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Hierarchical ID-Based Cryptography
TLDR
We present hierarchical identity-based encryption schemes and signature schemes that have total collusion resistance on an arbitrary number of levels and that have chosen ciphertext security in the random oracle model assuming the difficulty of Bilinear Diffie-Hellman problem. Expand
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Applications of Multilinear Forms to Cryptography
TLDR
We study the problem of finding efficiently computable non-degenerate multilinear maps from G1 to G2, where G1 and G2 are groups of the same prime order, and where computing discrete logarithms in G1 is hard. Expand
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Torus-Based Cryptography
TLDR
We introduce the concept of torus-based cryptography, give a new public key system called CEILIDH, and compare it to other discrete log based systems including Lucas-based systems and XTR. Expand
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Applications of list decoding to tracing traitors
TLDR
We apply algebraic coding theory to solve problems in cryptography, by using recent results on list decoding of error-correcting codes to efficiently find traitors who collude to create pirates. Expand
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Efficient Traitor Tracing Algorithms Using List Decoding
TLDR
We use powerful new techniques for list decoding errorcorrecting codes to efficiently trace traitors. Expand
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Ranks of elliptic curves
This paper gives a general survey of ranks of elliptic curves over the field of rational numbers. The rank is a measure of the size of the set of rational points. The paper includes discussions ofExpand
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Supersingular Abelian Varieties in Cryptology
TLDR
This paper determines exactly which values can occur as the security parameters of supersingular abelian varieties (in terms of the dimension of the abelIAN variety and the size of the finite field), and gives constructions of supersingsular abeloian varieties that are optimal for use in cryptography. Expand
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Fields of definition for homomorphisms of abelian varieties
We give results on when homomorphisms between abelian varieties are or are not defined over fields obtained from division points on the varieties. For example, if A and B are abelian varietiesExpand
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Corrigendum: Torsion points on abelian varieties of CM-type
© Foundation Compositio Mathematica, 1988, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditionsExpand
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Finding composite order ordinary elliptic curves using the Cocks-Pinch method
TLDR
We apply the Cocks–Pinch method to obtain pairing-friendly composite order groups with prescribed embedding degree associated to ordinary elliptic curves and we show that new security issues arise in the composite order setting. Expand
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