ABSTRACT. This paper surveys RSA-type implementations based on Lucas sequences and on elliptic curves. The main focus is the way how some known attacks on RSA were extended to LUC, KMOV and Demytko's system. It also gives some directions for the choice of the most appropriate RSA-type system for a given application. 1.
|
2181
|
A method for obtaining digital signatures and public-key cryptosystems
– Rivest, Shamir, et al.
- 1978
|
|
1952
|
New Directions in Cryptography
– Diffie, Hellman
- 1976
|
|
868
|
A public key cryptosystem and a signature scheme based on discrete logarithms
– ElGamal
- 1985
|
|
551
|
A course in computational algebraic number theory
– Cohen
- 1993
|
|
493
|
The Art of Computer Programming, Volume 2, Seminumerical Algorithms
– Knuth
- 1998
|
|
433
|
Elliptic Curve Cryptosystems
– Koblitz
- 1987
|
|
375
|
Identity-based cryptosystems and signature schemes
– Shamir
- 1984
|
|
365
|
The Arithmetic of Elliptic Curves
– Silverman
- 1986
|
|
262
|
Elliptic Curve Public Key Cryptosystems
– Menezes
- 1993
|
|
217
|
Digitalized signatures and public-key functions as intractable as factorization
– Rabin
- 1979
|
|
189
|
On the importance of checking cryptographic protocols for faults
– Boneh, DeMillo, et al.
- 1997
|
|
122
|
Elliptic curves over finite fields and the computation of square roots mod p
– Schoof
- 1985
|
|
118
|
An introduction to the Theory of
– Hardy, Wright
- 1979
|
|
109
|
Small solutions to polynomial equations, and low exponent RSA vulnerabilities
– Coppersmith
- 1997
|
|
101
|
Speeding the Pollard and elliptic curve methods of factorization
– Montgomery
- 1987
|
|
87
|
Cryptanalysis of short RSA secret exponents
– Wiener
- 1990
|
|
69
|
Low-exponent RSA with related messages
– Coppersmith, Franklin, et al.
- 1996
|
|
63
|
A modification of the RSA public-key encryption procedure
– Williams
- 1980
|
|
56
|
Prime Numbers and Computer Methods for Factorization
– Riesel
- 1985
|
|
52
|
Cryptographic Protocols
– Demillo, Lynch, et al.
- 1982
|
|
41
|
A new elliptic curve based analogue of RSA
– Demytko
- 1994
|
|
39
|
New Public-Key Schemes based on Elliptic Curves over the ring Zn
– Koyama, Maurer, et al.
- 1992
|
|
35
|
Digital signatures with RSA and other public-key cryptosystems
– Denning
- 1984
|
|
33
|
Chosen signature cryptanalysis of the RSA (MIT) public key cryptosystem
– Davida
- 1982
|
|
32
|
On Using RSA with Low Exponent in a Public Key Network
– Hastad
- 1986
|
|
30
|
Rational Points on Elliptic Curves
– Silverman, Tate
- 1992
|
|
30
|
A public-key cryptosystem and a digital signature system based on the Lucas function analogue to discrete logarithms
– Smith, Skinner
- 1995
|
|
29
|
A Chosen Text Attack on the RSA Cryptosystem and Some Discrete Logarithm Schemes
– Desmedt, Odlyzko
- 1986
|
|
28
|
Breaking public key cryptosystems on tamper resistant devices in the presence of transient faults
– Bao, Deng, et al.
- 1997
|
|
22
|
A new public key system
– Smith, Lennon
- 1993
|
|
21
|
Memo on RSA Signature Generation in the Presence of Faults
– Lenstra
- 1996
|
|
17
|
Some remarks on Lucas-based cryptosystems
– Bleichenbacher, Bosma, et al.
- 1995
|
|
17
|
The Little Book of Big Primes
– Ribenboim
- 1991
|
|
16
|
A further weakness in the common modulus protocol for the RSA cryptoalgorithm
– DeLaurentis
- 1984
|
|
16
|
A "weak" privacy protocol using the RSA crypto algorithm
– Simmons
- 1983
|
|
14
|
Precautions taken against various potential attacks
– Guillou, Walker, et al.
- 1991
|
|
12
|
Factorization and primality testing. Undergraduate Texts in Mathematics
– Bressoud
- 1989
|
|
11
|
Selective forgery of RSA signatures using redundancy
– Girault, Misarsky
- 1997
|
|
11
|
Attacks on some RSA signatures
– Jonge, Chaum
- 1986
|
|
9
|
Uses of elliptic curves in cryptography, advances in cryptology
– Miller
- 1986
|
|
9
|
Some remarks on public-key cryptosystems
– Müller, Nöbauer
- 1981
|
|
8
|
A linear protocol failure for RSA with exponent three
– Franklin, Reiter
- 1995
|
|
8
|
On the importance of securing your bins: The garbage-man-in-the-middle attack
– Joye, Quisquater
- 1997
|
|
7
|
Elliptic curves, Graduate Texts
– Husemoller
- 1987
|
|
7
|
Elliptic curves: Diophantine analysis. Grundlehren der Mathematischen Wissenschaften 231
– Lang
- 1978
|
|
6
|
Low exponent attack against elliptic curve
– Kurosawa, Okada, et al.
- 1995
|
|
6
|
Some serious protocol failures for RSA with exponent e of less than � 32 bits
– Patarin
- 1995
|
|
4
|
A new and optimal chosen message attack on RSA-type cryptosystems, Unpublished manuscript
– Bleichenbacher, Joye, et al.
- 1997
|
|
4
|
Factoring Polynomials with Integer Coefficients", Mathematische Annalen 261
– Lenstra, Lenstra, et al.
- 1982
|
|
4
|
Public-Key Encryption, Dr
– Smith, LUC
- 1993
|
|
