Fletcher's checksum

Fletcher's checksum(introduction)

• The Fletcher checksum was devised to weight each data item according to its position
• Fletcher has many algorithms: 8-bit, 16-bit, 32-bit and 64-bit
• 8-bit Fletcher will creates a 16-bit checksum 
   

Fletcher's checksum( 16 bit checksum )

A = ['1','2']
L = 0
R = 0


def Fletcher(A,n):
       global L,R

       for i in range(n):
              R = (R+int(A[i])) % 255
              L = (L+R) % 255
       print hex((L << 8) | R) #'<<' mean binary left shift and '|' mean binary OR

def CheckBytes(L,R):
       tempR = 255 - ((R+L) % 255)
       tempL = 255 - ((R+tempR) % 255)
       print hex(tempR),hex(tempL)

#Checksum
Fletcher(A,len(A))
#Checkbytes
CheckBytes(L,R)
#check sum
print (L*65536)+R

Implement in python

Example calculation of the Fletcher-16 checksum :

Weaknesses

The Fletcher checksum cannot distinguish between blocks of all 0 bits and blocks of all 1 bits

For example:

         0x0000 (0) have checksum as 0xff (255)

          0xFFFF (65535) also have checksum as 0xff (255)

Adler's checksum

Adler's checksum(introduction)

• The Adler checksum is a 32-bit checksum
• ​ It is similar to the 16-bit Fletcher 

Adler's checksum( 32 bit checksum )

A = 'abcd123456' #data

L = 0
R = 1 #

def Adler(A,n):
       global L,R

       for i in range(n):
              R = (R+ord(A[i])) % 65521 #2^16 = 65536 and 65521 is prime number that close to 2^16
              L = (L+R) % 65521
             
Adler(A,len(A))

#check sum
print (L*65536)+R

Implement in python

Example calculation of the Adler-32 checksum :

Weaknesses

• Adler-32 is weak for short messages because the checksums for these messages have a poor coverage of the 32 available bits
• The maximum sum of a 128-byte message is 32640, which is below the value 65521 used by the modulo operation, meaning that roughly half of the output space is unused