A large and growing body of research has sought to secure cryptographic systems against physical attacks. Motivated by a large variety of real-world physical attacks on memory, an important line of work was initiated by Akavia, Goldwasser, and Vaikuntanathan [1] where security is sought under the assumptions that: (1) all memory is leaky, and (2) leakage can be an arbitrarily chosen (efficient) function of the memory.#R##N##R##N#However, physical attacks onmemory are not limited to leakagethrough side-channels, but can also include active tampering attacks through a variety of physical attacks, including heat and EM radiation. Nevertheless, protection against the analogous model for tampering - where (1) all memory is tamperable, and (2) where the tampering can be an arbitrarily chosen (efficient) function applied to the memory - has remained an elusive target, despite significant effort on tampering-related questions.#R##N##R##N#In this work, we tackle this question by considering a model where we assume that both of these pairs of statements are true - that all memory is both leaky and (arbitrarily) tamperable. Furthermore, we assume that this leakage and tampering can happen repeatedly and continually (extending the model of [10,7] in the context of leakage). We construct a signature scheme and an encryption scheme that are provably secure against such attacks, assuming that memory can be updated in a randomized fashion between episodes of tampering and leakage. In both schemes we rely on the linear assumption over bilinear groups.#R##N##R##N#We also separately consider a model where only continual and repeated tampering (but only bounded leakage) is allowed, and we are able to obtain positive results assuming only that "self-destruct" is possible, without the need for memory updates.#R##N##R##N#Our results also improve previous results in the continual leakage regime without tampering [10,7]. Whereas previous schemes secure against continual leakage (of arbitrary bounded functions of the secret key), could tolerate only 1/2-e leakage-rate between key updates under the linear assumption over bilinear groups, our schemes can tolerate 1-e leakage-rate between key updates, under the same assumption.
['Yael Tauman Kalai', 'Bhavana Kanukurthi', 'Amit Sahai']
Cryptography with tamperable and leaky memory