Zobrazeno 1 - 10
of 73
pro vyhledávání: '"Jao, David"'
Publikováno v:
Journal of Mathematical Cryptology, Vol 15, Iss 1, Pp 18-30 (2020)
Password authenticated key establishment (PAKE) is a cryptographic primitive that allows two parties who share a low-entropy secret (a password) to securely establish cryptographic keys in the absence of public key infrastructure. We propose the firs
Externí odkaz:
https://doaj.org/article/4d6f16639c144a83bfae2fa0104e4c18
Publikováno v:
Journal of Mathematical Cryptology, Vol 14, Iss 1, Pp 129-138 (2020)
We present a quantum algorithm which computes group action inverses of the complex multiplication group action on isogenous ordinary elliptic curves, using subexponential time, but only polynomial quantum space. One application of this algorithm is t
Externí odkaz:
https://doaj.org/article/2d897826772d441e8227b65078b2a646
Autor:
Urbanik David, Jao David
Publikováno v:
Journal of Mathematical Cryptology, Vol 14, Iss 1, Pp 120-128 (2020)
We consider the problem of producing an efficient, practical, quantum-resistant non-interactive key exchange (NIKE) protocol based on Supersingular Isogeny Diffie-Hellman (SIDH). An attack of Galbraith, Petit, Shani and Ti rules out the use of naïve
Externí odkaz:
https://doaj.org/article/f29adf189f2f452899aea032a6d0fef6
Publikováno v:
J. Math. Cryptol., 8(1):1-29, 2014
Given two elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit an isogeny between them, but finding such an isogeny is believed to be computationally difficult. The fastest known cla
Externí odkaz:
http://arxiv.org/abs/1012.4019
Autor:
Jao, David, Soukharev, Vladimir
Publikováno v:
ANTS-IX, LNCS 6197, pp. 219-233, 2010
An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between elliptic curves efficiently. For ordinary curves of the same endomorphism r
Externí odkaz:
http://arxiv.org/abs/1002.4228
Publikováno v:
J. Number Theory 129 (2009), pp. 1491-1504
We present a construction of expander graphs obtained from Cayley graphs of narrow ray class groups, whose eigenvalue bounds follow from the Generalized Riemann Hypothesis. Our result implies that the Cayley graph of (Z/qZ)* with respect to small pri
Externí odkaz:
http://arxiv.org/abs/0811.0647
Publikováno v:
Advances in Cryptology -- Asiacrypt 2005, LNCS 3788, pp. 21-40.
The aim of this paper is to justify the common cryptographic practice of selecting elliptic curves using their order as the primary criterion. We can formalize this issue by asking whether the discrete log problem (DLOG) has the same difficulty for a
Externí odkaz:
http://arxiv.org/abs/math/0411378
Autor:
Jao, David
Publikováno v:
Journal of Number Theory, Volume 113, Issue 2, August 2005, pp. 208-225
For small odd primes $p$, we prove that most of the rational points on the modular curve $X_0(p)/w_p$ parametrize pairs of elliptic curves having infinitely many supersingular primes. This result extends the class of elliptic curves for which the inf
Externí odkaz:
http://arxiv.org/abs/math/0408065
Publikováno v:
Journal of Mathematical Cryptology, Vol 8, Iss 3, Pp 209-247 (2014)
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 b
Externí odkaz:
https://doaj.org/article/06a778de154c4b83b71417d3c977ba98
Publikováno v:
Journal of Mathematical Cryptology, Vol 8, Iss 1, Pp 1-29 (2014)
Given two ordinary elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit a nonzero isogeny between them, but finding such an isogeny is believed to be computationally difficult. The f
Externí odkaz:
https://doaj.org/article/398121efe757425994d4fbe5a897fe6e