Create my own check sum algorithm

Question

I know it is always better to use check sum algorithms that people already invented. I want to be able to compare if two files are the same by performing the check-sum. The files are in two different computers over a network and because they are across a network it is faster to perform a check sum rather than copying the entire file when dealing with large files like in my case. (I will perform other test first such as making sure the files are the same length etc..)

so I have created this simple algorithm:

private static double GetChecksum2(string file)
    {
        double checkSum = 0;

        var stream = File.OpenRead(file);

        // the bigger the chunck size the faster but the more memory usage by cpu
        // also when sending file over network it should not be that much more efficient

        int chunckSize = (int) Math.Pow(2,20); // 10 => kilobite   20 => megabite  30 => gigabite etc..
        byte[] buffer = new byte[chunckSize];

        int bytesRead = 0;

        while ( // while bytesRead > 0
            (bytesRead =
                (stream.Read(buffer, 0, buffer.Length)) // returns the number of bytes read or 0 if no bytes read
            ) > 0)
        {
            //buffer is now an array of size bytesRead

            // write those bytes to a file, perform checksum of file
            // etc...


            // temp check sum use a better algorithm I dont know if other computers will round 
            // doubles diferently

            for (int i = 0; i < bytesRead; i++)
            {
                checkSum = (((buffer[i] + i)/2 + checkSum))*.45;
            }


            //SHA256Managed sha = new SHA256Managed();
            //byte[] checksum = sha.ComputeHash(buffer);

        }

        return checkSum;
    }

I don't know what are the odds that the checksum of two different files comes true using this algorithm.

when performing the checksum of a file of 1.06 GB it takes: 5.2 seconds to complete and the checksum comes out to be 321840.207306214

when I use the SHA256Managed() algorithm instead it takes 35.8 seconds.

7 times longer

I know that the odds of two files having the same checksum with this algorithm them being different is much lower than with my algorithm. But using my algorithm is much more faster and I think that the odds should be also pretty low...

Or perhaps I should use a even faster algorithm that I don't know and it already exists...

edit

My question is:

will it be safe to implement this algorithm. I require to do a lot of file transfer over my network and it will be nice if I can use a checksum algorithm to compare files. Maybe I could split each file in chuncks and just replace the chuncks where the checksum does not match!

Answer 1

Floating point math is non deterministic. You might get slightly different results on different computers or versions of .net. In your algorithm that can be avoided with an epsilon comparison, but in many algorithms it can't be avoided at all.

Another issue with your algorithm is that the contribution of early bytes becomes exponentially small. i.e. only the last part of the file influences the hash. A quick estimate is that only the last few kB are taken into account. This means your hash it not fit for its purpose.

If we neglect rounding errors we can simplify your formula:

(((buffer[i] + i)/2 + checkSum))*.45

buffer[i]*0.45/2 + i*0.45/2 + checkSum*0.45

Solving the recursion gives us:

Sum(buffer[i]/2*(0.45^(length-1)) + i*(0.45^(length-1)))

The second term does only depend on the length, so when comparing files with equal length you're left with:

Sum(buffer[i]/2*(0.45^(length-1)))