International Association for Cryptologic Research

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2013-10-24
09:17 [Pub][ePrint]

Let $E_p$ be an elliptic curve over a prime finite field $\\Fp$, $p\\ge5$, and $P_p,Q_p\\in E_p(\\Fp)$. The elliptic curve discrete logarithm problem, ECDLP, on $E_p$ is to find $m_p\\in\\mathbb{F}_p^{\\times}$ such that $Q_p=m_p P_p$ if $Q_p\\in\\langle P_p\\rangle$. We propose an algorithm to attack the ECDLP relying on a Hasse principle detecting linear dependence in Mordell-Weil groups of elliptic curves via a finite number of reductions.

09:17 [Pub][ePrint]

While multiparty computations are becoming more and more efficient, their performance has not reached the needed level to be widely deployed for many applications. Nevertheless, the heterogeneous environment of modern computing needs this functionality to provide users their right to privacy. For a wide range of applications there is no need for complex computations, operations such as multiplication or addition might be sufficient. In this work we introduce the concepts of Anonymous Aggregation and Anonymous Aggregators, two lightweight cryptographic primitives that can perform specific private computations efficiently in restricted environments.

09:17 [Pub][ePrint]

Groth-Sahai proofs are efficient non-interactive zero-knowledge proofs that have found widespread use in pairing-based cryptography. We propose efficiency improvements of Groth-Sahai proofs in the SXDH setting, which is the one that yields the most efficient non-interactive zero-knowledge proofs.

- We replace some of the commitments with ElGamal encryptions, which reduces the prover\'s computation and for some types of equations reduces the proof size.

- Groth-Sahai proofs are zero-knowledge when no public elements are paired to each other. We observe that they are also zero-knowledge when base elements for the groups are paired to public constants.

- The prover\'s computation can be reduced by letting her pick her own common reference string. By giving a proof she has picked a valid common reference string this does not compromise soundness.

- We define a type-based commit-and-prove scheme, which allows commitments to be reused in many different proofs.

09:17 [Pub][ePrint]

SIMON [3] is a family of lightweight block ciphers which has been recently proposed by U.S National Security Agency (NSA). Although the original proposal does not include any detailed security analysis but several detailed analysis has been published on this recently [1,2].

In this paper we investigate the security of this family of block ciphers against linear cryptanalysis. We present several linear characteristics for all variants of SIMON. Our best linear

