Substantial Number of Cryptographic Keys and Its Application to Encryption Designs

  • Eiji Okamoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 330)


A new concept of the substantial number of cryptographic keys (SNK) in key spaces is proposed and is applied to encryption designs. SNK is defined as the number of keys which is far from each other. It must be greater than 256, for instance, to have essentially the same number of keys in DES. This SNK condition restricts design parameters of encryption systems. In this paper, SNK is strictly defined in key spaces, followed by illustrations of SNK’s in fundamental encryption algorithms and product ciphers. Then SNK is applied to the design of encryption systems to decide the design parameters. It is useful for designing product cipher in particular. SNK should be considered as one of the criteria of encipherment strength.


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    K. Nakamura, “On Self-synchronization Encryption Systems,” 24th Allerton Conf., pp.1057–1063, 1986, (also in Proc. of SITA, pp.371–377, in Japanese).Google Scholar
  2. [2]
    E. Okamoto and K. Nakamura, “Permutation Ciphers Based on Reed-Solomon Codes,” 1983 IECE Conf., pp.1.463–1.464 (in Japanese).Google Scholar
  3. [3]
    E. Okamoto and K. Nakamura,“Relation between Error Propagation and Non-linearity in Cryptosystems,” 1985 IECE Conf., p.6.27 (in Japanese).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Eiji Okamoto
    • 1
  1. 1.C&C Information Research LaboratoriesNEC corporationKawasakiJapan

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