### Abstract

We consider the question of how to store a value secretly on devices that continually leak information about their internal state to an external attacker. If the secret value is stored on a single device from which it is efficiently retrievable, and the attacker can leak even a single predicate of the internal state of that device, then she may learn some information about the secret value itself. Therefore, we consider a setting where the secret value is shared between multiple devices (or multiple components of a single device), each of which continually leaks arbitrary adaptively chosen predicates its individual state. Since leakage is continual, each device must also continually update its state so that an attacker cannot just leak it entirely one bit at a time. In our model, the devices update their state individually and asynchronously, without any communication between them. The update process is necessarily randomized, and its randomness can leak as well. As our main result, we construct a sharing scheme for two devices, where a constant fraction of the internal state of each device can leak in between and during updates. Our scheme has the structure of a public-key encryption, where one share is a secret key and the other is a ciphertext. As a contribution of independent interest, we also get public-key encryption in the continual leakage model, introduced by Brakerski et al. and Dodis et al. (FOCS '10). This scheme tolerates continual leakage on the secret key and the updates, and simplifies the recent construction of Lewko, Lewko and Waters (STOC '11). For our main result, we show how to update the ciphertexts of the encryption scheme so that the message remains hidden even if an attacker interleaves leakage on secret key and ciphertext shares. The security of our scheme is based on the linear assumption in prime-order bilinear groups. We also provide an extension to general access structures realizable by linear secret sharing schemes across many devices. The main advantage of this extension is that the state of some devices can be compromised entirely, while that of the all remaining devices is susceptible to continual leakage. Lastly, we show impossibility of information theoretic sharing schemes in our model, where continually leaky devices update their state individually.

Original language | English (US) |
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Title of host publication | Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 |

Pages | 688-697 |

Number of pages | 10 |

DOIs | |

State | Published - 2011 |

Event | 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 - Palm Springs, CA, United States Duration: Oct 22 2011 → Oct 25 2011 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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ISSN (Print) | 0272-5428 |

### Other

Other | 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 |
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Country | United States |

City | Palm Springs, CA |

Period | 10/22/11 → 10/25/11 |

### ASJC Scopus subject areas

- Computer Science(all)

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## Cite this

*Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011*(pp. 688-697). [6108231] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS). https://doi.org/10.1109/FOCS.2011.35