## Public-Key Cryptosystems Resilient to Key Leakage

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Citations: | 51 - 6 self |

### BibTeX

@MISC{Naor_public-keycryptosystems,

author = {Moni Naor and Gil Segev},

title = {Public-Key Cryptosystems Resilient to Key Leakage},

year = {}

}

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### Abstract

Most of the work in the analysis of cryptographic schemes is concentrated in abstract adversarial models that do not capture side-channel attacks. Such attacks exploit various forms of unintended information leakage, which is inherent to almost all physical implementations. Inspired by recent side-channel attacks, especially the “cold boot attacks ” of Halderman et al. (USENIX Security ’08), Akavia, Goldwasser and Vaikuntanathan (TCC ’09) formalized a realistic framework for modeling the security of encryption schemes against a wide class of sidechannel attacks in which adversarially chosen functions of the secret key are leaked. In the setting of public-key encryption, Akavia et al. showed that Regev’s lattice-based scheme (STOC ’05) is resilient to any leakage of

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Citation Context ...s is a very natural extension by providing the adversary with access to both a leakage oracle and a decryption oracle. On the theoretical side, we show that the Naor-Yung “double encryption” paradigm =-=[14, 37]-=- can be used as a general transformation from chosen-plaintext security to chosen-ciphertext security in the presence of key leakage. As an immediate corollary of our above-mentioned results, we obtai... |

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Citation Context ...eakage that is sufficiently hard to invert. Specifically, the only modification to the above construction is that the strong extractor Ext(... |

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Citation Context ... internal faults, timing information, and many more. Over the years side-channel attacks exposed crucial vulnerabilities of schemes that are considered secure in the standard model (see, for example, =-=[3, 5, 31, 32]-=-). Countermeasures for protecting against side-channel attacks follow two complementing approaches. The first approach is to make the physical world similar to the standard model by preventing uninten... |

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Citation Context ... computationally indistinguishable, where ... |

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Citation Context ...s is a very natural extension by providing the adversary with access to both a leakage oracle and a decryption oracle. On the theoretical side, we show that the Naor-Yung “double encryption” paradigm =-=[14, 37]-=- can be used as a general transformation from chosen-plaintext security to chosen-ciphertext security in the presence of key leakage. As an immediate corollary of our above-mentioned results, we obtai... |

223 | Differential Fault Analysis of Secret Key Cryptosystems
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Citation Context ... internal faults, timing information, and many more. Over the years side-channel attacks exposed crucial vulnerabilities of schemes that are considered secure in the standard model (see, for example, =-=[3, 5, 31, 32]-=-). Countermeasures for protecting against side-channel attacks follow two complementing approaches. The first approach is to make the physical world similar to the standard model by preventing uninten... |

223 | Lower bounds for discrete logarithms and related problems
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Citation Context ...he place of DDH in groups where DDH is easy (specifically, in bilinear groups). They showed that the hardness of DDH implies that hardness of Linear, but at least in generic groups (see, for example, =-=[28, 45]-=-), Linear remains hard even if DDH is easy. The DDH and Linear assumptions naturally generalize to the family of ... |

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Citation Context ...ameter, let Ext : ... |

196 | On lattices, learning with errors, random linear codes, and cryptography
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Citation Context ...ecret key are leaked in an adaptive fashion, with the only restriction that the total amount of leakage is bounded. Akavia et al. showed that the lattice-based public-key encryption scheme 2of Regev =-=[40]-=- and the identity-based encryption of Gentry, Peikert, and Vaikuntanathan [17] are resilient to such bounded key leakage. Our contributions. In this work we revisit the framework of key-leakage attack... |

193 | Design and analysis of practical public-key encryption schemes secure against chosen ciphertext attack - Cramer, Shoup |

190 | Noninteractive Zero-Knowledge
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Citation Context ...mption (see, for example, [57] for a complete proof). 2.4 Non-Interactive Simulation-Sound Zero-Knowledge Proofs We define the notion of a non-interactive simulation-sound zero-knowledge proof system =-=[11, 12, 36, 73]-=- that is used by our construction in Section 6.1. Definition 2.6. A non-interactive simulation-sound adaptive zero-knowledge proof system for a language L = ∪ n∈N L(n) with a witness relation RL = ∪ n... |

