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The paradigm of partial erasures

Shafi Goldwasser, Ran Canetti, Dah-Yoh Lim

Published Jan 1, 2008• 1 citation
OpenAlex

Abstract

This thesis is a study of erasures in cryptographic protocols. Erasing old data and keys is an important capability of honest parties in cryptographic protocols. It is useful in many settings, including proactive security in the presence of a mobile adversary, adaptive security in the presence of an adaptive adversary, forward security, and intrusion resilience. Some of these settings, such as achieving proactive security, is provably impossible without some form of erasures. Other settings, such as designing protocols that are secure against adaptive adversaries, are much simpler to achieve when erasures are allowed. Protocols for all these contexts typically assume the ability to perfectly erase information. Unfortunately, as amply demonstrated in the systems literature, perfect erasures are hard to implement in practice. We propose a model of imperfect or partial erasures where erasure instructions are only partially effective and leave almost all the data intact, thus giving the honest parties only a limited capability to dispose old data. Nonetheless, we show how to design protocols for all of the above settings (including proactive security, adaptive security, forward security, and intrusion resilience) for which this weak form of erasures suffices. We do not have to invent entirely new protocols, but rather show how to automatically modify protocols relying on perfect erasures into ones for which partial erasures suffices. Stated most generally, we provide a compiler that transforms any protocol relying on perfect erasures for security into one with the same functionality that remains secure even if the erasures are only partial. The key idea is a new redundant representation of secret data which can still be computed on, and yet is rendered useless when partially erased. We prove that any such compiler must incur a cost in additional storage, and that our compiler is near optimal in terms of its storage overhead. We also give computationally more efficient compilers for a number of special cases: (1) when all the computations on secrets can be done in constant parallel time (NC0); (2) for a class of proactive secret sharing protocols where we leave the protocol intact except for changing the representation of the shares of the secret and the instructions that modify the shares (to correspondingly modify the new representation instead). (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

