Some remarks on FCSRs and implications for stream ciphers. (English) Zbl 1234.94022
Summary: Feedback with carry shift registers (FCSRs) are extensively discussed in the context of pseudorandom number generation and as building blocks for stream ciphers. Similarly to linear feedback shift registers, FCSRs may be represented in Galois and in Fibonacci architecture. We describe the first formal characterization of periodic Galois states and show an efficient mapping between periodic Galois states and periodic Fibonacci states. Additionally we provide a method for explicitly computing the autocorrelation of maximum-period FCSR sequences and discuss the impact of our findings on the design of FCSR-based stream ciphers.
MSC:
| 94A55 | Shift register sequences and sequences over finite alphabets in information and communication theory |
| 11B37 | Recurrences |
| 11T71 | Algebraic coding theory; cryptography (number-theoretic aspects) |
Keywords:
Feedback with carry shift registers; periodic Galois states; periodic Fibonacci states; stream cipher designReferences:
| [1] | DOI: 10.1109/TC.2005.181 · doi:10.1109/TC.2005.181 |
| [2] | DOI: 10.1137/0215025 · Zbl 0602.65002 · doi:10.1137/0215025 |
| [3] | DOI: 10.1006/jsco.1996.0125 · Zbl 0898.68039 · doi:10.1006/jsco.1996.0125 |
| [4] | DOI: 10.2307/2153540 · Zbl 0803.65005 · doi:10.2307/2153540 |
| [5] | DOI: 10.1109/18.605605 · Zbl 0878.94047 · doi:10.1109/18.605605 |
| [6] | DOI: 10.1109/TIT.2002.804048 · Zbl 1062.94028 · doi:10.1109/TIT.2002.804048 |
| [7] | Distribution Periodicity, LNCS 4086 pp 334– (2006) |
| [8] | Klapper A., LNCS 3486 pp 56– (2004) |
| [9] | DOI: 10.1007/s001459900024 · Zbl 0874.94029 · doi:10.1007/s001459900024 |
| [10] | DOI: 10.1214/aoap/1177005878 · Zbl 0733.65005 · doi:10.1214/aoap/1177005878 |
| [11] | DOI: 10.1109/TIT.2002.808130 · Zbl 1063.94068 · doi:10.1109/TIT.2002.808130 |
| [12] | DOI: 10.1109/18.825844 · Zbl 0996.94031 · doi:10.1109/18.825844 |
| [13] | DOI: 10.1137/050633974 · Zbl 1128.94006 · doi:10.1137/050633974 |
| [14] | DOI: 10.1007/s12095-008-0008-5 · Zbl 1172.94602 · doi:10.1007/s12095-008-0008-5 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
