<p>In this thesis we present new results in two areas – cryptographic protocols and lattice problems. </p><p>• We present a new protocol for electronic cash which is designed to function on hardware with limited computing power. The scheme has provable security properties and low computational requirements, but it still gives a fair amount of privacy. Another feature of the system is that there is no master secret that could be used for counterfeiting money if stolen. </p><p>• We introduce the notion of hierarchical group signatures. This is a proper generalization of group signatures, which allows multiple group managers organized in a tree with the signers as leaves. For a signer that is a leaf of the subtree of a group manager, the group manager learns which of its children that (perhaps indirectly) manages the signer. We provide definitions for the new notion and construct a scheme that is provably secure given the existence of a family of trapdoor permutations. We also present a construction which is relatively practical, and prove its security in the random oracle model under the strong RSA assumption and the DDH assumption.</p><p>• We show a weakness in the specification for offline capable EMV payment cards. The weakness, which applies to cards without RSA capability, enables an attacker to duplicate a card and make transactions that cannot be tied to the original card.</p><p>• We give a method for approximating any n-dimensional lattice with a lattice Λ whose factor group Z<i>n</i>/Λ has <i>n</i> - 1 cycles of equal length with arbitrary precision. We also show that a direct consequence of this is that the Shortest Vector Problem and the Closest Vector Problem cannot be easier for this type of lattices than for general lattices.</p>
| Identifer | oai:union.ndltd.org:UPSALLA/oai:DiVA.org:kth-151 |
| Date | January 2005 |
| Creators | Trolin, Mårten |
| Publisher | KTH, Numerical Analysis and Computer Science, NADA |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Licentiate thesis, monograph, text |
| Relation | Trita-NA, 0348-2952 ; 0504 |
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