484 research outputs found
Computing cardinalities of Q-curve reductions over finite fields
We present a specialized point-counting algorithm for a class of elliptic
curves over F\_{p^2} that includes reductions of quadratic Q-curves modulo
inert primes and, more generally, any elliptic curve over F\_{p^2} with a
low-degree isogeny to its Galois conjugate curve. These curves have interesting
cryptographic applications. Our algorithm is a variant of the
Schoof--Elkies--Atkin (SEA) algorithm, but with a new, lower-degree
endomorphism in place of Frobenius. While it has the same asymptotic asymptotic
complexity as SEA, our algorithm is much faster in practice.Comment: To appear in the proceedings of ANTS-XII. Added acknowledgement of
Drew Sutherlan
Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography
Short Weierstrass's elliptic curves with underlying hard Elliptic Curve
Discrete Logarithm Problems was widely used in Cryptographic applications. This
paper introduces a new security notation 'trusted security' for computation
methods of elliptic curves for cryptography. Three additional "trusted security
acceptance criteria" is proposed to be met by the elliptic curves aimed for
cryptography. Further, two cryptographically secure elliptic curves over 256
bit and 384 bit prime fields are demonstrated which are secure from ECDLP, ECC
as well as trust perspectives. The proposed elliptic curves are successfully
subjected to thorough security analysis and performance evaluation with respect
to key generation and signing/verification and hence, proven for their
cryptographic suitability and great feasibility for acceptance by the
community.Comment: CYBERNETICS AND INFORMATION TECHNOLOGIES, Volume 21, No
IMPLEMENTING ELLIPTIC CURVE CRYPTOGRAPHY ON PC AND SMART CARD
Elliptic Curve Cryptography (ECC) is a relatively new branch of public key
cryptography. Its main advantage is that it can provide the same level of
security as RSA with significantly shorter keys, which is beneficial for a
smart card based implementation. It is also important as a possible alternative
of RSA. This paper presents the author´s research concerning ECC and smart
cards.
The authors introduce their ECC prototype implementation that relies on Java
Card technology and is capable of running on smart cards. Test results with
various cards are attached. It is also analyzed in what extent algorithms with
the complexity of ECC can be executed in smart card environment with limited
resources
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