Geodesic
A review about public cryptography protocols based on RSA or elliptic curves
Rendiconto della Accademia delle scienze fisiche e matematiche, Série 4, Tome 86 (2019) no. 1, pp. 123-146.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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.
In questa nota forniamo le definizioni di base relative alla teoria della complessitá computazionale ed esaminiamo alcuni semplici protocolli crittografici basati su RSA e curve ellittiche. Questi protocolli riassumono la storia degli ultimi cinquant’anni della crittografia e sono onnipresenti nelle applicazioni, come ad esempio SSL (secure socket layers), smartcards, creazione di portafogli per bitcoin etc. Poiché é noto che rientrano nella classe di problemi polinomiali per l’algoritmo di Shor, un possibile sviluppo dei computer quantistici, necessari per eseguire questi algoritmi, rappresenterebbe un drammatico cambiamento nella ricerca crittografica e nelle applicazioni. 
@article{RASFM_2019_4_86_1_a2,
     author = {Corbo Esposito, Antonio and Tirelli, Cristian},
     title = {A review about public cryptography protocols based on {RSA} or elliptic curves},
     journal = {Rendiconto della Accademia delle scienze fisiche e matematiche},
     pages = {123--146},
     publisher = {mathdoc},
     volume = {Ser. 4, 86},
     number = {1},
     year = {2019},
     zbl = {1244.94031},
     mrnumber = {2590642},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RASFM_2019_4_86_1_a2/}
}
TY  - JOUR
AU  - Corbo Esposito, Antonio
AU  - Tirelli, Cristian
TI  - A review about public cryptography protocols based on RSA or elliptic curves
JO  - Rendiconto della Accademia delle scienze fisiche e matematiche
PY  - 2019
SP  - 123
EP  - 146
VL  - 86
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RASFM_2019_4_86_1_a2/
LA  - en
ID  - RASFM_2019_4_86_1_a2
ER  - 
%0 Journal Article
%A Corbo Esposito, Antonio
%A Tirelli, Cristian
%T A review about public cryptography protocols based on RSA or elliptic curves
%J Rendiconto della Accademia delle scienze fisiche e matematiche
%D 2019
%P 123-146
%V 86
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RASFM_2019_4_86_1_a2/
%G en
%F RASFM_2019_4_86_1_a2
Corbo Esposito, Antonio; Tirelli, Cristian. A review about public cryptography protocols based on RSA or elliptic curves. Rendiconto della Accademia delle scienze fisiche e matematiche, Série 4, Tome 86 (2019) no. 1, pp. 123-146. http://geodesic.mathdoc.fr/item/RASFM_2019_4_86_1_a2/

Bernstein D.J., Buchmann J., Dahmen E. (2009) Post-Quantum Cryptography. Springer, pp.1-32 | DOI | MR

Blackburn S. R., Cid C., Mullan C. (2010) Group Theory in Cryptography. Department of Mathematics, Royal Holloway, University of London Egham, Surrey TW20 0EX, United Kingdom, pp. 2-6 | MR | Zbl

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 | MR | Zbl

Corbellini A. (2015) Elliptic Curve Cryptography: A gentle introduction http://andrea.corbellini.name/2015/05/17/elliptic-curve-cryptography-a-gentle-introduction

Hankerson D., Menezes A., Vanstone S.A. (2004) Guide to Elliptic Curve Cryptography, Springer-Verlag, pp. 76-83 | DOI | MR | Zbl

Koblitz N. (1998), Algebraic Aspects of Cryptography. Springer (Corrected Second Printing 1999), pp. 18-21, 133-136 | DOI | MR

Mceliece R. J. (1979) Finite Fields for Computer Scientists and Engineers. Springer, pp. 3-28 | DOI | MR

Mermin N. D. (March 28, 2006). Breaking RSA Encryption with a Quantum Computer: Shors' Factoring Algorithm, Cornell University, Physics 481-681 Lecture Notes

Schneier B. (1996), Applied Cryptography. John Wiley & Sons, pp. 238-241, 233-263 | Zbl

Shor P.W. (1994) Algorithms for quantum computation: Discrete logarithms and factoring, Proc. 35th Annu. Symp. Foundations of Computer Science, pp. 124-134. | DOI | MR

Silverman J. H. (1986). The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics, Springer-Verlag, pp. 137-139 | DOI | MR