Comparison of Four Methods of Checking the Integrity of Transmitted Message Blocks

Abstract—

We consider the quantity $\alpha$, which is the error probability in each of four data block integrity checking methods: electronic signature, cyclic redundancy code, checksums in a vector space over a field of two elements, and checksums in a ring of integers modulo 2^k, where k is the length of the check code. Asymptotic representations for α are compared for a small value of p-distortion of a transmitted binary symbol and a large volume n of a transmitted data block. For the above integrity checking methods, the values of the main terms of the asymptotic expansion of α under the condition “np tends to zero for n tending to infinity” are obtained and calculated as an example for the parameters of TCP protocol segments.