# Decimal sequences for cryptography

**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:

- a
_{i}= 2^{i}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[edit]

- S. Kak, Encryption and error-correction coding using D sequences. IEEE Transactions on Computers, C-34: 803-809, 1985.

## External links[edit]

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