Cryptographic mappings with pseudo-inverses, random-number generators and tessellations

Richard Gabriel

Kybernetika (1982)

  • Volume: 18, Issue: 6, page 485-504
  • ISSN: 0023-5954

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Gabriel, Richard. "Verschlüsselungsabbildungen mit Pseudo-Inversen, Zufallsgeneratoren und Täfelungen." Kybernetika 18.6 (1982): 485-504. <http://eudml.org/doc/28012>.

@article{Gabriel1982,
author = {Gabriel, Richard},
journal = {Kybernetika},
keywords = {linear enciphering; linear cryptography; generalized inverse},
language = {ger},
number = {6},
pages = {485-504},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Verschlüsselungsabbildungen mit Pseudo-Inversen, Zufallsgeneratoren und Täfelungen},
url = {http://eudml.org/doc/28012},
volume = {18},
year = {1982},
}

TY - JOUR
AU - Gabriel, Richard
TI - Verschlüsselungsabbildungen mit Pseudo-Inversen, Zufallsgeneratoren und Täfelungen
JO - Kybernetika
PY - 1982
PB - Institute of Information Theory and Automation AS CR
VL - 18
IS - 6
SP - 485
EP - 504
LA - ger
KW - linear enciphering; linear cryptography; generalized inverse
UR - http://eudml.org/doc/28012
ER -

References

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  1. R. E. Cline, An Application of Representations for the Generalized Inverse of a Matrix, MRC Technical Report 592, 1965. (1965) 
  2. R. E. Cline, Note on an extension of the Moore-Penrose inverse, (submitted for publication). Zbl0468.15003
  3. W. Diffie M. E. Hellman, New directions in cryptography, IEEE Trans. Inform. Theory IT-22 (1976), 644-654. (1976) MR0437208
  4. M. P. Drazin, Pseudo-inverses in associate rings and semigroups, Amer. Math. Monthly 65 (1958), 506-514. (1958) MR0098762
  5. R. Gabriel, Das verallgemeinerte Inverse, deren Elemente einem beliebligen Körper angehören, J. reine angew. Math. 234 (1969), 107-122; 244 (1970), 83-93. (1969) 
  6. R. Gabriel, Das verallgemeinerte Inverse einer Matrix über einem beliebigen Körper - mit Skelettzerlegungen berechnet, Rev. Roumaine Math. Pures Appl. XX 1975, 2, 213 - 225. (1975) Zbl0314.15004MR0387298
  7. R. Gabriel, Eine Kollinearitatsbedingung für Involutionen in Gruppen und Algebren, J. reine angew. Math. 268 (1974), 20-49. (1974) MR0344987
  8. R. Gabriel, Das verallgemeinerte Inverse in Algebren, Rev. Roumaine Math. Pures Appl. XX (1975), 3, 311-324. (1975) Zbl0313.15006MR0387300
  9. R. Gabriel, Dreinachrichtenprobleme in verallgemeinerter Definition, J. reine angew. Math. 290 (1977), 199-202. (1977) MR0689020
  10. R. Gabriel, Ein kryptographisches System definiert mit verallgemeinerten Inversen, Vorgetragen Univ. Bukarest, Dezember 1971. (1971) 
  11. R. Gabriel, Pseudoinversen mit Schlüssel und ein System der algebraischen Kryptographie, Rev. Roumaine Math. Pures Appl. XXII (1977), 8, 1077-1099. (1977) MR0485912
  12. R. Gabriel, Über spektrale Pseudo-Inversen, Lineare Kryptographie und umkehrbare Zufallsgeneratoren, (in Druck). 
  13. R. Gabriel R. E. Hartwig, The Drazin inverse as a gradient, (submitted for publication). 
  14. R. E. Hartwig, Drazin inverses in cryptography, (submitted for publication). 
  15. E. Henze, Kryptographie und Nachrichtenübertragung, Informationsverarbeitung und Kommunikation, Band 8. 
  16. L. S. Hill, Cryptography in an algebraic alphabet, Amer. Math. Monthly 36 (1929), 306-312. (1929) MR1521759
  17. B. Jansson, Random Number Generators, Almqvist - Wiksell, Stockholm 1966. (1966) Zbl0173.45502MR0224253
  18. J. Levine R. E. Hartwig, Application of the Drazin Inverse to the Hill Cryptographic System, I, II, III, IV, Cryptologia (1980). (1980) MR0561958
  19. J. Levine J. V. Brawley, Involutory commutants with some applications to algebraic cryptography, I, J. reine angew. Math. 224 (1966), 20-43; II. 227 (1967), 1 - 24. (1966) MR0200089
  20. R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1958), 406-413. (1958) MR0069793
  21. R. L. Rives A. Shamir L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Comm. ACM 21 (1978), 120-126. (1978) MR0700103

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