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 = 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.

External links

• Watermarking using decimal sequences
• Decimal sequence based random number generator