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This thesis is a study of erasures in cryptographic protocols. Erasing old data and keys is an important capability of honest parties in cryptographic protocols. It is useful in many settings, including proactive security in the presence of a mobile adversary, adaptive security in the presence of an adaptive adversary, forward security, and intrusion resilience. Some of these settings, such as achieving proactive security, is provably impossible without some form of erasures. Other settings, such as designing protocols that are secure against adaptive adversaries, are much simpler to achieve when erasures are allowed. Protocols for all these contexts typically assume the ability to perfectly erase information. Unfortunately, as amply demonstrated in the systems literature, perfect erasures are hard to implement in practice.
We propose a model of imperfect or partial erasures where erasure instructions are only partially effective and leave almost all the data intact, thus giving the honest parties only a limited capability to dispose old data. Nonetheless, we show how to design protocols for all of the above settings (including proactive security, adaptive security, forward security, and intrusion resilience) for which this weak form of erasures suffices.
We do not have to invent entirely new protocols, but rather show how to automatically modify protocols relying on perfect erasures into ones for which partial erasures suffices. Stated most generally, we provide a compiler that transforms any protocol relying on perfect erasures for security into one with the same functionality that remains secure even if the erasures are only partial. The key idea is a new redundant representation of secret data which can still be computed on, and yet is rendered useless when partially erased. We prove that any such compiler must incur a cost in additional storage, and that our compiler is near optimal in terms of its storage overhead.
We also give computationally more efficient compilers for a number of special cases: (1) when all the computations on secrets can be done in constant parallel time (NC0); (2) for a class of proactive secret sharing protocols where we leave the protocol intact except for changing the representation of the shares of the secret and the instructions that modify the shares (to correspondingly modify the new representation instead). (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)
In the setting of multiparty computation a set of parties with private inputs wish to compute some joint function of their inputs, whilst preserving certain security properties (like privacy and correctness). An adaptively secure protocol is one in which the security properties are preserved even if an adversary can adaptively and dynamically corrupt parties during a computation. This provides a high level of security, that is arguably necessary in today’s world of active computer break-ins. Until now, the work on adaptively secure multiparty computation has focused almost exclusively on the setting of an honest majority, and very few works have considered the honest minority and two-party cases. In addition, significant computational and communication costs are incurred by most protocols that achieve adaptive security. In this work, we consider the two-party setting and assume that honest parties may erase data. We show that in this model it is possible to securely compute any two-party functionality in the presence of adaptive semi-honest adversaries. Furthermore, our protocol remains secure under concurrent general composition (meaning that it remains secure irrespective of the other protocols running together with it). Our protocol is based on Yao’s garbled-circuit construction and, importantly, is as efficient as the analogous protocol for static corruptions. We argue that the model of adaptive corruptions with erasures has been unjustifiably neglected and that it deserves much more attention. 1
Adaptive security is a strong corruption model that captures "hacking" attacks where an external attacker breaks into parties' machines in the midst of a protocol execution. There are two types of adaptively-secure protocols: adaptive with erasures and adaptive without erasures. Achieving adaptivity without erasures is preferable, since secure erasures are not always trivial. However, it seems far harder. We introduce a new model of adaptive security called adaptive security with partial erasures that allows erasures, but only assumes them in a minimal sense. Specifically, if all parties are corrupted then security holds as long as any single party successfully erases. In addition, security holds if any proper subset of the parties is corrupted without erasures. We initiate a theoretical study of this new notion and demonstrate that secure computation in this setting is as efficient as static secure computation. In addition, we study the relations between semi-adaptive security [GWZ09], adaptive security with partial erasures, and adaptive security without any erasures. We prove that the existence of semi-adaptive OT implies secure computation in all these settings.
Cryptographic protocols, though used in a wide range of everyday tasks, are typically built for certain unrealistic ideal conditions in which the user is assumed to work. For example, one such condition that is implicitly assumed is that the user has perfect randomness that she can use as her cryptographic secret key. Another commonly made assumption is that the user runs her cryptographic tasks (such as encryption) on a device that is perfectly secure; that is, its internals are not tampered with or even observed by an adversary. In this thesis, we focus on designing cryptographic techniques that are secure under less-than-ideal conditions. In order to remove the assumption that users share perfectly random secret keys, we study the problem of privacy amplification: key agreement between two parties who both know a weak secret w, such as a password. The goal of the protocol is to convert this non-uniform secret w into a uniformly distributed string R that is fully secret from the adversary. R may then be used as a key for running symmetric cryptographic protocols (such as encryption or authentication). Because we make no computational assumptions, the entropy in R can come only from w. Thus such a protocol must minimize the entropy loss during its execution, so that R is as long as possible. In this thesis, we present the first protocol for information-theoretic key agreement that has entropy loss linear in the security parameter. The result is optimal up to constant factors. We also extend our results to the case where the users share correlated secrets w and w' . This setting occurs, for example, when the secrets are biometric readings taken at different points of time and is more generally known as information-reconciliation.
Adaptive security is a strong corruption model that captures “hacking ” attacks where an external attacker breaks into parties ’ machines in the midst of a protocol execution. There are two types of adaptively-secure protocols: adaptive with erasures and adaptive without erasures. Achieving adaptivity without erasures is preferable, since secure erasures are not always trivial. However, it seems far harder. We introduce a new model of adaptive security called adaptive security with partial erasures that allows erasures, but only assumes them in a minimal sense. Specifically, if all parties are corrupted then security holds as long as any single party successfully erases. In addition, security holds if any proper subset of the parties is corrupted without erasures. We initiate a theoretical study of this new notion and demonstrate that secure computation in this setting is as efficient as static secure computation. In addition, we study the relations between semi-adaptive security [GWZ09], adaptive security with partial erasures, and adaptive security without any erasures. We prove that the existence of semi-adaptive OT implies secure computation in all these settings.
In this thesis we are interested in practical cryptographic protocols that give strong security guarantees.This means that the protocols must remain secure in arbitrary contexts and against adversaries who adaptively attack these protocols during their execution, that they must have realistic prerequisites (setup assumptions, required resources), and that they be efficient enough to be used in a practical setting.The former can be achieved by designing the protocols in a security composition framework, however simultaneously making them practical is challenging.The goal of this thesis is to simplify the design of adaptively secure and practical protocols.To that effect, we first design two protocols that satisfy the above properties, and thereby uncover design principles that make it easier to achieve the goal.These protocols, and many other adaptively secure protocols in the literature, assume the existence of perfectly erasable memory.This is not always available in practice: we therefore also study imperfectly erasable memory and how it can be improved.Finally, we have noticed that there were problems with the existing composition frameworks in which we designed our protocols: we have extended the basic IITM framework to provide a sound and unambiguous framework for future protocol design.
Traditional modern cryptography relies on unproven complexity assumptions that certain problems, such as integer factorization, are computationally hard, and the adversary is bounded in computing power. However, advances in algorithms and computing technology may render current cryptosystems insecure, and lead to the decryption of past secret messages. On the other hand, Shannon's pessimistic negative result essentially implies that if the adversary is all-powerful and has complete access to the communication line, then efficient practical solutions for information-theoretic security do not exist. This thesis is a study of cryptography in the bounded storage model, where provable everlasting security can be achieved efficiently without any complexity assumption. It first presents an efficient scheme for encryption and authentication that is provably secure against strong adaptive attacks, by an adversary who is computationally unbounded and only storage-bounded. A major new result is that the shared secret key employed by the sender and the receiver can be re-used to send an exponential number of messages. Our encryption scheme further enjoys the surprising property that even if the secret key is captured by the adversary after the transmission of the ciphertext, the secrecy of the message is assured. The above is joint work with Michael Rabin. Oblivious transfer is a cryptographic protocol that can serve as a basic primitive for all of cryptography. This thesis presents an implementation of oblivious transfer in the bounded storage model, which is again provably secure without complexity assumption.