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abelian varieties and whose edges are isogenies between these varieties. In
his thesis, Kohel described the structure of isogeny graphs for elliptic
curves and showed that one may compute the endomorphism ring of an elliptic
curve defined over a finite field by using a depth first search algorithm
in the graph. In dimension 2, the structure of isogeny graphs is less understood and existing algorithms for computing endomorphism rings are very expensive.
Our setting considers genus 2 jacobians with complex multiplication,
with the assumptions that the real multiplication subring is maximal and
has class number one. We fully describe the isogeny graphs in that
Over finite fields, we derive a depth first search algorithm for computing endomorphism rings locally at prime numbers, if the real multiplication is maximal. To the best of our knowledge, this is the first DFS-based algorithm in genus 2.
In this paper, we propose an efficient SUE scheme and its extended schemes. First, we propose an SUE scheme with short public parameters in prime-order bilinear groups and prove its security under a $q$-type assumption. Next, we extend our SUE scheme to a time-interval SUE (TI-SUE) scheme that supports a time interval in ciphertexts. Our TI-SUE scheme has short public parameters and also secure under the $q$-type assumption. Finally, we propose the first large universe RS-ABE scheme with short public parameters in prime-order bilinear groups and prove its security in the selective revocation list model under a $q$-type assumption.
With ORAM, a curious adversary cannot tell what data address the user is accessing when observing the bits moving between the user and the storage system.
All existing ORAM schemes achieve obliviousness by adding redundancy to the storage system, i.e., each access is turned into multiple random accesses.
Such redundancy incurs a large performance overhead.
Though traditional data prefetching techniques successfully hide memory latency in DRAM based systems, it turns out that they do not work well for ORAM.
In this paper, we exploit ORAM locality by taking advantage of the ORAM internal structures.
Though it might seem apparent that obliviousness and locality are two contradictory concepts, we challenge this intuition by exploiting data locality in ORAM without sacrificing provable security.
In particular, we propose an ORAM prefetching technique called dynamic super block scheme and comprehensively explore its design space.
The dynamic super block scheme detects data locality in the program\'s working set at runtime, and exploits the locality in a data-independent way.
% based on the key observation that position map ORAMs have better locality than the data ORAM.
Our simulation results show that with dynamic super block scheme, ORAM performance without super blocks can be significantly improved. After adding timing protection to ORAM, the average performance gain is 25.5\\% (up to 49.4\\%) over the baseline ORAM and 16.6\\% (up to 30.1\\%) over the best ORAM prefetching technique proposed previously.
Next we identify an optimal security notion for EFSE. We demonstrate that existing schemes do not meet our security definition and propose a new scheme that we prove secure under basic assumptions. Unfortunately, the scheme requires large ciphertext length, but we show that, in a sense, this space-inefficiency is unavoidable for a general, optimally-secure scheme.
Seeking the right balance between efficiency and security, we then show how to construct schemes that are more efficient and satisfy a weaker security notion that we propose. To illustrate, we present and analyze a more space-efficient scheme for supporting fuzzy search on biometric data that achieves the weaker notion.