{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:57:46Z","timestamp":1772283466262,"version":"3.50.1"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1993,3,1]],"date-time":"1993-03-01T00:00:00Z","timestamp":730944000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AAECC"],"published-print":{"date-parts":[[1993,3]]},"DOI":"10.1007\/bf01270400","type":"journal-article","created":{"date-parts":[[2005,3,24]],"date-time":"2005-03-24T04:36:14Z","timestamp":1111638974000},"page":"59-76","source":"Crossref","is-referenced-by-count":2,"title":["Cryptanalysis of R\ufffddei- and Dickson permutations on arbitrary finite rings"],"prefix":"10.1007","volume":"4","author":[{"given":"Reinhold","family":"Pieper","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1090\/S0025-5718-1962-0148632-7","volume":"16","author":"P. T. Bateman","year":"1962","unstructured":"Bateman, P. T., Horn, R. A.: A heuristic asymptotic formula concerning the distribution of prime numbers. Math. Comp.16, 363?367 (1962)","journal-title":"Math. Comp."},{"key":"CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-663-14034-4","volume-title":"Mathematische Methoden der Kryptoanalyse","author":"F. P. Heider","year":"1985","unstructured":"Heider, F. P., Kraus, D., Welschenbach, M.: Mathematische Methoden der Kryptoanalyse. Vieweg, Braunschweig 1985"},{"key":"CR3","first-page":"88","volume":"261","author":"H. Lausch","year":"1973","unstructured":"Lausch, H., M\u00fcller, W. B., N\u00f6bauer, W.: \u00dcber die Struktur einer durch Dicksonpolynome dargestellten Permutationsgruppe des Restklassenringes modulon. J. Reine Angew. Math.261, 88?99 (1973)","journal-title":"J. Reine Angew. Math"},{"key":"CR4","unstructured":"Lenstra, H. W. jr.: Factoring integers with elliptic curves. Rep. 86-18, Universiteit van Amsterdam 1986"},{"key":"CR5","volume-title":"Finite fields","author":"R. Lidl","year":"1983","unstructured":"Lidl, R., Niederreiter, H.: Finite fields. Addison-Wesley, Reading, Mass. 1983"},{"key":"CR6","volume-title":"Finite rings with identity","author":"B. R. McDonald","year":"1974","unstructured":"McDonald, B. R.: Finite rings with identity. Marcel Dekker, New York 1974"},{"key":"CR7","first-page":"361","volume":"6","author":"W. B. M\u00fcller","year":"1971","unstructured":"M\u00fcller, W. B.: \u00dcber eine Klasse von durch Dickson-Polynome dargestellten Gruppen. Colloq. Math. Soc. Janos Bolyai6, 361?376 (1971)","journal-title":"Colloq. Math. Soc. Janos Bolyai"},{"key":"CR8","first-page":"50","volume-title":"Lecture Notes in Comp. Science, vol. 219","author":"W. B. M\u00fcller","year":"1985","unstructured":"M\u00fcller, W. B., N\u00f6bauer, R.: Cryptanalysis of the Dickson-Scheme. Lecture Notes in Comp. Science, vol. 219, pp. 50?61. Berlin, Heidelberg, New York: Springer 1985"},{"key":"CR9","first-page":"93","volume":"192","author":"W. B. M\u00fcller","year":"1983","unstructured":"M\u00fcller, W. B., N\u00f6bauer, W.: \u00dcber die Fixpunkte der Potenzpermutationen. Sitzungsber. \u00d6ster. Akad. d. Wiss. math.-nat. Kl, Abt. II,192, 93?97 (1983)","journal-title":"Sitzungsber. \u00d6ster. Akad. d. Wiss. math.-nat. Kl, Abt. II"},{"key":"CR10","first-page":"521","volume":"193","author":"R. N\u00f6bauer","year":"1984","unstructured":"N\u00f6bauer, R.: \u00dcber die Fixpunkte einer Klasse von Dickson-Permutationen. Sitzungsber. \u00d6ster. Akad. d. Wiss. math.-nat. Kl., Abt. II,193, 521?547 (1984)","journal-title":"Sitzungsber. \u00d6ster. Akad. d. Wiss. math.-nat. Kl., Abt. II"},{"key":"CR11","first-page":"255","volume-title":"Contributions to General Algebra 3","author":"R. N\u00f6bauer","year":"1985","unstructured":"N\u00f6bauer, R.: Cryptanalysis of the R\u00e9dei-Scheme. Contributions to General Algebra 3, H\u00f6lder-Pichler-Tempsky, Wien 1985, pp. 255?264"},{"key":"CR12","doi-asserted-by":"crossref","first-page":"173","DOI":"10.4064\/aa-45-2-173-181","volume":"45","author":"R. N\u00f6bauer","year":"1985","unstructured":"N\u00f6bauer, R.: \u00dcber die Fixpunkte von durch Dickson-Polynome dargestellten Permutationen. Acta Arithmetica45, 173?181 (1985)","journal-title":"Acta Arithmetica"},{"key":"CR13","first-page":"287","volume":"50","author":"R. N\u00f6bauer","year":"1986","unstructured":"N\u00f6bauer, R.: R\u00e9dei-Funktionen und ihre Anwendung in der Kryptographie. Acta Sci. Math.50, 287?298 (1986)","journal-title":"Acta Sci. Math."},{"key":"CR14","first-page":"235","volume-title":"Contributions to General Algebra 5","author":"R. N\u00f6bauer","year":"1987","unstructured":"N\u00f6bauer, R.: R\u00e9dei-Permutationen endlicher K\u00f6rper. Contributions to General Algebra 5, H\u00f6lder-Pichler-Tempsky, Wien 1987, pp. 235?246"},{"key":"CR15","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/BF01579188","volume":"58","author":"W. N\u00f6bauer","year":"1954","unstructured":"N\u00f6bauer, W.: \u00dcber eine Gruppe der Zahlentheorie. Monatshefte Math.58, 181?192 (1954)","journal-title":"Monatshefte Math."