A review about public cryptography protocols based on RSA or elliptic curves

Antonio Corbo Esposito; Cristian Tirelli

Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche (2019)

  • Volume: 86, Issue: 1, page 123-146
  • ISSN: 0370-3568

Abstract

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We provide the basic definitions regarding computational complexity theory and review some basic cryptography protocols based on RSA or elliptic curves. These protocols summarize the history of the last fifty years in cryptography and are actually ubiquitous in applications, as for example SSL (secure socket layers), smartcards, creation of a bitcoin wallet etc. Since it is known they are in the polynomial class for the Shor’s algorithm, the possible development of quantum computers, needed to run such algorithm, will represent a dramatic shift in cryptography research and in applications.

How to cite

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Corbo Esposito, Antonio, and Tirelli, Cristian. "A review about public cryptography protocols based on RSA or elliptic curves." Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche 86.1 (2019): 123-146. <http://eudml.org/doc/296411>.

@article{CorboEsposito2019,
abstract = {We provide the basic definitions regarding computational complexity theory and review some basic cryptography protocols based on RSA or elliptic curves. These protocols summarize the history of the last fifty years in cryptography and are actually ubiquitous in applications, as for example SSL (secure socket layers), smartcards, creation of a bitcoin wallet etc. Since it is known they are in the polynomial class for the Shor’s algorithm, the possible development of quantum computers, needed to run such algorithm, will represent a dramatic shift in cryptography research and in applications.},
author = {Corbo Esposito, Antonio, Tirelli, Cristian},
journal = {Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche},
keywords = {RSA; Diffie-Hellman; Discrete Logarithm; Elliptic Curve},
language = {eng},
month = {12},
number = {1},
pages = {123-146},
publisher = {Società Nazione di Scienze, Lettere e Arti in Napoli; Giannini},
title = {A review about public cryptography protocols based on RSA or elliptic curves},
url = {http://eudml.org/doc/296411},
volume = {86},
year = {2019},
}

TY - JOUR
AU - Corbo Esposito, Antonio
AU - Tirelli, Cristian
TI - A review about public cryptography protocols based on RSA or elliptic curves
JO - Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche
DA - 2019/12//
PB - Società Nazione di Scienze, Lettere e Arti in Napoli; Giannini
VL - 86
IS - 1
SP - 123
EP - 146
AB - We provide the basic definitions regarding computational complexity theory and review some basic cryptography protocols based on RSA or elliptic curves. These protocols summarize the history of the last fifty years in cryptography and are actually ubiquitous in applications, as for example SSL (secure socket layers), smartcards, creation of a bitcoin wallet etc. Since it is known they are in the polynomial class for the Shor’s algorithm, the possible development of quantum computers, needed to run such algorithm, will represent a dramatic shift in cryptography research and in applications.
LA - eng
KW - RSA; Diffie-Hellman; Discrete Logarithm; Elliptic Curve
UR - http://eudml.org/doc/296411
ER -

References

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  3. Cohen, H., Frey, G., Avanzi, R., Doche, C., Lange, T., Nguyen, K., Vercauteren, F. (2005) Handbook of Elliptic and Hyperelliptic Curve Cryptography. Chapman and Hall/CRC, pp. 19-35, 268-285, 591-607 Zbl1082.94001MR2162727
  4. Corbellini, A. (2015) Elliptic Curve Cryptography: A gentle introductionhttp://andrea.corbellini.name/2015/05/17/elliptic-curve-cryptography-a-gentle-introduction 
  5. Hankerson, D., Menezes, A., Vanstone, S.A. (2004) Guide to Elliptic Curve Cryptography, Springer-Verlag, pp. 76-83 Zbl1059.94016MR2054891DOI10.1016/s0012-365x(04)00102-5
  6. Koblitz, N. (1998), Algebraic Aspects of Cryptography. Springer (Corrected Second Printing 1999), pp. 18-21, 133-136 MR1610535DOI10.1007/978-3-662-03642-6
  7. McEliece, R. J. (1979) Finite Fields for Computer Scientists and Engineers. Springer, pp. 3-28 MR884528DOI10.1007/978-1-4613-1983-2
  8. Mermin, N. D. (March 28, 2006). Breaking RSA Encryption with a Quantum Computer: Shors' Factoring Algorithm, Cornell University, Physics 481-681 Lecture Notes 
  9. Schneier, B. (1996), Applied Cryptography. John Wiley & Sons, pp. 238-241, 233-263 Zbl0853.94001
  10. Shor, P.W. (1994) Algorithms for quantum computation: Discrete logarithms and factoring, Proc. 35th Annu. Symp. Foundations of Computer Science, pp. 124-134. MR1489242DOI10.1109/SFCS.1994.365700
  11. Silverman, J. H. (1986). The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics, Springer-Verlag, pp. 137-139 MR817210DOI10.1007/978-1-4757-1920-8

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