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Citation Context ...mption (see, for example, [57] for a complete proof). 2.4 Non-Interactive Simulation-Sound Zero-Knowledge Proofs We define the notion of a non-interactive simulation-sound zero-knowledge proof system =-=[11, 12, 36, 73]-=- that is used by our construction in Section 6.1. Definition 2.6. A non-interactive simulation-sound adaptive zero-knowledge proof system for a language L = ∪ n∈N L(n) with a witness relation RL = ∪ n... |

156 | Non-malleable non-interactive zero knowledge and adaptive chosen-ciphertext security
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Citation Context ...ove that the resulting CCA-secure scheme is resilient to exactly the same amount of leakage as the underlying CPA-secure scheme. Our construction in this section are based on the refinements of Sahai =-=[43]-=- and Lindell [34] to the encryption schemes of Naor and Yung [37] and Dolev, Dwork and Naor [14]. These refinements enable us to achieve CCA2 security without increasing the size of the secret key. We... |

141 | Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption
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Citation Context ...tion. We present a generic construction of a public-key encryption scheme that is resilient to key leakage from any universal hash proof system, a very useful primitive introduced by Cramer and Shoup =-=[8]-=- for protecting against chosen-ciphertext attacks. The construction does not rely on additional computational assumptions, and the resulting scheme is as efficient as the underlying hash proof system.... |

116 |
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Citation Context ...mption (see, for example, [57] for a complete proof). 2.4 Non-Interactive Simulation-Sound Zero-Knowledge Proofs We define the notion of a non-interactive simulation-sound zero-knowledge proof system =-=[11, 12, 36, 73]-=- that is used by our construction in Section 6.1. Definition 2.6. A non-interactive simulation-sound adaptive zero-knowledge proof system for a language L = ∪ n∈N L(n) with a witness relation RL = ∪ n... |

109 | E.W.: Lest We Remember: Cold Boot Attacks on Encryption Keys
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Citation Context ...on has led to the construction of various cryptographic primitives that are robust to “computational” leakage (see, for example, [16, 20, 36, 38, 39]). Key-leakage attacks. Recently, Halderman et al. =-=[22]-=- presented a suite of attacks that violate the basic assumption underlying the framework of Micali and Reyzin. Halderman et al. showed that, contrary to popular assumptions, a computer’s memory is not... |

104 | Trapdoors for hard lattices and new cryptographic constructions
- Gentry, Peikert, et al.
- 2008
(Show Context)
Citation Context ...e total amount of leakage is bounded. Akavia et al. showed that the lattice-based public-key encryption scheme 2of Regev [40] and the identity-based encryption of Gentry, Peikert, and Vaikuntanathan =-=[17]-=- are resilient to such bounded key leakage. Our contributions. In this work we revisit the framework of key-leakage attacks introduced by Akavia et al. in the setting of public-key encryption. We pres... |

84 | Leakage-resilient cryptography
- Dziembowski, Pietrzak
- 2008
(Show Context)
Citation Context ...age of information in the absence of computation. This assumption has led to the construction of various cryptographic primitives that are resilient to such “computational” leakage (see, for example, =-=[26, 34, 55, 58, 59]-=-). Key-leakage attacks. Recently, Halderman et al. [36] presented a suite of attacks that violate the basic assumption underlying the framework of Micali and Reyzin. Halderman et al. showed that, cont... |

79 | Efficient cryptographic schemes provably as secure as subset sum
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- 1996
(Show Context)
Citation Context ...system [1, 48, 51]). Our approach was also used by Lyubashevsky, Palacio and Segev [53] who constructed a leakageresilient public-key encryption scheme based on the hardness of the subset-sum problem =-=[40]-=-, and by Brakerski and Goldwasser [12] who constructed a leakage-resilient public-key encryption scheme based on the hardness of the quadratic residuosity problem. 1.3 Paper Organization The remainder... |

77 | Conditionally-perfect secrecy and a provably-secure randomized cipher
- Maurer
- 1992
(Show Context)
Citation Context ...ng the decisional Diffie-Hellman (DDH) assumption and its progressively weaker d-Linear 1 The model of Akavia et al. can be viewed as a variant of the bounded-storage and the bounded-retrieval models =-=[63, 32]-=-. These models consider adversaries that may receive a bounded amount of information from a secret state of a system, but also require that the efficiency of systems should be essentially independent ... |

