نتایج جستجو برای: supersingular elliptic curves

تعداد نتایج: 120919  

2010
Sanjit Chatterjee Darrel Hankerson Alfred Menezes

We focus on the implementation and security aspects of cryptographic protocols that use Type 1 and Type 4 pairings. On the implementation front, we report improved timings for Type 1 pairings derived from supersingular elliptic curves in characteristic 2 and 3 and the first timings for supersingular genus-2 curves in characteristic 2 at the 128-bit security level. In the case of Type 4 pairings...

2008
EVERETT W. HOWE Enric Nart Christophe Ritzenthaler

Let C be a supersingular genus-2 curve over an algebraically closed field of characteristic 3. We show that if C is not isomorphic to the curve y = x + 1 then up to isomorphism there are exactly 20 degree-3 maps φ from C to the elliptic curve E with j-invariant 0. We study the coarse moduli space of triples (C, E, φ), paying particular attention to questions of rationality. The results we obtai...

2000
Atsuko Miyaji Masaki Nakabayashi Shunzo Takano

Elliptic curve cryptosystems([19, 25]) are based on the elliptic curve discrete logarithm problem(ECDLP). If elliptic curve cryptosystems avoid FR-reduction([11, 17]) and anomalous elliptic curve over Fq ([34, 3, 36]), then with current knowledge we can construct elliptic curve cryptosystems over a smaller de nition eld. ECDLP has an interesting property that the security deeply depends on elli...

2001
Atsuko MIYAJI Masaki NAKABAYASHI

Elliptic curve cryptosystems([19],[25]) are based on the elliptic curve discrete logarithm problem(ECDLP). If elliptic curve cryptosystems avoid FRreduction([11],[17]) and anomalous elliptic curve over Fq ([3], [33], [35]), then with current knowledge we can construct elliptic curve cryptosystems over a smaller definition field. ECDLP has an interesting property that the security deeply depends...

Journal: :Journal of the Institute of Mathematics of Jussieu 2007

2007
Masato Kurihara Robert Pollack

Let E be an elliptic curve over Q. We assume that E has good supersingular reduction at a prime p, and for simplicity, assume p is odd and ap = p+ 1− #E(Fp) is zero. Then, as the second author showed, the p-adic L-function Lp,α(E) of E corresponding to α = ±√−p (by Amice-Vélu and Vishik) can be written as Lp,α(E) = f log+p +g logp α by using two Iwasawa functions f and g ∈ Zp[[Gal(Q∞/Q)]] ([20]...

Journal: :IACR Cryptology ePrint Archive 2011
David Jao Luca De Feo

We present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases under the isogeny in order to allow the two parties to arrive at a common shared key despite the noncommutativity of the endomorphism ring. Ou...

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