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PublicKey Cryptosystems Resilient to Key Leakage
"... Most of the work in the analysis of cryptographic schemes is concentrated in abstract adversarial models that do not capture sidechannel attacks. Such attacks exploit various forms of unintended information leakage, which is inherent to almost all physical implementations. Inspired by recent sidec ..."
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Cited by 89 (6 self)
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Most of the work in the analysis of cryptographic schemes is concentrated in abstract adversarial models that do not capture sidechannel attacks. Such attacks exploit various forms of unintended information leakage, which is inherent to almost all physical implementations. Inspired by recent sidechannel 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 publickey encryption, Akavia et al. showed that Regev’s latticebased scheme (STOC ’05) is resilient to any leakage of
A leakageresilient mode of operation
 In EUROCRYPT
, 2009
"... Abstract. A weak pseudorandom function (wPRF) is a pseudorandom functions with a relaxed security requirement, where one only requires the output to be pseudorandom when queried on random (and not adversarially chosen) inputs. We show that unlike standard PRFs, wPRFs are secure against memory attack ..."
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Cited by 76 (5 self)
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Abstract. A weak pseudorandom function (wPRF) is a pseudorandom functions with a relaxed security requirement, where one only requires the output to be pseudorandom when queried on random (and not adversarially chosen) inputs. We show that unlike standard PRFs, wPRFs are secure against memory attacks, that is they remain secure even if a bounded amount of information about the secret key is leaked to the adversary. As an application of this result we propose a simple mode of operation which – when instantiated with any wPRF – gives a leakageresilient streamcipher. Such a cipher is secure against any sidechannel attack, as long as the amount of information leaked per round is bounded, but overall can be arbitrary large. This construction is simpler than the only previous one (DziembowskiPietrzak FOCS’08) as it only uses a single primitive (a wPRF) in a straight forward manner. 1
Separating succinct noninteractive arguments from all falsifiable assumptions
 In Proceedings of the 43rd Annual ACM Symposium on Theory of Computing, STOC ’11
, 2011
"... An argument system (computationally sound proof) for N P is succinct, if its communication complexity is polylogarithmic the instance and witness sizes. The seminal works of Kilian ’92 and Micali ’94 show that such arguments can be constructed under standard cryptographic hardness assumptions with f ..."
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Cited by 75 (4 self)
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An argument system (computationally sound proof) for N P is succinct, if its communication complexity is polylogarithmic the instance and witness sizes. The seminal works of Kilian ’92 and Micali ’94 show that such arguments can be constructed under standard cryptographic hardness assumptions with four rounds of interaction, and that they be made noninteractive in the randomoracle model. The latter construction also gives us some evidence that succinct noninteractive arguments (SNARGs) may exist in the standard model with a common reference string (CRS), by replacing the oracle with a sufficiently complicated hash function whose description goes in the CRS. However, we currently do not know of any construction of SNARGs with a proof of security under any simple cryptographic assumption. In this work, we give a broad blackbox separation result, showing that blackbox reductions cannot be used to prove the security of any SNARG construction based on any falsifiable cryptographic assumption. This includes essentially all common assumptions used in cryptography (oneway functions, trapdoor permutations, DDH, RSA, LWE etc.). More generally, we say that an assumption is falsifiable if it can be modeled as an interactive game between an adversary and an efficient challenger that can efficiently decide if the adversary won the game. This is similar, in spirit, to the notion of falsifiability of Naor ’03, and captures the fact that we can efficiently check if an adversarial strategy breaks the assumption. Our separation result also extends to designated verifier SNARGs, where the verifier needs a trapdoor associated with the CRS to verify arguments, and slightly succinct SNARGs, whose size is only required to be sublinear in the statement and witness size.
From extractable collision resistance to succinct noninteractive arguments of knowledge, and back again
 In Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, ITCS '12
, 2012
"... The existence of noninteractive succinct arguments (namely, noninteractive computationallysound proof systems where the verifier’s time complexity is only polylogarithmically related to the complexity of deciding the language) has been an intriguing question for the past two decades. The question ..."
