On the Low Weight Polynomial Multiple Problem
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914971529510912 |
|---|---|
| author | Ţiplea, Ferucio Laurenţiu Lăzărescu, Simona-Maria |
| author_facet | Ţiplea, Ferucio Laurenţiu Lăzărescu, Simona-Maria |
| contents | Finding a low-weight multiple (LWPM) of a given polynomial is very useful in the cryptanalysis of stream ciphers and arithmetic in finite fields. There is no known deterministic polynomial time complexity algorithm for solving this problem, and the most efficient algorithms are based on a time/memory trade-off. The widespread perception is that this problem is difficult. In this paper, we establish a relationship between the LWPM problem and the MAX-SAT problem of determining an assignment that maximizes the number of valid clauses of a system of affine Boolean clauses. This relationship shows that any algorithm that can compute the optimum of a MAX-SAT instance can also compute the optimum of an equivalent LWPM instance. It also confirms the perception that the LWPM problem is difficult. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10224 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Low Weight Polynomial Multiple Problem Ţiplea, Ferucio Laurenţiu Lăzărescu, Simona-Maria Computational Complexity 68Q15, 68Q25, 14G50, 94A60 Finding a low-weight multiple (LWPM) of a given polynomial is very useful in the cryptanalysis of stream ciphers and arithmetic in finite fields. There is no known deterministic polynomial time complexity algorithm for solving this problem, and the most efficient algorithms are based on a time/memory trade-off. The widespread perception is that this problem is difficult. In this paper, we establish a relationship between the LWPM problem and the MAX-SAT problem of determining an assignment that maximizes the number of valid clauses of a system of affine Boolean clauses. This relationship shows that any algorithm that can compute the optimum of a MAX-SAT instance can also compute the optimum of an equivalent LWPM instance. It also confirms the perception that the LWPM problem is difficult. |
| title | On the Low Weight Polynomial Multiple Problem |
| topic | Computational Complexity 68Q15, 68Q25, 14G50, 94A60 |
| url | https://arxiv.org/abs/2410.10224 |