75 | Simultaneous hardcore bits and cryptography against memory attacks
- Akavia, Goldwasser, et al.
- 2009
(Show Context)
Citation Context ...ult), and to reconstruct DES, AES, and RSA keys (see also the improvements and further analysis of Heninger and Shacham [24]). Inspired by the cold boot attacks, Akavia, Goldwasser and Vaikuntanathan =-=[2]-=- formalized a general framework for modeling “memory attacks” in which adversarially chosen functions of the secret key are leaked in an adaptive fashion, with the only restriction that the total amou... |

74 | Private circuits: Securing hardware against probing attacks
- Ishai, Sahai, et al.
- 2003
(Show Context)
Citation Context ...: a deterministic function whose output appears random even if almost all the bits of the input are known (see also the work of Dodis et al. [12] on adaptive security of such functions). Ishai et al. =-=[26, 27]-=- considered the more general problem of protecting privacy in circuits, where the adversary can access a bounded number of wires in the circuit. Ishai et al. proposed several techniques for dealing wi... |

61 | Exposure-Resilient Functions and All-or-Nothing Transform
- Canetti, Dodis, et al.
(Show Context)
Citation Context ...Specifically, in their attack the adversary requests the top n/3 bits of P . This was later improved by Maurer [34] who showed that ɛn questions are sufficient, for any constant ɛ > 0. Canetti et al. =-=[7]-=- introduced the notion of exposure resilient cryptographic primitives, which remain secure even if an adversary is able to learn almost all of the secret key of the primitive. Most notably, they intro... |

58 | Deterministic extractors for bit-fixing sources and exposureresilient cryptography
- Kamp, Zuckerman
- 2003
(Show Context)
Citation Context ...) can identify that the public key was not sampled from its specified distribution. 5a deterministic function whose output appears random even if almost all the bits of the input are known (see also =-=[22, 45]-=-). Ishai et al. [41, 42] considered the seemingly more general problem of protecting privacy in secure computation of circuits, where the adversary can access a bounded number of wires in the circuit.... |

56 | Tag-KEM/DEM: A new framework for hybrid encryption
- Abe, Gennaro, et al.
(Show Context)
Citation Context ...en problem to construct a practical CCA-secure scheme that is resilient to any leakage of ... |

51 | On cryptographic assumptions and challenges
- Naor
- 2003
(Show Context)
Citation Context ...onential security is resilient to a certain amount of key leakage. However, such a sub-exponential hardness assumption does not seem to be “efficiently falsifiable” according to Naor’s classification =-=[56]-=- (that is, if the assumption is false it is not clear that this fact can be demonstrated in polynomial time). Challenge-dependent leakage. In the key-leakage framework that is considered in our work, ... |

50 | A Leakage-Resilient Mode of Operation
- Pietrzak
- 2009
(Show Context)
Citation Context ... no leakage of information in the absence of computation. This assumption has led to the construction of various cryptographic primitives that are robust to “computational” leakage (see, for example, =-=[16, 20, 36, 38, 39]-=-). Key-leakage attacks. Recently, Halderman et al. [22] presented a suite of attacks that violate the basic assumption underlying the framework of Micali and Reyzin. Halderman et al. showed that, cont... |

49 | Circular-secure encryption from decision diffie-hellman
- Boneh, Halevi, et al.
- 2008
(Show Context)
Citation Context ...cryption scheme is then obtained by instantiating our generic construction with this hash proof system. For our second proposal, we show the recent “circular-secure” encryption scheme of Boneh et al. =-=[6]-=- fits into our generic approach using a different hash proof system (that satisfies the same weaker universality property). Chosen-ciphertext security. We extend the framework of key leakage to the se... |

47 | Encryption-scheme security in the presence of key-dependent messages
- Black, Rogaway, et al.
- 2002
(Show Context)
Citation Context ...ed for encrypting sk i+1 mod k , or an encryption clique where each pki is used for encrypting all skj’s. Circular security is a particular form of the more general notion of “key-dependent security” =-=[7]-=- in which an adversary may obtain encryptions of messages that depend on the secret key of the scheme, where the dependency can be chosen adversarially. The scheme of Boneh et al. in fact satisfies th... |

