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Gabriel, Richard

Verschluesselungsabbildungen mit Pseudo-Inversen, Zufallsgeneratoren und Taefelungen. (German) Zbl 0519.94004

Kybernetika 18, 485-504 (1982).
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Cited in 1 Review

MSC:

94A99 Communication, information
94A05 Communication theory
94A11 Application of orthogonal and other special functions
15A09 Theory of matrix inversion and generalized inverses
65C10 Random number generation in numerical analysis
05B45 Combinatorial aspects of tessellation and tiling problems

Keywords:

linear enciphering; linear cryptography; generalized inverse

Citations:

Zbl 0398.15006; Zbl 0427.94015; Zbl 0444.94012; Zbl 0491.94015; Zbl 0491.94016
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\textit{R. Gabriel}, Kybernetika 18, 485--504 (1982; Zbl 0519.94004)
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References:

[1] R. E. Cline: An Application of Representations for the Generalized Inverse of a Matrix. MRC Technical Report 592, 1965. · Zbl 0142.26904
[2] R. E. Cline: Note on an extension of the Moore-Penrose inverse. · Zbl 0468.15003 · doi:10.1016/0024-3795(81)90137-3
[3] W. Diffie M. E. Hellman: New directions in cryptography. IEEE Trans. Inform. Theory IT-22 (1976), 644-654. · Zbl 0435.94018 · doi:10.1109/TIT.1976.1055638
[4] M. P. Drazin: Pseudo-inverses in associate rings and semigroups. Amer. Math. Monthly 65 (1958), 506-514. · Zbl 0083.02901
[5] R. Gabriel: Das verallgemeinerte Inverse, deren Elemente einem beliebligen Körper angehören. J. reine angew. Math. 234 (1969), 107-122; 244 (1970), 83-93. · Zbl 0165.34603 · doi:10.1515/crll.1969.234.107
[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. · Zbl 0314.15004
[7] R. Gabriel: Eine Kollinearitatsbedingung für Involutionen in Gruppen und Algebren. J. reine angew. Math. 268 (1974), 20-49. · Zbl 0284.20051 · doi:10.1515/crll.1974.267.20
[8] R. Gabriel: Das verallgemeinerte Inverse in Algebren. Rev. Roumaine Math. Pures Appl. XX (1975), 3, 311-324. · Zbl 0313.15006
[9] R. Gabriel: Dreinachrichtenprobleme in verallgemeinerter Definition. J. reine angew. Math. 290 (1977), 199-202. · Zbl 0358.15020 · doi:10.1515/crll.1977.290.199
[10] R. Gabriel: Ein kryptographisches System definiert mit verallgemeinerten Inversen. Vorgetragen Univ. Bukarest, Dezember 1971.
[11] R. Gabriel: Pseudoinversen mit Schlüssel und ein System der algebraischen Kryptographie. Rev. Roumaine Math. Pures Appl. XXII (1977), 8, 1077-1099. · Zbl 0398.15006
[12] R. Gabriel: Über spektrale Pseudo-Inversen, Lineare Kryptographie und umkehrbare Zufallsgeneratoren.
[13] R. Gabriel R. E. Hartwig: The Drazin inverse as a gradient. · Zbl 0562.15001
[14] R. E. Hartwig: Drazin inverses in cryptography.
[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. · JFM 55.0062.08
[17] B. Jansson: Random Number Generators. Almqvist - Wiksell, Stockholm 1966. · Zbl 0173.45502
[18] J. Levine R. E. Hartwig: Application of the Drazin Inverse to the Hill Cryptographic System, I, II, III, IV. Cryptologia (1980). · Zbl 0427.94015 · doi:10.1080/0161-118091854906
[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. · Zbl 0168.28204
[20] R. Penrose: A generalized inverse for matrices. Proc. Cambridge Philos. Soc. 51 (1958), 406-413. · Zbl 0065.24603
[21] R. L. Rives A. Shamir L. Adleman: A method for obtaining digital signatures and public-key cryptosystems. Comm. ACM 21 (1978), 120-126. · Zbl 0368.94005 · doi:10.1145/359340.359342
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