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

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

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

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

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 of… Expand

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

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 varieties… Expand

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