An Improved Modular Addition Checksum Algorithm
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913289958588416 |
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| author | Koopman, Philip |
| author_facet | Koopman, Philip |
| contents | This paper introduces a checksum algorithm that provides a new point in the performance/complexity/effectiveness checksum tradeoff space. It has better fault detection properties than single-sum and dual-sum modular addition checksums. It is also simpler to compute efficiently than a cyclic redundancy check (CRC) due to exploiting commonly available hardware and programming language support for unsigned integer division. The key idea is to compute a single running sum, but introduce a left shift by the size (in bits) of the modulus before performing the modular reduction after each addition step. This approach provides a Hamming Distance of 3 for longer data word lengths than dual-sum approaches such as the Fletcher checksum. Moreover, it provides this capability using a single running sum that is only twice the size of the final computed check value, while providing fault detection capabilities even better than large-block variants of dual-sum approaches that require larger division operations. A variant that includes a parity bit achieves Hamming Distance 4 for the same size check value, approximating the fault detection capabilities of a good CRC for about half the data word length attainable by such a CRC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_13496 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Improved Modular Addition Checksum Algorithm Koopman, Philip Data Structures and Algorithms Networking and Internet Architecture This paper introduces a checksum algorithm that provides a new point in the performance/complexity/effectiveness checksum tradeoff space. It has better fault detection properties than single-sum and dual-sum modular addition checksums. It is also simpler to compute efficiently than a cyclic redundancy check (CRC) due to exploiting commonly available hardware and programming language support for unsigned integer division. The key idea is to compute a single running sum, but introduce a left shift by the size (in bits) of the modulus before performing the modular reduction after each addition step. This approach provides a Hamming Distance of 3 for longer data word lengths than dual-sum approaches such as the Fletcher checksum. Moreover, it provides this capability using a single running sum that is only twice the size of the final computed check value, while providing fault detection capabilities even better than large-block variants of dual-sum approaches that require larger division operations. A variant that includes a parity bit achieves Hamming Distance 4 for the same size check value, approximating the fault detection capabilities of a good CRC for about half the data word length attainable by such a CRC. |
| title | An Improved Modular Addition Checksum Algorithm |
| topic | Data Structures and Algorithms Networking and Internet Architecture |
| url | https://arxiv.org/abs/2304.13496 |