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981
IdentityBased Encryption from the Weil Pairing
, 2001
"... We propose a fully functional identitybased encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational DiffieHellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic ..."
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Cited by 1699 (29 self)
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We propose a fully functional identitybased encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational DiffieHellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic curves is an example of such a map. We give precise definitions for secure identity based encryption schemes and give several applications for such systems.
SUPERSINGULAR SCATTERING
, 2000
"... Abstract: In ’supersingular ’ scattering the potential g2UA(r) involves a variable nonlinear parameter A upon the increase of which the potential also increases beyond all limits everywhere off the origin and develops a uniquely high level of singularity in the origin. The problem of singular scatte ..."
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Abstract: In ’supersingular ’ scattering the potential g2UA(r) involves a variable nonlinear parameter A upon the increase of which the potential also increases beyond all limits everywhere off the origin and develops a uniquely high level of singularity in the origin. The problem of singular
Efficient Pairing Computation on Supersingular Abelian Varieties
 Designs, Codes and Cryptography
, 2004
"... We present a general technique for the efficient computation of pairings on supersingular Abelian varieties. As particular cases, we describe efficient pairing algorithms for elliptic and hyperelliptic curves in characteristic 2. The latter is faster than all previously known pairing algorithms, and ..."
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Cited by 176 (25 self)
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We present a general technique for the efficient computation of pairings on supersingular Abelian varieties. As particular cases, we describe efficient pairing algorithms for elliptic and hyperelliptic curves in characteristic 2. The latter is faster than all previously known pairing algorithms
An example of double confluent Heun equation: Schrödinger equation with supersingular plus Coulomb potential
, 2009
"... A recently proposed algorithm to obtain global solutions of the double confluent Heun equation is applied to solve the quantum mechanical problem of finding the energies and wave functions of a particle bound in a potential sum of a repulsive supersingular term, A r −4, plus an attractive Coulombian ..."
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A recently proposed algorithm to obtain global solutions of the double confluent Heun equation is applied to solve the quantum mechanical problem of finding the energies and wave functions of a particle bound in a potential sum of a repulsive supersingular term, A r −4, plus an attractive
Explicit parameterizations of ordinary and supersingular regions of
 X0(pn), Modular Curves and Abelian Varieties (Barcelona, 2002), 165–179, Prog. Math
, 2004
"... Abstract. In this paper, we explore the geometry of the modular curves X0(p n), over Cp in a few nontrivial examples. In particular, we give explicit rigidanalytic parameterizations of the ordinary and supersingular regions. This is done by first building towers of models for X0(p i), 0 ≤ i ≤ n, an ..."
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Cited by 3 (3 self)
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Abstract. In this paper, we explore the geometry of the modular curves X0(p n), over Cp in a few nontrivial examples. In particular, we give explicit rigidanalytic parameterizations of the ordinary and supersingular regions. This is done by first building towers of models for X0(p i), 0 ≤ i ≤ n
Evaluation of supersingular integrals: second order boundary derivatives
 Int. J. Numer. Meth. Engrg., xx
"... The boundary integral representation of secondorder derivatives of the primary function involves secondorder (hypersingular) and thirdorder (supersingular) derivatives of the Green’s function. By defining these highly singular integrals as a difference of boundary limits, interior minus exterior, ..."
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Cited by 1 (1 self)
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The boundary integral representation of secondorder derivatives of the primary function involves secondorder (hypersingular) and thirdorder (supersingular) derivatives of the Green’s function. By defining these highly singular integrals as a difference of boundary limits, interior minus exterior
Explicit Generators for Endomorphism Rings of Supersingular Elliptic Curves
, 2004
"... Let p be a prime, and let E/Fp2 be a supersingular elliptic curve. Then it is straightforward to show that EndF̄p(E) is isomorphic to a maximal order within Qp,∞, the unique quaternion algebra ramified precisely at p and ∞. In fact, it is a wellknown result of Deuring that this defines a 1: 1 corre ..."
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Let p be a prime, and let E/Fp2 be a supersingular elliptic curve. Then it is straightforward to show that EndF̄p(E) is isomorphic to a maximal order within Qp,∞, the unique quaternion algebra ramified precisely at p and ∞. In fact, it is a wellknown result of Deuring that this defines a 1: 1
A ForwardSecure PublicKey Encryption Scheme
, 2003
"... Cryptographic computations are often carried out on insecure devices for which the threat of key exposure represents a serious and realistic concern. In an e#ort to mitigate the damage caused by exposure of secret data (e.g., keys) stored on such devices, the paradigm of forward security was int ..."
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Cited by 251 (14 self)
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Cryptographic computations are often carried out on insecure devices for which the threat of key exposure represents a serious and realistic concern. In an e#ort to mitigate the damage caused by exposure of secret data (e.g., keys) stored on such devices, the paradigm of forward security was introduced. In a forwardsecure scheme, secret keys are updated at regular periods of time; furthermore, exposure of a secret key corresponding to a given time period does not enable an adversary to "break" the scheme (in the appropriate sense) for any prior time period.
Results 1  10
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981