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Impossibility of Black-Box Simulation Against Leakage Attacks

Rafail Ostrovsky, Giuseppe Persiano

Published Jan 1, 2015• 1 citation
OpenAlex

Abstract

In this work, we show how to use the positive results on succinct argument systems to prove impossibility results on leakage-resilient black-box zero knowledge. This recently proposed notion of zero knowledge deals with an adversary that can make leakage queries on the state of the prover. Our result holds for black-box simulation only and we also give some insights on the non-black-box case. Additionally, we show that, for several functionalities, leakage-resilient multi-party computation is impossible (regardless of the number of players and even if just one player is corrupted). More in details, we achieve the above results by extending a technique of [Nielsen, Venturi, Zottarel – PKC 13] to prove lower bounds for leakage-resilient security. Indeed, we use leakage queries to run an execution of a communication-efficient protocol in the head of the adversary. Moreover, to defeat the black-box simulator we connect the above technique for leakage resilience to security against reset attacks. Our results show that the open problem of [Ananth, Goyal, Pandey – Crypto 14] (i.e., continual leakage-resilient proofs without a common reference string) has a negative answer when security through black-box simulation is desired. Moreover our results close the open problem of [Boyle et al. – STOC 12] for the case of black-box simulation (i.e., the possibility of continual leakage-resilient secure computation without a leak-free interactive preprocessing).

Related papers

Impossibility Results for Leakage-Resilient Zero Knowledge and Multi-Party Computation.

Rafail Ostrovsky, Giuseppe Persiano, Ivan Visconti

In [AGP14] Ananth et al. showed that continual leakage-resilient non-transferable interactive proofs exist when a leak-free input-encoding phase is allowed and a common reference string is available. They left open the problem of removing the need of a common reference string. In [BGJK12] Boyle et al. showed that for some interesting functionalities continual leakage-resilient secure computation is possible when leak-free interactive preprocessing and input-encoding phases are allowed. They left open the problem of removing the interactive pre-processing. In this work we study the above questions. Our main contribution shows that leakage-resilient black-box zero-knowledge is impossible when relying on a leak-free input-encoding phase only (i.e., without CRS/preprocessing). Additionally, we also show that leakage-resilient multi-party computation for all functionalities is impossible (regardless of the number of players assuming just one corrupted player) when relying only on a leak-free input-encoding phase (i.e., without CRS/preprocessing). Our results are achieved by extending a technique of [NVZ13] to prove lower bounds for leakage-resilient security. Indeed as in [NVZ13] we use leakage queries to run an execution of a communication-efficient protocol in the head of the adversary. Moreover, to defeat the black-box simulator we connect the above technique for leakage resilience to security against reset attacks.

•Jan 1, 2014•0 citations

On Non-Black-Box Simulation and the Impossibility of Approximate Obfuscation

Nir Bitansky, Omer Paneth

The introduction of a non-black-box simulation technique by Barak (FOCS 2001) has been a major landmark in cryptography, breaking the previous barriers of black-box impossibility. Barak's technique has given rise to various powerful applications and is a key component in all known protocols with non-black-box simulation. We present the first non-black-box simulation technique that does not rely on Barak's technique (or on nonstandard assumptions). Invoking this technique, we obtain new and improved protocols resilient to various resetting attacks. These improvements include weaker computational assumptions and better round complexity. A prominent feature of our technique is its compatibility with rewinding techniques from classic black-box zero-knowledge protocols. The combination of rewinding with non-black-box simulation has proven instrumental in coping with challenging goals such as simultaneously resettable zero-knowledge, proofs of knowledge, and resettable security from one-way functions. While previous works required tailored modifications to Barak's technique, we give a general recipe for combining our technique with rewinding. This yields simplified resettable protocols in the above settings, as well as improvements in round complexity and required computational assumptions. The main ingredient in our technique is a new impossibility result for general program obfuscation. The results extend the impossibility result of Barak et al. (CRYPTO 2001) to the case of obfuscation with approximate functionality, thus settling a question left open by Barak et al. In the converse direction, we show a generic transformation from any resettably sound zero-knowledge protocol to a family of functions that cannot be obfuscated.

