Paper 2021/1129

Beauty of Cryptography: the Cryptographic Sequences and the Golden Ratio

Shenghui Su, Jianhua Zheng, and Shuwang Lv


In this paper, the authors construct a new type of cryptographic sequence which is named an extra-super increasing sequence, and give the definitions of the minimal super increasing sequence {a[1], a[2], ..., a[n]} and minimal extra-super increasing sequence {z[1], z[2], ..., z[n]}. Prove that the minimal extra-super increasing sequence is the odd-positioned subsequence of the Fibonacci sequence, namely {z[1], z[2], ..., z[n], ...} = {F[1], F[3], ..., F[2n-1], ...}, which indicates that the approach to the golden ratio phi through the term difference ratio (z[n+1] - z[n]) / z[n] is more smooth and expeditious than through the term ratio (F[n+1] / F[n]). Further prove that the limit of the term ratio difference between the two cryptographic sequences equals the golden ratio conjugate PHI, namely lim (n to infinity) (z[n+1] / z[n] - a[n+1] / a[n]) = PHI, which reveals the beauty of cryptography.

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Preprint. MINOR revision.
Minimal extra-super increasing sequenceFibonacci sequenceGolden ratioGolden ratio conjugateTerm ratio difference
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idology98 @ gmail com
2021-09-07: revised
2021-09-06: received
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      author = {Shenghui Su and Jianhua Zheng and Shuwang Lv},
      title = {Beauty of Cryptography: the Cryptographic Sequences and the Golden Ratio},
      howpublished = {Cryptology ePrint Archive, Paper 2021/1129},
      year = {2021},
      note = {\url{}},
      url = {}
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