43 | A new paradigm of hybrid encryption scheme
- Kurosawa, Desmedt
- 2004
(Show Context)
Citation Context ...en problem to construct a practical CCA-secure scheme that is resilient to any leakage of L(1 − o(1)) bits (where a possible approach is to examine recent refinements of the Cramer-Shoup cryptosystem =-=[1, 29, 32]-=-). “Weak” key-leakage security. Akavia et al. also considered the following weaker notion of key leakage (which they refer to as “non-adaptive” leakage): a leakage function f with output length λ is c... |

40 | A Simpler Construction of CCA2-Secure Public-Key Encryption Under General Assumptions. Cryptology ePrint Archive, Report 2002/057
- Lindell
- 2002
(Show Context)
Citation Context ...lting CCA-secure scheme is resilient to exactly the same amount of leakage as the underlying CPA-secure scheme. Our construction in this section are based on the refinements of Sahai [43] and Lindell =-=[34]-=- to the encryption schemes of Naor and Yung [37] and Dolev, Dwork and Naor [14]. These refinements enable us to achieve CCA2 security without increasing the size of the secret key. We refer the reader... |

39 | On perfect and adaptive security in exposureresilient cryptography
- Dodis, Sahai, et al.
- 2001
(Show Context)
Citation Context ...hey introduced the notion of an exposure resilient function: a deterministic function whose output appears random even if almost all the bits of the input are known (see also the work of Dodis et al. =-=[12]-=- on adaptive security of such functions). Ishai et al. [26, 27] considered the more general problem of protecting privacy in circuits, where the adversary can access a bounded number of wires in the c... |

38 | Physically observable cryptography
- Micali, Reyzin
- 2004
(Show Context)
Citation Context ...s protecting against side-channel attacks by modeling them, as much as possible, using abstract notions of computation. Physically observable cryptography. In their pioneering work, Micali and Reyzin =-=[36]-=- put forward a comprehensive framework for modeling security against side-channel attacks. Their framework captures any such attack in which leakage of information occurs as a result of computation. T... |

38 | Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems
- Applebaum
- 2009
(Show Context)
Citation Context ... key of the scheme, where the dependency can be chosen adversarially. The scheme of Boneh et al. in fact satisfies this more general notion with respect to the class of all affine functions (see also =-=[7, 17]-=- for additional schemes that are secure against affine functions, and [6, 8, 18] for schemes that are secure against more general classes of functions). 4classes of side-channel attacks. For example,... |

36 | Leakage-resilient signatures
- Faust, Kiltz, et al.
- 2010
(Show Context)
Citation Context ...can obtain bounded leakage information only from the portions of memory that were accessed during that round. Additional work in this model include a leakageresilient signature scheme by Faust et al. =-=[27]-=-, and general leakage-resilient compilers that assume leak-free hardware components by Juma and Vahlis [44] and by Goldwasser and Rothblum [32]. We note that on one hand this framework only imposes a ... |

34 |
Separating Decision Diffie-Hellman from Computational Diffie-Hellman in Cryptographic Groups
- Joux, Nguyen
(Show Context)
Citation Context ...he place of DDH in groups where DDH is easy (specifically, in bilinear groups). They showed that the hardness of DDH implies that hardness of Linear, but at least in generic groups (see, for example, =-=[28, 45]-=-), Linear remains hard even if DDH is easy. The DDH and Linear assumptions naturally generalize to the family of ... |

29 | Intrusion-resilience via the bounded-storage model
- Dziembowski
- 2006
(Show Context)
Citation Context ...ng the decisional Diffie-Hellman (DDH) assumption and its progressively weaker d-Linear 1 The model of Akavia et al. can be viewed as a variant of the bounded-storage and the bounded-retrieval models =-=[63, 32]-=-. These models consider adversaries that may receive a bounded amount of information from a secret state of a system, but also require that the efficiency of systems should be essentially independent ... |