SIAM Journal on Computing•Jan 1, 2015•15 citations

What Information is Leaked under Concurrent Composition

Vipul Goyal, Divya Gupta, Abhishek Jain

A long series of works have established far reaching impossibility results for concurrently secure computation. On the other hand, some positive results have also been obtained according to various weaker notions of security (such as by using a super-polynomial time simulator). This suggest that somehow, “not all is lost in the concurrent setting.” In this work, we ask what and exactly how much private information can an adversary learn by launching a concurrent attack? Inspired by the recent works on leakage-resilient protocols, we consider a security model where the ideal world adversary (a.k.a simulator) is allowed to query the trusted party for some “leakage ” on the honest party inputs. Intuitively, the amount of leakage required by the simulator upper bounds the security loss in the real world. This model generalizes the multiple ideal query model (MIQ) for concurrent security proposed by Goyal, Jain and Ostrovsky [CRYPTO’10]. Positive Results. As our main result, we show, for the first time, how to compute any efficiently computable functionality in the concurrent setting such that full security is guaranteed for “most ” of the sessions. At the heart of this result is a new precise simulation strategy (first

•Jan 1, 2015•2 citations

On Non-Black-Box Simulation and the Impossibility of Approximate Obfuscation

Nir Bitansky, Omer Paneth

Abstract. The introduction of a non-black-box simulation technique by Barak (FOCS 2001) has been a major landmark in cryptography, breaking the previous barriers of black-box impossibility. Barak’s technique has given rise to various powerful applications and it is a key component in all known protocols with non-black-box simulation. We present the first non-black-box simulation technique that does not rely on Barak’s technique (or on non-standard assumptions). Invoking this technique, we obtain new and improved protocols resilient to various resetting attacks. These improvements include weaker computational assumptions and better round complexity. A prominent feature of our technique is its compatibility with rewinding techniques from classic black-box zero-knowledge protocols. The combination of rewinding with non-black-box simulation has proven instrumental in coping with challenging goals as: simultaneously-resettable zero-knowledge, proofs of knowledge, and resettable-security from one-way functions. While previous works required tailored modifications to Barak’s technique, we give a general recipe for combining our technique with rewinding. This yields simplified resettable protocols in the above settings, as well as improvements in round complexity and required computational assumptions. The main ingredient in our technique is a new impossibility result for general program obfuscation. The results extend the impossibility result of Barak et al. (CRYPTO 2001) to the case of obfuscation with approximate function-ality; thus, settling a question left open by Barak et al.. In the converse direction, we show a generic transformation

•Jan 1, 2015•0 citations

Leakage-Resilient Secret Sharing Against Colluding Parties

Ashutosh Kumar, Raghu Meka, Amit Sahai

In this work, we consider the natural goal of designing secret sharing schemes that ensure security against an adversary who may learn some “leaked'' information about all the shares. We say that a secret sharing scheme is p-party leakage-resilient, if the secret remains statistically hidden even after a computationally unbounded adversary learns a bounded amount of leakage, where each bit of leakage adaptively and jointly depends on the shares of an adaptively chosen subset of p parties. Existing multi-party secret sharing schemes (Dziembowski and Pietrzak FOCS 07), (Goyal and Kumar STOC 18) and (Benhamouda, Degwekar, Ishai and Rabin CRYPTO 18) have focused on handling non-adaptive and individual leakage for (limited special cases of) threshold secret sharing schemes. (1) We give an unconditional compiler that transforms any secret sharing scheme on n parties into a p-party leakage-resilient one for p upto O(log n). This yields the first multi-party secret sharing schemes that are secure against adaptive or joint leakage. (2) As a natural extension, we initiate the study of leakage-resilient non-malleable secret sharing. We empower the adversary to adaptively leak from each of the shares and then use the leakage to tamper with all of them arbitrarily and independently. Leveraging our p-party leakage-resilient schemes, we compile any secret sharing scheme into a non-malleable one ensuring that any such tampering either preserves the secret or completely `destroys' it. This improves upon the non-malleable secret sharing scheme of (Goyal and Kumar CRYPTO 18) where no leakage was permitted. Leakage-resilient non-malleable codes can be seen as 2-out-of-2 schemes satisfying our guarantee and have already found many applications in cryptography. (3) Our constructions rely on a clean connection we draw to communication complexity in the well-studied number-on-forehead (NOF) model and rely on functions that have strong communication-complexity lower bounds in the NOF model (in a black-box way). We get efficient p-party leakage-resilient schemes for p upto O(log n) as our share sizes have exponential dependence on p. We observe that improving this exponential dependence, even for simultaneous, non-adaptive leakage, will lead to progress on longstanding open problems in complexity theory.

