Decimal sequences for cryptography
From HandWiki
Decimal sequences for cryptography. A recurring decimal such as 1/7=.142857142857... can be considered a periodic series with the digits 142857 in the base 10. In general, such sequences may be written to any base. The maximum period of such a d-sequence (when the base is not necessarily 10) written for 1/q, q prime, is q-1.
A binary d-sequence may be written as:
- ai = 2i mod q mod 2
As example, the d-sequence for 1/19 is 000011010111100101.
S. Kak has proposed their use for error correction coding, cryptography and as random sequences. These sequences have fairly good autocorrelation properties.
References
- S. Kak, Encryption and error-correction coding using D sequences. IEEE Transactions on Computers, C-34: 803-809, 1985.
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