D. Coppersmith and M. Jakobsson. Almost optimal hash sequence traversal. In Proceedings of the Fourth Conference on Financial Cryptography (FC '02), Lecture Notes in Computer Science, 2002.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....trade o for back steps as the Ben Amram Petersen algorithm, while supporting simultaneously constant time per forward step. In addition, our algorithm extends to support O(k) time per back step, using memory of size O(kn ) Recently, and independently to our work, Jakobsson and Coppersmith [6, 4] proposed a so called fractal hashing technique that enables backtracking hashchains in O(log n) amortized time using O(log n) memory. Thus, by keeping O(log n) hash values along the hash chain, their algorithms enables, starting at the end of the chain, to get repeatedly the preceding hash value ....

D. Coppersmith and M. Jakobsson. Almost optimal hash sequence traversal. In Fifth Conference on Financial Cryptography, 2002.

....as the Ben Amram Petersen algorithm, while supporting simultaneously constant time per forward step. In addition, our algorithm extends to support O(k) time per back step, using memory of size O(kn ) for every k lg n, Recently, and independently to our work, Jakobsson and Coppersmith [8, 4] proposed a so called fractal hashing technique that enables backtracking hash chains in O(lg n) amortized time using O(lg n) memory. Thus, by keeping O(lg n) hash values along the hash chain, their algorithms 4 enables, starting at the end of the chain, to get repeatedly the preceding hash value ....

....a sequence of back steps only. We rst describe in Section 2.1 algorithms based on skeleton data structures, of which the most advanced supports a sequence of back steps in O(lg n) amortized time per back step, using lg n pebbles. These data structures are similar in nature to the ones used by [1, 8, 4, 5]. A full algorithm must support an arbitrary sequence of forward and backward steps, and we will also be interested in re nements, such as reducing to minimum the number of pebbles. Adapting the skeleton data structures to support the full algorithm and its re nements may be quite complicated, ....

D. Coppersmith and M. Jakobsson. Almost optimal hash sequence traversal. In Fifth Conference on Financial Cryptography, 2002.

....dlog(n)e and space dlog(n)e 1. The technique was named fractal hash chain traversal due to the fractal storage and traversal patterns that it generates along the hash chain. The computational complexity has been further reduced by a factor of 2 in a recent work by Coppersmith and Jakobsson [2], at the price of a slightly more complex protocol than Jakobsson s. It is worth noting that some forward secure signature schemes [5, 7] use a sequence of activations of a one way function (although not necessarily a one way hash function) as a building block. Such schemes may also bene t from ....

....of rounds, where in each round a single (new) hash chain link is output, and some hash function evaluations are performed in preparation for the next rounds. Our requirement is that the number of hash function evaluations per round be bounded by a constant unrelated to n (not even to log(n) as in [6, 2]) This seems like a very natural requirement, especially for applications with harsh timing constraints (e.g. real time systems, heavily loaded servers) Of course, in return to enforcing a constant bound on the computation, such applications must accept some penalty in storage. We present a ....

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D. Coppersmith, and M. Jakobsson. Almost Optimal Hash Sequence Traversal. Proc. of The Fifth Conference on Financial Cryptography (FC'02), Bermuda, March 2002.

....time computes the key to be disclosed from the last key as in the key chain generation. However, this scheme is not scalable in terms of computational costs. Therefore, the size of a key chain impacts both memory requirements and computation costs. To address this issue, Coppersmith and Jakobsson [4] presents an optimization algorithm that can be used to trade storage and computation costs. Their algorithm performs 2 N# hashes per output element, and uses 2 N# memory cells, where the size of each cell is slightly larger than that of a key and N is the length of the key chain. The ....

....key K A (i) that generated A (i, j)#. Then the keys in the key chain A (i 1, j)# are disclosed, and so on. One advantage of this scheme is it allows a low level key chain to be generated on the fly. Note both the high level and the low level key chains can use the optimization scheme in [4] to trade off between storage and computation. 6.3 Supporting Fast Verification Consider the following two scenarios. One is illustrated in Fig. 2, where node E only has node A s first TESLA key which it obtained at the time of node A s join. It moved out of the transmission range of node A ....

D. Coppersmith, M. Jakobsson, Almost Optimal Hash Sequence Traversal, Finanical Cryptography (FC) 02

....authenticate any received value on the one way chain, a node applies this equation to the received value to determine if the computed value matches a previous known authentic key on the chain. Coppersmith and Jakobsson present efficient mechanisms for storing and generating values of hash chains [12]. Each sender pre determines a schedule at which it publishes (or discloses) each key of its one way key chain, in the reverse order from generation; that is, a sender publishes its keys in the order ( A simple key disclosure schedule, for example, would be to publish ....