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Cited by 62 (18 self)
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The existence of noninteractive succinct arguments (namely, noninteractive computationallysound proof systems where the verifier’s time complexity is only polylogarithmically related to the complexity of deciding the language) has been an intriguing question for the past two decades. The question has gained renewed importance in light of the recent interest in delegating computation to untrusted workers. Still, other than Micali’s CS proofs in the Random Oracle Model, the only existing candidate construction is based on an elaborate assumption that is tailored to the specific proposal [Di Crescenzo and Lipmaa, CiE ’08]. We modify and reanalyze that construction: • We formulate a general and relatively mild notion of extractable collisionresistant hash functions (ECRHs), and show that if ECRHs exist then the modified construction is a noninteractive succinct argument (SNARG) for NP. Furthermore, we show that (a) this construction is a proof of knowledge, and (b) it remains secure against adaptively chosen instances. These two properties are arguably essential for using the construction as a delegation of computation scheme. • We show that existence of SNARGs of knowledge (SNARKs) for NP implies existence of ECRHs, as well as extractable variants of some other cryptographic primitives. This provides further evi
Appendonly signatures
 in International Colloquium on Automata, Languages and Programming
, 2005
"... Abstract. The strongest standard security notion for digital signature schemes is unforgeability under chosen message attacks. In practice, however, this notion can be insufficient due to “sidechannel attacks ” which exploit leakage of information about the secret internal state. In this work we pu ..."
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Cited by 53 (10 self)
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Abstract. The strongest standard security notion for digital signature schemes is unforgeability under chosen message attacks. In practice, however, this notion can be insufficient due to “sidechannel attacks ” which exploit leakage of information about the secret internal state. In this work we put forward the notion of “leakageresilient signatures, ” which strengthens the standard security notion by giving the adversary the additional power to learn a bounded amount of arbitrary information about the secret state that was accessed during every signature generation. This notion naturally implies security against all sidechannel attacks as long as the amount of information leaked on each invocation is bounded and “only computation leaks information.” The main result of this paper is a construction which gives a (treebased, stateful) leakageresilient signature scheme based on any 3time signature scheme. The amount of information that our scheme can safely leak per signature generation is 1/3 of the information the underlying 3time signature scheme can leak in total. Signature schemes that remain secure even if a bounded total amount of information is leaked were recently constructed, hence instantiating our construction with these schemes gives the first constructions of provably secure leakageresilient signature schemes. The above construction assumes that the signing algorithm can sample truly random bits, and thus an implementation would need some special hardware (randomness gates). Simply generating this randomness using a leakageresilient streamcipher will in general not work. Our second contribution is a sound general principle to replace uniform random bits in any leakageresilient construction with pseudorandom ones: run two leakageresilient streamciphers (with independent keys) in parallel and then apply a twosource extractor to their outputs. 1
Signature schemes with bounded leakage resilience
 In ASIACRYPT
, 2009
"... A leakageresilient cryptosystem remains secure even if arbitrary, but bounded, information about the secret key (or possibly other internal state information) is leaked to an adversary. Denote the length of the secret key by n. We show a signature scheme tolerating (optimal) leakage of up to n − nǫ ..."
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Cited by 41 (1 self)
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A leakageresilient cryptosystem remains secure even if arbitrary, but bounded, information about the secret key (or possibly other internal state information) is leaked to an adversary. Denote the length of the secret key by n. We show a signature scheme tolerating (optimal) leakage of up to n − nǫ bits of information about the secret key, and a more efficient onetime signature scheme that tolerates leakage of ( 1 4 −ǫ) ·n bits of information about the signer’s entire state. The latter construction extends to give a leakageresilient ttime signature scheme. All these constructions are in the standard model under general assumptions. 1
Provably Secure HigherOrder Masking of AES
 IN CHES 2010, VOLUME 6225 OF LNCS
, 2010
"... Implementations of cryptographic algorithms are vulnerable to Side Channel Analysis (SCA). To counteract it, masking schemes are usually involved which randomize keydependent data by the addition of one or several random value(s) (the masks). When dthorder masking is involved (i.e. when d masks ..."
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Cited by 40 (2 self)
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Implementations of cryptographic algorithms are vulnerable to Side Channel Analysis (SCA). To counteract it, masking schemes are usually involved which randomize keydependent data by the addition of one or several random value(s) (the masks). When dthorder masking is involved (i.e. when d masks are used per keydependent variable), the complexity of performing an SCA grows exponentially with the order d. The design of generic dthorder masking schemes taking the order d as security parameter is therefore of great interest for the physical security of cryptographic implementations. This paper presents the first generic dthorder masking scheme for AES with a provable security and a reasonable software implementation overhead. Our scheme is based on the hardwareoriented masking scheme published by Ishai et al. at Crypto 2003. Compared to this scheme, our solution can be efficiently implemented in software on any generalpurpose processor. This result is of importance considering the lack of solution for d >= 3.
