Summary
The security of communication systems requires more and more tehnical tools and approaches. This involves in particular cryptographic aspects. We describe here an overview of some algorithms used for public-key cryptography, and digital signatures. The focus here is mainly on the description of the approaches, and does not address an exhaustive description of the available publicc-key cryptosystems.
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References
AES Home Page. http://csrc.nist.gov/encryption/aes/.
IEEE-P1363 standard on public-key cryptology.
L.M. Adelman, R.L. Rivest, and A. Shamir, “A method for obtaining digital signatures and public-key cryptosystems.” Commun. ACM 21, 120–126 (1978).
A.O.L. Atkin and F. Morain, “Elliptic curves and primality proving,” Math. Comput. 61, 29–68 (1993).
I. Blake, G. Seroussi, and N. Smart, “Elliptic curves in cryptography,” London Math. Soc. LNS 265 (1999).
H. Cohen, A Course in Algorithmic Algebraic Number Theory, Graduate Texts in Mathematics vol. 138, (Springer-Verlag, New York, 1993).
N. Koblitz, A Course in Number Theory and Cryptology, Graduate Texts in Mathematics 114, (Springer-Verlag, New York, 1994).
H.W. Lenstra, Jr., “Factoring integers with elliptic curves,” Ann. Math. 126, 649–673 (1987).
A.K. Lenstra and H.W. Lenstra, Jr., The Development of the Number Field Sieve, A.K. Lenstra and H.W. Lenstra, Jr., eds., Lecture Notes in Mathematics 1554 (Springer-Verlag, Berlin, 1993).
F. Leprévost, “Encryption and cryptosystems in electronic surveillance: A survey of the technology assessment issues,” European Parliament (1998). Global Project No. EP/IV/B/SSSTOA/98/111401/01: Development of surveillance technology and risk of abuse of economic information.
F. Leprévost and B. Warusfel, “Security technologies for digital media,” European Parliament (2001). Study No. EP/IV/A/STOA/2000/06/01.
F. Leprévost and B. Warusfel, “Protection and implementation of intellectual property rights in security technologies for digital media,” European Parliament (2002–2003). Study No. EP/IV/STOA/2002/13/02.
F. Leprévost and B. Warusfel, Echelon: origines et perspectives d’un débat transnational. Annulaire Franais des Relations Internationales, Vol. 2 (2001).
R. Leprévost, Cryptographie et lutte contre le terrorisme: éviter les fausses solutions sécuritaires. Revue Droit et Défense (Publications du Centre de Recherche Droit et Défense de l’Université Paris V, Paris, 2002).
F. Leprévost, Les standards cryptographiques du XXI-eme siecle: AES et IEEE-P1363,” Gazette Math.
A.J. Menezes, Elliptic Curve Public-Key Cryptosystems (Kluwer Academic Publishers, Dordrecht, 1993).
A.J. Menezes, P.C. van Oorschot, and S.A. Vanstone, Handbook of Applied Cryptography, (CRC Press, Boca Raton, 1997)
J.-L. Nicolas, “Tests de primalité,” Expo. Math. 2, 223–234 (1984).
A. Odlyzko, “Discrete logarithms in finite fields and their cryptographic significance,” In Advances in Cryptology-Eurocrypt’ 84, Lecture Notes in Computer Science, 209, 224–314 (Springer-Verlag, Berlin, 1985).
J. Pollard, “Theorems on factorization and primality testing,” Proc. Cambridge Philos. Soc. 76, 521–528 (1974).
J. Pollard, “A Monte-Carlo method for factorization,” Bit 15, 331–334 (1975).
C. Pomerance, J.L. Selfridge, and S.S. Wagstaff, Jr., “The pseudoprimes to 25 · 109,” Math. Comput., 35, 1003–1026 (1980).
P. Ribenboim, The New Book of Prime Number Records, 3rd ed., (Springer-Verlag, New York, 1996).
O. Schirauker, D. Weber, and T. Denny, “Discrete logarithm: The effectiveness of the index calculus method,” in H. Cohen, ed., Algorithmic Number Theory Symposium, Proceedings of the Second International Symposium ANTS II, Talence, France, May 1996, Lecture Notes in Computer Science, 1122 (Springer-Verlag, Berlin, 1996).
B. Schneier, Applied Cryptography, 2nd ed. (John Wiley and Sons, New York, 1996).
D. Shanks, “Class number, a theory of factorization, and genera.” in Proceedings of Symposia in Pure Mathematics, 20, pp. 415–440 (American Mathematical Society, Providence, RI, 1971).
J. Silverman, The Arthmetic of Elliptic Curves, Graduate Texts in Mathematics 106, (Springer, New York, 1992).
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Leprévost, F. (2005). Public-Key Cryptography: An Overview of some Algorithms. In: Javidi, B. (eds) Optical and Digital Techniques for Information Security. Advanced Sciences and Technologies for Security Applications, vol 1. Springer, New York, NY . https://doi.org/10.1007/0-387-25096-4_17
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DOI: https://doi.org/10.1007/0-387-25096-4_17
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