Annual Symposium on Foundations of Computer Science•Nov 1, 2019•28 citations

Constructing Non-malleable Commitments: A Black-Box Approach

Vipul Goyal, Chen-Kuei Lee, Rafail Ostrovsky +1 more

We propose the first black-box construction of non-malleable commitments according to the standard notion of non-malleability with respect to commitment. Our construction additionally only requires a constant number of rounds and is based only on (black-box use of) one-way functions. Prior to our work, no black-box construction of non-malleable commitments was known (except for relaxed notions of security) in any (polynomial) number of rounds based on any cryptographic assumption. This closes the wide gap existent between black-box and non-black-box constructions for the problem of non-malleable commitments. Our construction relies on (and can be seen as a generalization of) the recent non-malleable commitment scheme of Goyal (STOC 2011). We also show how to get black-box constructions for a host of other cryptographic primitives. We extend our construction to get constant-round concurrent non-malleable commitments, constant-round multi-party coin tossing, and non-malleable statistically hiding commitments (satisfying the notion of non-malleability with respect to opening). All of the mentioned results make only a black-box use of one-way functions. Our primary technical contribution is a novel way of implementing the proof of consistency typically required in the constructions of non-malleable commitments (and other related primitives). We do this by relying on ideas from the ``zero-knowledge from secure multi-party computation" paradigm of Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC 2007). We extend in a novel way this ``computation in the head" paradigm (which can be though of as bringing powerful error-correcting codes into purely computational setting). To construct a non-malleable commitment scheme, we apply our computation in the head techniques to the recent (constant-round) construction of Goyal. Along the way, we also present a simplification of the construction of Goyal where a part of the protocol is implemented in an information theoretic manner. Such a simplification is crucial for getting a black-box construction. This is done by making use of pair wise-independent hash functions and strong randomness extractors. We show that our techniques have multiple applications, as elaborated in the paper. Hence, we believe our techniques might be useful in other settings in future.