Nonmalleable extractors and symmetric key cryptography from weak secrets
 In Proceedings of the 41stACM Symposium on the Theory of Computing
, 2009
"... We study the question of basing symmetric key cryptography on weak secrets. In this setting, Alice and Bob share an nbit secret W, which might not be uniformly random, but the adversary has at least k bits of uncertainty about it (formalized using conditional minentropy). Since standard symmetrick ..."
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Cited by 36 (11 self)
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We study the question of basing symmetric key cryptography on weak secrets. In this setting, Alice and Bob share an nbit secret W, which might not be uniformly random, but the adversary has at least k bits of uncertainty about it (formalized using conditional minentropy). Since standard symmetrickey primitives require uniformly random secret keys, we would like to construct an authenticated key agreement protocol in which Alice and Bob use W to agree on a nearly uniform key R, by communicating over a public channel controlled by an active adversary Eve. We study this question in the information theoretic setting where the attacker is computationally unbounded. We show that singleround (i.e. one message) protocols do not work when k ≤ n 2, and require poor parameters even when n 2 < k ≪ n. On the other hand, for arbitrary values of k, we design a communication efficient tworound (challengeresponse) protocol extracting nearly k random bits. This dramatically improves the previous construction of Renner and Wolf [RW03], which requires Θ(λ + log(n)) rounds where λ is the security parameter. Our solution takes a new approach by studying and constructing “nonmalleable” seeded randomness extractors — if an attacker sees a random seed X and comes up with an arbitrarily related seed X ′, then we bound the relationship between R = Ext(W; X) and R ′ = Ext(W; X ′). We also extend our tworound key agreement protocol to the “fuzzy ” setting, where Alice and Bob share “close ” (but not equal) secrets WA and WB, and to the Bounded Retrieval Model (BRM) where the size of the secret W is huge.
On cryptography with auxiliary input
 DKL09] [DS05] [FGK+ 10] [FOR12] [GHV10
, 2009
"... We study the question of designing cryptographic schemes which are secure even if an arbitrary function f(sk) of the secret key is leaked, as long as the secret key sk is still (exponentially) hard to compute from this auxiliary input. This setting of auxiliary input is more general than the more tr ..."
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Cited by 33 (4 self)
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We study the question of designing cryptographic schemes which are secure even if an arbitrary function f(sk) of the secret key is leaked, as long as the secret key sk is still (exponentially) hard to compute from this auxiliary input. This setting of auxiliary input is more general than the more traditional setting, which assumes that some of information about the secret key sk may be leaked, but sk still has high minentropy left. In particular, we deal with situations where f(sk) informationtheoretically determines the entire secret key sk. As our main result, we construct CPA/CCA secure symmetric encryption schemes that remain secure with exponentially hardtoinvert auxiliary input. We give several applications of such schemes. • We construct an averagecase obfuscator for the class of point functions, which remains secure with exponentially hardtoinvert auxiliary input, and is reusable. • We construct a reusable and robust extractor that remains secure with exponentially hardtoinvert auxiliary input. Our results rely on a new cryptographic assumption, Learning SubspacewithNoise (LSN), which is related to the well known Learning ParitywithNoise (LPN) assumption.
Vulnerability bounds and leakage resilience of blinded cryptography under timing attacks
 in 2010 IEEE Computer Security Foundations
, 2010
"... Abstract—We establish formal bounds for the number of minentropy bits that can be extracted in a timing attack against a cryptosystem that is protected by blinding, the stateofthe art countermeasure against timing attacks. Compared with existing bounds, our bounds are both tighter and of greater ..."
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Abstract—We establish formal bounds for the number of minentropy bits that can be extracted in a timing attack against a cryptosystem that is protected by blinding, the stateofthe art countermeasure against timing attacks. Compared with existing bounds, our bounds are both tighter and of greater operational significance, in that they directly address the key’s oneguess vulnerability. Moreover, we show that any semantically secure publickey cryptosystem remains semantically secure in the presence of timing attacks, if the implementation is protected by blinding and bucketing. This result shows that, by considering (and justifying) more optimistic models of leakage than recent proposals for leakageresilient cryptosystems, one can achieve provable resistance against sidechannel attacks for standard cryptographic primitives. I.