characteristic covers SIMON 32/64 reduced to 13 rounds out of 32 rounds with the bias $2^{-16}. In addition we present attacks for the round reduced variants of SIMON48/96, SIMON64/128, SIMON96/144 and SIMON128/256. Our results are the best known results on linear cryptanalysis for any variant of SIMON. 09:17 [Pub][ePrint] The anonymous communication (AC) protocol Tor constitutes the most widely deployed technology for providing anonymity for user communication over the Internet. Tor has been subject to several analyses which have shown strong anonymity guarantees for Tor. However, all previous analyses ignore time-sensitive leakage: timing patterns in web traffic allow for attacks such as website fingerprinting and traffic correlation, which completely break the anonymity provided by Tor. For conducting a thorough and comprehensive analysis of Tor that in particular includes all of these time-sensitive attacks, one of the main obstacles is the lack of a rigorous framework that allows for a time-sensitive analysis of complex AC protocols. In this work, we present TUC (for Time-sensitive Universal Composability): the first universal composability framework that includes a comprehensive notion of time, which is suitable for and tailored to the demands of analyzing AC protocols. As a case study, we extend previous work and show that the onion routing (OR) protocol, which underlies Tor, can be securely abstracted in TUC, i.e., all time-sensitive attacks are reflected in the abstraction. We finally leverage our framework and this abstraction of the OR protocol to formulate a countermeasure against website fingerprinting attacks and to prove this countermeasure secure. 09:17 [Pub][ePrint] In this note we revisit the problem of obfuscation with auxiliary inputs. We show that the existence of indistinguishablity obfuscation (iO) implies that all functions with sufficient \"pseudo-entropy\" cannot be obfuscated with respect to a virtual box definition (VBB) in the presence of (dependent) auxiliary input. Namely, we show that for any candidate obfuscation O and for any function family F={f_s} with sufficient pseudo-entropy, there exists an (efficiently computable) auxiliary input aux, that demonstrates the insecurity of O. This is true in a strong sense: given O(f_s) and aux one can efficiently recover the seed s, whereas given aux and oracle access to f_s it is computationally hard to recover s. A similar observation was pointed out in a recent work of Goldwasser et. al. (Crypto 2013), assuming *extractable* witness encryption. In this note we show that the extractability property of the witness encryption is not needed to get our negative result, and all that is needed is the existence of witness encryption, which in turn can be constructed from iO obfuscation. 09:17 [Pub][ePrint] Despite all the research efforts made so far, the design of protocols for password-authenticated key exchange (PAKE) still remains a non-trivial task. One of the major challenges in designing such protocols is to protect low-entropy passwords from the notorious dictionary attacks. In this work, we revisit Abdalla and Pointcheval\'s three-party PAKE protocol presented in Financial Cryptography 2005, and demonstrate that the protocol is vulnerable to an off-line dictionary attack whereby a malicious client can find out the passwords of other clients. 09:17 [Pub][ePrint] This note describes a Diffie-Hellman oracle, constructed using standard Trusted Platform Module (TPM) signature APIs. The oracle allows one to compute the exponentiation of an arbitrary group element to a specified TPM-protected private key. By employing the oracle, the security provided by a group of order p is reduced by log k bits, provided k oracle queries are made and p +/- 1 is divisible by k. The security reduction follows from a straightforward application of results from Brown and Gallant (IACR ePrint 2004/306) and Cheon (Eurocrypt 2006) on the strong Diffie-Hellman problem. On a more positive note, the oracle may allow a wider range of cryptographic protocols to make use of the TPM. 09:17 [Pub][ePrint] An evasive circuit family is a collection of circuits C such that for every input x, a random circuit from C outputs 0 on x with overwhelming probability. We provide a combination of definitional, constructive, and impossibility results regarding obfuscation for evasive functions: - The (average case variants of the) notions of virtual black box obfuscation (Barak et al, CRYPTO \'01) and virtual gray box obfuscation (Bitansky and Canetti, CRYPTO \'10) coincide for evasive function families. We also define the notion of input-hiding obfuscation for evasive function families, stipulating that for a random c \\in C it is hard to find, given O(c), a value outside the preimage of 0. Interestingly, this natural definition, also motivated by applications, is likely not implied by the seemingly stronger notion of average-case virtual black-box obfuscation. - If there exist average-case virtual gray box obfuscators for all evasive function families, then there exist (quantitatively weaker) average-case virtual gray obfuscators for all function families. - There does not exist a worst-case virtual black box obfuscator even for evasive circuits, nor is there an average-case virtual gray box obfuscator for evasive Turing machine families. - Let C be an evasive circuit family consisting of functions that test if a low-degree polynomial (represented by an efficient arithmetic circuit) evaluates to zero modulo some large prime p. Then under a natural analog of the discrete logarithm assumption in a group supporting multilinear maps, there exists an input-hiding obfuscator O for C. Under a new perfectly-hiding multilinear encoding assumption, there is an average-case virtual black box obfuscator for the family C. 09:17 [Pub][ePrint] We present an Attribute Based Encryption system where access policies are expressed as polynomial size arithmetic circuits. We prove security against arbitrary collusions of users based on the learning with errors problem on integer lattices. The system has two additional useful properties: first, it naturally handles arithmetic circuits with arbitrary fan-in (and fan-out) gates. Second, secret keys are much shorter than in previous schemes: secret key size is proportional to the depth of the circuit where as in previous constructions the key size was proportional to the number of gates or wires in the circuit. The system is well suited for environments where access policies are naturally expressed as arithmetic circuits as is the case when policies capture statistical properties of the data or depend on arithmetic transformations of the data. The system also provides complete key delegation capabilities. 09:17 [Pub][ePrint] We state a switching lemma for tests on adversarial inputs involving bilinear pairings in hard groups, where the tester can effectively switch the randomness used in the test from being given to the adversary to being chosen after the adversary commits its input. The switching lemma can be based on any$k$-linear hardness assumptions on one of the groups. In particular, this enables convenient information theoretic arguments in the construction of sequence of games proving security of cryptographic schemes, paralleling proofs and constructions in the random oracle model. As an immediate application, we show that the quasi-adaptive NIZK proofs of Jutla and Roy (ASIACRYPT 2013) for linear subspaces can be further shortened to \\emph{constant}-size proofs, independent of the number of witnesses and equations. In particular, under the SXDH assumption, a length$n$vector of group elements can be proven to belong to a subspace of rank$t\$ with a quasi-adaptive NIZK proof of just a single group element. Similar quasi-adaptive aggregation of proofs is also shown for Groth-Sahai NIZK proofs of linear multi-scalar multiplication equations, as well as linear pairing-product equations (equations without any quadratic terms).