Annual Symposium on Foundations of Computer Science•Oct 1, 2012•87 citations
In this work, we show how to use the positive results on succinct argument systems to prove impossibility results on leakage-resilient black-box zero knowledge. This recently proposed notion of zero knowledge deals with an adversary that can make leakage queries on the state of the prover. Our result holds for black-box simulation only and we also give some insights on the non-black-box case. Additionally, we show that, for several functionalities, leakage-resilient multi-party computation is impossible (regardless of the number of players and even if just one player is corrupted). More in details, we achieve the above results by extending a technique of [Nielsen, Venturi, Zottarel – PKC 13] to prove lower bounds for leakage-resilient security. Indeed, we use leakage queries to run an execution of a communication-efficient protocol in the head of the adversary. Moreover, to defeat the black-box simulator we connect the above technique for leakage resilience to security against reset attacks. Our results show that the open problem of [Ananth, Goyal, Pandey – Crypto 14] (i.e., continual leakage-resilient proofs without a common reference string) has a negative answer when security through black-box simulation is desired. Moreover our results close the open problem of [Boyle et al. – STOC 12] for the case of black-box simulation (i.e., the possibility of continual leakage-resilient secure computation without a leak-free interactive preprocessing).
In [AGP14] Ananth et al. showed that continual leakage-resilient non-transferable interactive proofs exist when a leak-free input-encoding phase is allowed and a common reference string is available. They left open the problem of removing the need of a common reference string. In [BGJK12] Boyle et al. showed that for some interesting functionalities continual leakage-resilient secure computation is possible when leak-free interactive preprocessing and input-encoding phases are allowed. They left open the problem of removing the interactive pre-processing. In this work we study the above questions. Our main contribution shows that leakage-resilient black-box zero-knowledge is impossible when relying on a leak-free input-encoding phase only (i.e., without CRS/preprocessing). Additionally, we also show that leakage-resilient multi-party computation for all functionalities is impossible (regardless of the number of players assuming just one corrupted player) when relying only on a leak-free input-encoding phase (i.e., without CRS/preprocessing). Our results are achieved by extending a technique of [NVZ13] to prove lower bounds for leakage-resilient security. Indeed as in [NVZ13] we use leakage queries to run an execution of a communication-efficient protocol in the head of the adversary. Moreover, to defeat the black-box simulator we connect the above technique for leakage resilience to security against reset attacks.
The introduction of a non-black-box simulation technique by Barak (FOCS 2001) has been a major landmark in cryptography, breaking the previous barriers of black-box impossibility. Barak's technique has given rise to various powerful applications and is a key component in all known protocols with non-black-box simulation. We present the first non-black-box simulation technique that does not rely on Barak's technique (or on nonstandard assumptions). Invoking this technique, we obtain new and improved protocols resilient to various resetting attacks. These improvements include weaker computational assumptions and better round complexity. A prominent feature of our technique is its compatibility with rewinding techniques from classic black-box zero-knowledge protocols. The combination of rewinding with non-black-box simulation has proven instrumental in coping with challenging goals such as simultaneously resettable zero-knowledge, proofs of knowledge, and resettable security from one-way functions. While previous works required tailored modifications to Barak's technique, we give a general recipe for combining our technique with rewinding. This yields simplified resettable protocols in the above settings, as well as improvements in round complexity and required computational assumptions. The main ingredient in our technique is a new impossibility result for general program obfuscation. The results extend the impossibility result of Barak et al. (CRYPTO 2001) to the case of obfuscation with approximate functionality, thus settling a question left open by Barak et al. In the converse direction, we show a generic transformation from any resettably sound zero-knowledge protocol to a family of functions that cannot be obfuscated.
A long series of works have established far reaching impossibility results for concurrently secure computation. On the other hand, some positive results have also been obtained according to various weaker notions of security (such as by using a super-polynomial time simulator). This suggest that somehow, “not all is lost in the concurrent setting.” In this work, we ask what and exactly how much private information can an adversary learn by launching a concurrent attack? Inspired by the recent works on leakage-resilient protocols, we consider a security model where the ideal world adversary (a.k.a simulator) is allowed to query the trusted party for some “leakage ” on the honest party inputs. Intuitively, the amount of leakage required by the simulator upper bounds the security loss in the real world. This model generalizes the multiple ideal query model (MIQ) for concurrent security proposed by Goyal, Jain and Ostrovsky [CRYPTO’10]. Positive Results. As our main result, we show, for the first time, how to compute any efficiently computable functionality in the concurrent setting such that full security is guaranteed for “most ” of the sessions. At the heart of this result is a new precise simulation strategy (first
