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the security community that allows a client to verify integrity and availability of the data that
she outsourced to an untrusted remove storage server at a relatively low cost. Most recent
solutions to this problem allow the client to read and update (i.e., insert, modify, or delete)
stored data blocks while trying to lower the overhead associated with verifying the integrity
of the stored data. In this work we develop a novel scheme, performance of which favorably
compares with the existing solutions. Our solution enjoys a number of new features such as a
natural support for operations on ranges of blocks, revision control, and support for multiple
user access to shared content. The performance guarantees that we achieve stem from a novel
data structure termed a balanced update tree and removing the need to verify update operations.
The discrete logarithm problem is the basic ingredient of many\r\n public-key cryptosystems. It can be stated as follows: Given a\r\n cyclic group (G,?) of order n, a\r\n generator g of G, and another\r\n element h?G, find the unique\r\n integer a?[0,n) such that\r\n h=gˆa. The integer a is called\r\n the discrete logarithm of\r\n h to the base g.\r\n \r\n
There are key agreement protocols, public-key encryption schemes,\r\n and digital signatures employing the discrete logarithm problem.\r\n One example is the Diffie-Hellman key agreement protocol. It allows\r\n two parties, A and B, to agree on a secret key over an insecure\r\n channel. In order to achieve this goal they fix a finite cyclic\r\n group G and a generator g of G. Then A and B\r\n pick random integers a,b respectively and exchange\r\n hA=gˆa\r\n and hB=gˆb. Finally they\r\n compute hBˆa=gˆba\r\n and hAˆb=gˆab, and\r\n since gˆab=gˆba this element\r\n can be used as their secret key.\r\n\r\n
It is clear that solving the underlying discrete logarithm problem\r\n is sufficient for breaking the Diffie-Hellman protocol. For this\r\n reason one has been searching for groups in which the discrete\r\n logarithm problem is considered to be a computationally hard\r\n problem. Among the groups that have been proposed as candidates are\r\n the multiplicative group of a finite field and the group over an\r\n elliptic curve. It should however be pointed out that the\r\n infeasibility of the discrete logarithm problem has not been proved\r\n in any concrete group.
Discrete logarithm based cryptosystems can be generalized in the\r\n framework of semigroup actions (see e.[...]
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