D. Coppersmith and M. Jakobsson. Almost Optimal Hash Sequence Traversal. In Proceedings of the Fourth Conference on Financial Cryptography (FC '02), Lecture Notes in Computer Science, 2002.

....we store this chain We can either create it all at once and store each element of the chain, or we can just store s # and compute any other element on demand. In practice, a hybrid approach helps to reduce storage with a small recomputation penalty. Jakobsson [19] and Coppersmith and Jakobsson [9] propose a storage efficient mechanism for one way chains: a one way chain with N elements only requires log(N) storage and log(N) computation to access an element. In TESLA, the elements of the one way chain are keys, so we call the chain a one way key chain. Furthermore, any key of the one way ....

D. Coppersmith and M. Jakobsson. Almost optimal hash sequence traversal. In Proceedings of the Fourth Conference on Financial Cryptography (FC '02), Lecture Notes in Computer Science, 2002.

....Update time to log T modular squarings (this still more e#cient than all prior schemes) we can improve the speed of the o# line component of Signing, as further detailed in Section 4. This is a surprising and novel application of the techniques of Jakobsson [Jak02] and Coppersmith and Jakobsson [CJ02] for traversing hash sequences. Our construction was inspired by the work of Song in the area of forward secure Group Signature schemes [Son01] that in turn is based on the ordinary Group Signature scheme by Ateniese, Camenisch, Joye, and Tsudik [ACJT00] Since we do not need many features ....

...., y T , where y T = y and y j 1 = y j mod n. Note that this would be easy if the order of the values was reverse: the signer could just square the previous value each time. The direction we need is harder. This is exactly the problem that Jakobsson [Jak02] and Coppersmith and Jakobsson [CJ02] address, except that they consider any one way (hash) function, whereas we are interested specifically in modular squaring. They show that one can traverse a one way chain by storing a few of its elements and performing a few computations per step. Specifically, the simple algorithm of [Jak02] ....

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Don Coppersmith and Markus Jakobsson. Almost optimal hash sequence traversal. In 6th International Financial Cryptography Conference, March 11--16 2002.

.... 63, 79] server supported non repudiation [3] and for conditional anonymity [28] Hash chains were also used for efficient certificate revocation [57] and to authenticate link state routing updates [ 16, 26, 91] Coppersmith and Jakobsson propose a storage efficient mechanism for one way chains [19]: a one way chain with N elements only requires O(log(N) storage and O(log(N) computation to access an element. Each sender using TESLA for authentication generates a one way key chain, by repeatedly computing a one way hash function H on a randomly chosen key Kv. For example, Kv H[Kv] Kv 2 ....

Don Coppersmith and Markus Jakobsson. Almost optimal hash sequence traversal. In Proceedings of the Fifth Conference on Financial Cryptography (FC '02), February 2002.

....later to be authenticated using keys that have been disclosed earlier, and also allows a node hearing one key to calculate all keys previously disclosed, in case one or more key disclosures were skipped or lost. Coppersmith and Jakobsson propose a storage efficient mechanism for one way chains [10]: a one way chain with N elements only requires O(log(N) storage and O(log(N) computation to access an element. To maintain the security of TESLA, each node needs to know when each key of some other node is scheduled to be disclosed. We achieve this by disclosing keys at regular intervals. ....

Don Coppersmith and Markus Jakobsson. Almost Optimal Hash Sequence Traversal. In Proceedings of the Fifth Conference on Financial Cryptography (FC '02), February 2002.

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D. Coppersmith and M. Jakobsson. Almost optimal hash sequence traversal. In Proceedings of the Fourth Conference on Financial Cryptography (FC '02), Lecture Notes in Computer Science, 2002.

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D. Coppersmith and M. Jakobsson. Almost Optimal Hash Sequence Traversal. In Proceedings of Financial Cryptography, 2002.

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Don Coppersmith and Markus Jakobsson. Almost Optimal Hash Sequence Traversal. In Proceedings of the Fourth Conference on Financial Cryptography (FC '02), Lecture Notes in Computer Science, 2002.

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D. Coppersmith, M. Jakobsson, \Almost Optimal Hash Sequence Traversal", Financial Cryptography, 2002, 102-119

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D. Coppersmith, M. Jakobssony, "Almost Optimal Hash Sequence Traversal". Finacial Cryptography, 2002.

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D. Coppersmith and M. Jakobsson. Almost optimal hash sequence traversal. In Proceedings of the Fourth Conference on Financial Cryptography (FC '02), Springer-Verlag, 2002.

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D. Coppersmith and M. Jakobsson. Almost Optimal Hash Sequence Traversal. In Proceedings of the Fifth Conference on Financial Cryptography (FC '02), 2002.

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D. Coppersmith, M. Jakobsson. Almost Optimal Hash Sequence Traversal. In Finanical Cryptography (FC) 02.

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