Abstract. The introduction of a non-black-box simulation technique by Barak (FOCS 2001) has been a major landmark in cryptography, breaking the previous barriers of black-box impossibility. Barak’s technique has given rise to various powerful applications and it is a key component in all known protocols with non-black-box simulation. We present the first non-black-box simulation technique that does not rely on Barak’s technique (or on non-standard assumptions). Invoking this technique, we obtain new and improved protocols resilient to various resetting attacks. These improvements include weaker computational assumptions and better round complexity. A prominent feature of our technique is its compatibility with rewinding techniques from classic black-box zero-knowledge protocols. The combination of rewinding with non-black-box simulation has proven instrumental in coping with challenging goals as: simultaneously-resettable zero-knowledge, proofs of knowledge, and resettable-security from one-way functions. While previous works required tailored modifications to Barak’s technique, we give a general recipe for combining our technique with rewinding. This yields simplified resettable protocols in the above settings, as well as improvements in round complexity and required computational assumptions. The main ingredient in our technique is a new impossibility result for general program obfuscation. The results extend the impossibility result of Barak et al. (CRYPTO 2001) to the case of obfuscation with approximate function-ality; thus, settling a question left open by Barak et al.. In the converse direction, we show a generic transformation
In this work, we consider the natural goal of designing secret sharing schemes that ensure security against an adversary who may learn some “leaked'' information about all the shares. We say that a secret sharing scheme is p-party leakage-resilient, if the secret remains statistically hidden even after a computationally unbounded adversary learns a bounded amount of leakage, where each bit of leakage adaptively and jointly depends on the shares of an adaptively chosen subset of p parties. Existing multi-party secret sharing schemes (Dziembowski and Pietrzak FOCS 07), (Goyal and Kumar STOC 18) and (Benhamouda, Degwekar, Ishai and Rabin CRYPTO 18) have focused on handling non-adaptive and individual leakage for (limited special cases of) threshold secret sharing schemes. (1) We give an unconditional compiler that transforms any secret sharing scheme on n parties into a p-party leakage-resilient one for p upto O(log n). This yields the first multi-party secret sharing schemes that are secure against adaptive or joint leakage. (2) As a natural extension, we initiate the study of leakage-resilient non-malleable secret sharing. We empower the adversary to adaptively leak from each of the shares and then use the leakage to tamper with all of them arbitrarily and independently. Leveraging our p-party leakage-resilient schemes, we compile any secret sharing scheme into a non-malleable one ensuring that any such tampering either preserves the secret or completely `destroys' it. This improves upon the non-malleable secret sharing scheme of (Goyal and Kumar CRYPTO 18) where no leakage was permitted. Leakage-resilient non-malleable codes can be seen as 2-out-of-2 schemes satisfying our guarantee and have already found many applications in cryptography. (3) Our constructions rely on a clean connection we draw to communication complexity in the well-studied number-on-forehead (NOF) model and rely on functions that have strong communication-complexity lower bounds in the NOF model (in a black-box way). We get efficient p-party leakage-resilient schemes for p upto O(log n) as our share sizes have exponential dependence on p. We observe that improving this exponential dependence, even for simultaneous, non-adaptive leakage, will lead to progress on longstanding open problems in complexity theory.
We propose the first black-box construction of non-malleable commitments according to the standard notion of non-malleability with respect to commitment. Our construction additionally only requires a constant number of rounds and is based only on (black-box use of) one-way functions. Prior to our work, no black-box construction of non-malleable commitments was known (except for relaxed notions of security) in any (polynomial) number of rounds based on any cryptographic assumption. This closes the wide gap existent between black-box and non-black-box constructions for the problem of non-malleable commitments. Our construction relies on (and can be seen as a generalization of) the recent non-malleable commitment scheme of Goyal (STOC 2011). We also show how to get black-box constructions for a host of other cryptographic primitives. We extend our construction to get constant-round concurrent non-malleable commitments, constant-round multi-party coin tossing, and non-malleable statistically hiding commitments (satisfying the notion of non-malleability with respect to opening). All of the mentioned results make only a black-box use of one-way functions. Our primary technical contribution is a novel way of implementing the proof of consistency typically required in the constructions of non-malleable commitments (and other related primitives). We do this by relying on ideas from the ``zero-knowledge from secure multi-party computation" paradigm of Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC 2007). We extend in a novel way this ``computation in the head" paradigm (which can be though of as bringing powerful error-correcting codes into purely computational setting). To construct a non-malleable commitment scheme, we apply our computation in the head techniques to the recent (constant-round) construction of Goyal. Along the way, we also present a simplification of the construction of Goyal where a part of the protocol is implemented in an information theoretic manner. Such a simplification is crucial for getting a black-box construction. This is done by making use of pair wise-independent hash functions and strong randomness extractors. We show that our techniques have multiple applications, as elaborated in the paper. Hence, we believe our techniques might be useful in other settings in future.