Abstract
Erasable memory is an important resource for designing practical cryptographic protocols that are secure against adaptive attacks. Many practical memory devices such as solid state drives, hard disks, or file systems are not perfectly erasable because a deletion operation leaves traces of the deleted data in the system. A number of methods for constructing a large erasable memory from a small one, e.g., using encryption, have been proposed. Despite the importance of erasable memory in cryptography, no formal model has been proposed that allows one to formally analyse such memory constructions or cryptographic protocols relying on erasable memory.
The contribution of this paper is three-fold. First, we provide a formal model of erasable memory. A memory device allows a user to store, retrieve, and delete data, and it is characterised by a leakage function defining the extent to which erased data is still accessible to an adversary.
Second, we investigate how the erasability of such memories can be amplified. We provide a number of constructions of memories with strong erasability guarantees from memories with weaker guarantees. One of these constructions of perfectly erasable memories from imperfectly erasable ones can be considered as the prototypical application of Canetti et al.’s All-or-Nothing Transform (AoNT). Motivated by this construction, we propose some new and better AoNTs that are either perfectly or computationally secure. These AoNTs are of possible independent interest.
Third, we show (in the constructive cryptography framework) how the construction of erasable memory and its use in cryptographic protocols (for example to achieve adaptive security) can naturally be composed to obtain provable security of the overall protocol.
The first and second author were supported by the European Commission through the Seventh Framework Programme under the ERC grant #321310 (PERCY) and the third author was supported by the Zurich Information Security & Privacy Center (ZISC).
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Notes
- 1.
In this paper, we chose to consider monotone \(\rho \)’s. We chose to model the memory resource in such a way that it only responds on the same interface it was activated, hence it is not possible for the adversary to be notified of an event that causes the memory to become readable. To simplify the modelling of simulators, we consider the adversary to be eager and trying to read the memory as soon as possible and then placing the resulting data in an “intermediate buffer” that can then be collected through the Eve-interface at a later point.
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Camenisch, J., Enderlein, R.R., Maurer, U. (2016). Memory Erasability Amplification. In: Zikas, V., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2016. Lecture Notes in Computer Science(), vol 9841. Springer, Cham. https://doi.org/10.1007/978-3-319-44618-9_6
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