id: 01121318
dt: j
an: 01121318
au: Joye, Marc; Quisquater, Jean-Jacques
ti: Reducing the elliptic curve cryptosystem of Meyer-Müller to the
    cryptosystem of Rabin-Williams.
so: Des. Codes Cryptography 14, No.1, 53-56 (1998).
py: 1998
pu: Springer, Norwell, MA
la: EN
cc: 
ut: cryptography; Rabin-type cryptosystems; elliptic curves
ci: Zbl 0839.94007; Zbl 0466.94018
li: doi:10.1023/A:1008256404676
ab: From the introduction: In 1991, {\it K. Koyama, U. M. Maurer, T. Okamoto}
    and {\it S. A. Vanstone} [Lect. Notes Comput. Sci. 576, 252-266 (1992;
    Zbl 0839.94007)] pointed out the existence of new one-way trapdoor
    functions similar to the RSA on elliptic curves over a ring. At
    Eurocrypt’96, {\it B. Meyer} and {\it V. Müller} [Lect. Notes
    Comput. Sci. 1070, 49-59 (1996)] presented another elliptic RSA-type
    cryptosystem with a public encryption exponent equal to 2. The authors
    show that this cryptosystem may be reduced to the cryptosystem of
    Rabin-Williams [{\it M. O. Rabin}, Digitalized signatures and
    public-key functions as intractable as factorization. Technical Report
    MIT/LCS/TR-212, MIT, Laboratory for Computer Science, January (1979)
    and {\it H. C. Williams}, IEEE Trans. Inf. Theory. IT-26, 726-729
    (1980; Zbl 0466.94018)]. This has a lot of consequences. For example,
    Meyer and Müller claimed that 11 messages are required to mount
    successfully the so-called low exponent attack against their
    cryptosystem. However, since the system is reducible to the
    Rabin-Williams’ one, only two messages are required by using the
    algorithm of Coppersmith.
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