28 | Private circuits II: Keeping secrets in tamperable circuits
- Ishai, Prabhakaran, et al.
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(Show Context)
Citation Context ...: a deterministic function whose output appears random even if almost all the bits of the input are known (see also the work of Dodis et al. [12] on adaptive security of such functions). Ishai et al. =-=[26, 27]-=- considered the more general problem of protecting privacy in circuits, where the adversary can access a bounded number of wires in the circuit. Ishai et al. proposed several techniques for dealing wi... |

26 | One-time programs
- Goldwasser, Kalai, et al.
- 2008
(Show Context)
Citation Context ... no leakage of information in the absence of computation. This assumption has led to the construction of various cryptographic primitives that are robust to “computational” leakage (see, for example, =-=[16, 20, 36, 38, 39]-=-). Key-leakage attacks. Recently, Halderman et al. [22] presented a suite of attacks that violate the basic assumption underlying the framework of Micali and Reyzin. Halderman et al. showed that, cont... |

26 | A Cramer-Shoup encryption scheme from the Linear assumption and from progressively weaker Linear variants. Cryptology ePrint Archive, Report 2007/074
- Shacham
- 2007
(Show Context)
Citation Context ...on does not rely on additional computational assumptions, and the resulting scheme is as efficient as the underlying hash proof system. Existing constructions of hash proof systems (see, for example, =-=[8, 30, 44]-=-) imply that our construction can be based on a variety of number-theoretic assumptions, including the decisional Diffie-Hellman (DDH) assumption and its progressively weaker ... |

26 | Signature schemes with bounded leakage resilience
- Katz, Vaikuntanathan
- 2009
(Show Context)
Citation Context ...sidered in this paper has recently served as a basis for various studies of leakage-resilient cryptographic primitives. Leakage-resilient signature schemes were constructed by Katz and Vaikuntanathan =-=[46]-=-, and by Alwen, Dodis and 6Wichs [4] who constructed also identification schemes and authenticated key-agreement protocols. In addition, Boyle, Segev, and Wichs [11] recently showed that it is possib... |

24 | Leakage-resilient public-key cryptography in the bounded-retrieval model
- Alwen, Dodis, et al.
- 2009
(Show Context)
Citation Context ...erved as a basis for various studies of leakage-resilient cryptographic primitives. Leakage-resilient signature schemes were constructed by Katz and Vaikuntanathan [55], and by Alwen, Dodis and Wichs =-=[4]-=- who constructed also identification schemes and authenticated key-agreement protocols. In addition, Boyle, Segev, and Wichs [16] recently showed that it is possible to construct signature 6schemes i... |

23 |
E cient factoring based on partial information
- Rivest, Shamir
- 1985
(Show Context)
Citation Context ... beyond the scope of this paper to present an exhaustive overview of this ever-growing line of work. We focus here on the results that are most relevant to our work. Already in 1985 Rivest and Shamir =-=[41]-=- introduced a model for leakage attacks in the context of factoring. They considered a scenario in which an adversary is interested in factoring an ... |

23 |
Circular and leakage resilient public-key encryption under subgroup indistinguishability (or: Quadratic residuosity strikes back
- Brakerski, Goldwasser
- 2010
(Show Context)
Citation Context ...also used by Lyubashevsky, Palacio and Segev [53] who constructed a leakageresilient public-key encryption scheme based on the hardness of the subset-sum problem [40], and by Brakerski and Goldwasser =-=[12]-=- who constructed a leakage-resilient public-key encryption scheme based on the hardness of the quadratic residuosity problem. 1.3 Paper Organization The remainder of the paper is organized as follows.... |

22 | Finding collisions on a public road, or do secure hash functions need secret coins
- Hsiao, Reyzin
- 2004
(Show Context)
Citation Context ...versal one-way hash functions should be secure even if the adversary knows the random bits used for generating the description of a function. In general, this is a seemingly stronger requirement (see =-=[25]-=-), but in practice this is not a concern since the universal one-way hash functions can be instantiated with a fixed hash function, such as SHA-256. 8.3 Keys Generated using Weak Random Sources When c... |

20 | Chosen-ciphertext secure key-encapsulation based on gap hashed Diffie-Hellman
- Kiltz
- 2007
(Show Context)
Citation Context ...Linear, but at least in generic groups (see, for example, [28, 45]), Linear remains hard even if DDH is easy. The DDH and Linear assumptions naturally generalize to the family of ... |