and $O(n^2 · k)$, respectively.

Are these two complexities same?

I also have another pair of algorithms, with $$ C := M · k \bmod N $$ and $$ M_P := C · k^{-1} \bmod N.$$

How does the calculation of the modular inverse $k^{-1} \bmod N$ contribute to the time complexity?

I try calculate time complexity for this algorithm.because I able to compare between them

 private void encrypt()
    {
        M = new BigInteger(64,random);
        C = M.modPow(e,N);//O(n^2 * log e) Rather  O(n^2 * m) where m = log e

    }
    
    private void decrypt()
    {
        Mp = C.modPow(d, N); //O(n^2 * log d) Rather  O(n^2 * k) where k = log d
      
    }

Is two algorithms same time complexity or No.

also I want ask about mod inverse like the following

private void encrypt()
    {
        M = new BigInteger(64,random);
        C = M.multiply(k).mod(N);

    }
    
    private void decrypt()
    {
kk= k.modinverse(N);
 Mp = kk.multiply(c).mod(N); 
      
    }

I want to calculate the time complexity of two encryption and decryption algorithms.

The first one (RSA-like) has the encryption $$ C := M^e \bmod N $$ and decryption $$ M_P := C^d \bmod N. $$

Assuming $n = \log N$, $m = \log e$ and $k = \log d$, I think they have time complexities $O(n^2 · m)$ and $O(n^2 · k)$, respectively.

Are these two complexities same?

I also have another pair of algorithms, with $$ C := M · k \bmod N $$ and $$ M_P := C · k^{-1} \bmod N.$$

How does the calculation of the modular inverse $k^{-1}$ contribute to the complexity calculation?