},{"key":"CR16","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1007\/BF01303049","volume":"69","author":"W. N\u00f6bauer","year":"1965","unstructured":"N\u00f6bauer, W.: \u00dcber Permutationspolynome und Permutations funktionen f\u00fcr Primzahlpotenzen. Monatshefte Math.69, 230?238 (1965)","journal-title":"Monatshefte Math."},{"key":"CR17","first-page":"215","volume":"231","author":"W. N\u00f6bauer","year":"1968","unstructured":"N\u00f6bauer, W.: \u00dcber eine Klasse von Permutationspolynomen und die dadurch dargestellten Gruppen. J. Reine Angew. Math.231, 215?219 (1968)","journal-title":"J. Reine Angew. Math."},{"key":"CR18","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1007\/BF01300934","volume":"77","author":"W. N\u00f6bauer","year":"1973","unstructured":"N\u00f6bauer, W.: \u00dcber Gruppen von Dickson-Polynomfunktionen und einige damit zusammenhangende zahlentheoretische Fragen. Monatshefte Math.77, 330?334 (1973)","journal-title":"Monatshefte Math."},{"key":"CR19","first-page":"115","volume":"193","author":"W. N\u00f6bauer","year":"1984","unstructured":"N\u00f6bauer, W.: \u00dcber die Fixpunkte der Dickson-Permutationen. Sitzungsber. \u00d6ster. Akad. d. Wiss. math.-nat. Kl., Abt. II,193, 115?133 (1984)","journal-title":"Sitzungsber. \u00d6ster. Akad. d. Wiss. math.-nat. Kl., Abt. II"},{"key":"CR20","first-page":"121","volume":"121","author":"W. N\u00f6bauer","year":"1984","unstructured":"N\u00f6bauer, W.: \u00dcber die Zyklenl\u00e4nge der R\u00e9dei-Permutationen. Anzeiger d. \u00d6ster. Akad. d. Wiss. math.-nat. Kl.,121, 121?123 (1984)","journal-title":"Anzeiger d. \u00d6ster. Akad. d. Wiss. math.-nat. Kl."},{"key":"CR21","first-page":"267","volume-title":"Contributions to General Algebra 3","author":"W. N\u00f6bauer","year":"1985","unstructured":"N\u00f6bauer, W.: On the length of cycles of polynomial permutations. Contributions to General Algebra 3, H\u00f6lder-Pichler-Tempsky, Wien 1985, pp. 267?274"},{"issue":"1","key":"CR22","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/BF01848228","volume":"17","author":"W. N\u00f6bauer","year":"1986","unstructured":"N\u00f6bauer, W.: R\u00e9dei-Funktionen f\u00fcr Zweierpotenzen. Periodica Math. Hungar.17(1), 37?44 (1986)","journal-title":"Periodica Math. Hungar."},{"key":"CR23","unstructured":"Pieper, R.: Kryptoanalytische Untersuchungen rationaler Permutationen von kommutativen unit\u00e4ren Ringen. Dissertation, Universit\u00e4t Dortmund 1990"},{"key":"CR24","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1017\/S0305004100049252","volume":"76","author":"J. M. Pollard","year":"1974","unstructured":"Pollard, J. M.: Theorems on factorization and primality testing. Proc. Cambridge Philos. Soc.76, 521?528 (1974)","journal-title":"Proc. Cambridge Philos. Soc."},{"key":"CR25","volume-title":"Algebra I","author":"L. R\u00e9dei","year":"1967","unstructured":"R\u00e9dei, L.: Algebra I. Pergamon Press, Oxford 1967"},{"key":"CR26","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-1089-2","volume-title":"Prime numbers and computer methods for factorization","author":"H. Riesl","year":"1985","unstructured":"Riesl, H.: Prime numbers and computer methods for factorization. Birkh\u00e4user-Verlag, Boston 1985"},{"key":"CR27","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1080\/0161-117791833219","volume":"1","author":"G.J. Simmons","year":"1977","unstructured":"Simmons, G.J., Norris, M. J.: Preliminary comments on the M.I.T. public-key cryptosystem. Cryptologia1, 409?418 (1977)","journal-title":"Cryptologia"},{"issue":"159","key":"CR28","first-page":"225","volume":"39","author":"H. C. Williams","year":"1982","unstructured":"Williams, H. C.: Ap + 1 method of factoring. Math. Comp.39(159), 225?234 (1982)","journal-title":"Math. Comp."},{"key":"CR29","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1007\/BF01931269","volume":"19","author":"H. C. Williams","year":"1979","unstructured":"Williams, H. C., Schmid, B.: Some remarks concerning the M.I.T. public-key cryptosystem. BIT19, 525?538 (1979)","journal-title":"BIT"}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01270400.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01270400\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01270400","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T18:13:58Z","timestamp":1556648038000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01270400"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,3]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1993,3]]}},"alternative-id":["BF01270400"],"URL":"https:\/\/doi.org\/10.1007\/bf01270400","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,3]]}}}