Geodesic
Embedding of provably unsolvable problems into stream ciphers
Matematičeskie voprosy kriptografii, Tome 14 (2023) no. 1, pp. 65-83 Cet article a éte moissonné depuis la source Math-Net.Ru

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In view of intensively developing theories of quantum cryptography and of quantum computers, the possibility to construct ciphers with a potentially infinite set of cryptographic keys based on recursively enumerable, but not recursive sets is discussed. 
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F. M. Malyshev. Embedding of provably unsolvable problems into stream ciphers. Matematičeskie voprosy kriptografii, Tome 14 (2023) no. 1, pp. 65-83. http://geodesic.mathdoc.fr/item/MVK_2023_14_1_a4/

[1] Maltsev A.I., Algoritmy i rekursivnye funktsii, Nauka, M., 1965, 392 pp.

[2] Manin Yu.I., Dokazuemoe i nedokazuemoe, Sovetskoe radio, M., 1979

[3] Manin Yu.I., Vychislimoe i nevychislimoe, Sovetskoe radio, M., 1980

[4] Matiyasevich Yu.V., “Diofantovy mnozhestva”, Uspekhi matem. nauk, 27:5 (1972), 185–222 | MR | Zbl

[5] Jones J.P., “Universal diophantine equation”, J. Symb. Logic, 47:3 (1982) | MR | Zbl

[6] Friedman H.M., “The number of certain integral polinomials and nonrecursive sets of integers, part 2”, Trans. Amer. Math. Soc., 357:3 (2004), 1013–1023 | DOI | MR

[7] Yedidia A., Aaronson S., “A relatively small Turing machine whose behavior is independent of set theory”, Complex Systems, 25:4 (2016), 297–327 | DOI | MR | Zbl

[8] Feynman R.P., “Simulating physics with computers”, Int. J. Theor. Phys., 21 (1982), 467–488 | DOI | MR

[9] Deutsch D., “Quantum theory, the Church–Turing principle and the universalquantum computer”, Proc. R. Soc. Lond. A, 400:1818 (1985), 97–117 | DOI | MR | Zbl

[10] Deutsch D., “Quantum computational networks”, Proc. R. Soc. Lond. A, 425:1868 (1989), 73–90 | DOI | MR | Zbl

[11] Yao A.C.-C., “Quantum circuit complexity”, Proc. 34th Ann. Symp. Found. Comput. Sci., 1993, 352–360 | MR

[12] Nilsen M., Chang I., Kvantovye vychisleniya i kvantovaya informatsiya, Mir, M., 2006

[13] Shor P.W., “Algorithms for quantum computation: discrete log and factoring”, Proc. 35th Ann. Symp. Found. Comput. Sci., 1994, 124–134 | DOI | MR

[14] Shor P.W., “Scheme for reducing decoherence in quantum memory”, Phys. Rev., A 52 (1995), 2493–2496 | MR

[15] Kostrikin A.I., Manin Yu.I., Lineinaya algebra i geometriya, 1-e izd., MGU, M., 1979 ; 2-e изд., Наука, М., 1986 | MR

[16] Sidelnikov V.M., Teoriya kodirovaniya, FIZMATLIT, M., 2008

[17] Kitaev A., Shen A., Vyalyi M., Klassicheskie i kvantovye vychisleniya, MTsNMO–CheRo, M., 1999