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Algorithm for Generating Primes for the Giuliani-Gong Public Key System
2011
Journal of Internet Services and Information Security
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In this paper we propose an algorithm for computing large primes p and q such that q divides p 4 3 Correctness of the Algorithm Theorem 3.1. Let us fix n = 5 or n = 10. ...
Then Algorithm 1 generates primes p and q such that q divides Φ n (p). Proof. We begin by proving three auxiliary lemmas. Proof. ...
In order to generate key parameters to both cryptosystems one should find large primes p and q such that q divides Φ 5 (p) = p 4 + p 3 + p 2 + p + 1 in the Gong-Harn case and Φ 10 (p) = p 4 − p 3 + p 2 ...
doi:10.22667/jisis.2011.08.31.021
dblp:journals/jisis/Grzeskowiak11
fatcat:vpmajp77vjfw3gedohkipnv33q
A Practical Public Key Cryptosystem from Paillier and Rabin Schemes
[chapter]
2002
Lecture Notes in Computer Science
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This modification is reminiscent of the ones applied by Rabin [22] and Williams [25] to the well-known RSA cryptosystem. ...
Thanks to the special properties of such schemes, we obtain efficiency similar to that of RSA cryptosystem, provably secure encryption (since recovering plaintext from ciphertext is as hard as factoring ...
Acknowledgements We would like to thank Dario Catalano for sending us an early version of his paper [6] and the anonymous referees for their useful comments. ...
doi:10.1007/3-540-36288-6_21
fatcat:fqlpspal3zfidbdmxkubredkxy
Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems
[chapter]
2001
Lecture Notes in Computer Science
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We also discuss the applicability of our methods to general elliptic curves defined over finite fields which includes a classification of elliptic curve groups where distortion maps exist. ...
Menezes at the Crypto 2000 Rump Session on the possibility of efficiently inverting the MOV embedding into the XTR subgroup. ...
solve the Diffie-Hellman problem in the Gong & Harn subgroup of GF(p 3 ) * as well as in the related elliptic curve group of points. ...
doi:10.1007/3-540-44987-6_13
fatcat:2uwomdcb6vfc5k2evgfi67xpbq
Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems
2004
Journal of Cryptology
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We also discuss the applicability of our methods to general elliptic curves defined over finite fields which includes a classification of elliptic curve groups where distortion maps exist. ...
Menezes at the Crypto 2000 Rump Session on the possibility of efficiently inverting the MOV embedding into the XTR subgroup. ...
solve the Diffie-Hellman problem in the Gong & Harn subgroup of GF(p 3 ) * as well as in the related elliptic curve group of points. ...
doi:10.1007/s00145-004-0313-x
fatcat:jcgs3ac57raqlbpysr3hkap27q
Point compression for the trace zero subgroup over a small degree extension field
2014
Designs, Codes and Cryptography
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Using Semaev's summation polynomials, we derive a new equation for the F_q-rational points of the trace zero variety of an elliptic curve defined over F_q. ...
We give explicit equations and discuss in detail the practically relevant cases of cubic and quintic field extensions. ...
We are grateful to the mathematics department of the Univerity of Zürich for access to their computing facilities. ...
doi:10.1007/s10623-014-9921-0
fatcat:6xxb7mujczewbjjmocrps76eda
Subgroup Cryptosystems
[chapter]
Encyclopedia of Cryptography and Security
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In 1999 Gong and Harn generalize the LUC cryptosystem, as described in terms of a recurrent relation, to the third degree, reinventing much of the work of Carlitz. ...
For key generation, Gong and Harn propose working with an element of order p 2 + p + 1. ...
Het is bijvoorbeeld eenvoudig twee priemgetallen met elkaar te vermenigvuldigen, maar het is onbekend of het omgekeerde, factoriseren, ook snel kan. ...
doi:10.1007/0-387-23483-7_418
fatcat:gg3uycmc65a6thhy4gtslscxae
Trace zero varieties in cryptography, optimal representation and index calculus
2014
unpublished
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With the understanding that: Waiver -Any of the above conditions can be waived if you get permission from the copyright holder. ...
Public Domain -Where the work or any of its elements is in the public domain under applicable law, that status is in no way affected by the license. ...
Acknowledgements xv Acknowledgements I gratefully acknowledge financial support of the Swiss National Science Foundation throughout my PhD studies. ...
doi:10.5451/unibas-006246470
fatcat:vokt22qezzbybmhdjkddq4dioy