Further Optimizations Sample Clauses

Further Optimizations. Reduced computation costs by precomputing the (r, R)-pairs together with corresponding digital signa- tures. Whenever a device has to change its pair it makes a random selection from the precomputed set. Precomputing saves one multiplication in each proto- col, but is a trade-off between computation and mem- ory costs. • If a mobile device performs ECC operations in hard- ware then we suggest to use binary finite fields F2m In this section we discuss the security of µSTR-H proto- cols with respect to the requirements of Section 2.2. µSTR- H has reduced computation, communication and memory costs compared to STR and is suitable for heterogeneous mobile ad-hoc groups. The computation process of the group key still relies on the tree-based Xxxxxx-Xxxxxxx key exchange method as in STR, except for the difference that mathematical operations are peformed in a subgroup of points <G> of an elliptic curve E over a finite field Fq as p described in Section 3.1, and not in a cyclic group Z∗. We show that security of µSTR-H protocols benefits from the security of STR protocols as proven in [10] and [11]. The computational group key secrecy of STR protocols relies on the hardness of Computational Xxxxxx-Xxxxxxx (CDH) problem, that has also been proven hard in < G > [13]. The decisional group key secrecy of STR protocols relies on the hardness of Decisional Xxxxxx-Xxxxxxx (DDH) prob- lem [2], that has been proven hard in < G > for certain kinds of elliptic curves (non-supersingular and non-trace-2 elliptic curves [9]). Thus, adversary A can neither compute nor distinguish the group key knowing only the public keys and blinded session randoms (note communication broad- cast channel is public). Therefore, a group key can only be discovered if at least one secret value, either any ri or ki is known to A. Due to the hardness of Discrete Logarithm (DL) problem (its ECC counterpart is believed to be even more difficult to solve [13]) adversary is not able to reveal these values from their public values Ri and Ki. In case of backward secrecy we show that any A being a joining member is not able to obtain any of the previous used group keys. Assume, A becomes a new member of the group at position a in P . As a new member A is able to compute all secret keys ki (a ≤ i ≤ n). The sponsor of the addi- tive event changes own rs and causes the change of all ki, s ≤ i ≤ n. Since s < a A can only compute changed se- cret keys, and is therefore not able to compute the previ- ously used ...
Sample 1
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Further Optimizations. Although we have strived to make our protocol as efficient as possible, we have omitted several optimizations in order to simplify the presentation; they are described next. Some of them lead to a more flexible, “pipelined” execution of the protocol steps.
Sample 1

Related to Further Optimizations

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