International Association for Cryptologic Research

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2013-02-27
19:17 [Pub][ePrint]

Motivated by the goal of controlling the amount of work required to

access a shared resource or to solve a cryptographic puzzle,

we introduce and study the related notions of {\\em lossy chains} and {\\em fractional secret sharing}.

Fractional secret sharing generalizes traditional secret sharing by allowing a fine-grained control over the amount of uncertainty

about the secret. More concretely, a fractional secret sharing scheme realizes a fractional access structure $f:2^{[n]}\\to [m]$ by guaranteeing that from the point of view of each set $T\\subseteq [n]$ of parties, the secret is {\\em uniformly} distributed over a set of $f(T)$ potential secrets. We show that every (monotone) fractional access structure can be realized. For {\\em symmetric} structures, in which $f(T)$ depends only on the size of $T$, we give an efficient construction with share size $poly(n,\\log m)$.

Our construction of fractional secret sharing schemes is based on the new notion of {\\em lossy chains} which may be of independent interest.

A lossy chain is a Markov chain $(X_0,\\ldots,X_n)$ which starts with a random secret $X_0$ and gradually loses information about it at a rate which is specified by a {\\em loss function} $g$. Concretely, in every step $t$, the distribution of $X_0$ conditioned on the value of $X_t$ should always be uniformly distributed over a set of size $g(t)$.

We show how to construct such lossy chains efficiently for any possible loss function $g$, and prove that our construction achieves an optimal asymptotic information rate.

19:17 [Pub][ePrint]

Design efficient Lattice-based cryptosystem secure against adaptive chosen ciphertext attack (IND-CCA2) is a challenge problem. To the date, full CCA2-security of all proposed Lattice-based PKE schemes achieved by using a generic transformations such as either strongly unforgeable one-time signature schemes (SU-OT-SS), or a message authentication code (MAC) and weak form of commitment. The drawback of these schemes is that encryption requires \"separate encryption\". Therefore, the resulting encryption scheme is not sufficiently efficient to be used in practice and it is inappropriate for many applications such as small ubiquitous computing devices with limited resources such as smart cards, active RFID tags, wireless sensor networks and other embedded devices.

In this work, for the first time, we introduce an efficient universal random data padding (URDP) scheme, and show how it can be used to construct a \"direct\" CCA2-secure encryption scheme from \"any\" worst-case hardness problems in (ideal) lattice in the standard model, resolving a problem that has remained open till date. This novel approach is a \"black-box\" construction and leads to the elimination of separate encryption, as it avoids using general transformation from CPA-secure scheme to a CCA2-secure one. IND-CCA2 security of this scheme can be tightly reduced in the standard model to the assumption that the underlying primitive is an one-way trapdoor function.

19:17 [Pub][ePrint]

The Strassen algorithm for multiplying $2 \\times 2$ matrices requires seven multiplications and 18 additions. The recursive use of this algorithm for matrices of dimension $n$ yields a total arithmetic complexity of $(7n^{2.81}-6n^2)$ for $n=2^k$. Winograd showed that using seven multiplications for this kind of multiplications is optimal, so any algorithm for multiplying $2 \\times 2$ matrices with seven multiplications is therefore called a Strassen-like algorithm. Winograd also discovered an additively optimal Strassen-like algorithm with 15 additions. This algorithm is called the Winograd\'s variant, whose arithmetic complexity is $(6n^{2.81}-5n^2)$ for $n=2^k$ and $(3.73n^{2.81}-5n^2)$ for $n=8\\cdot 2^k$, which is the best-known bound for Strassen-like multiplications. This paper proposes a method that reduces the complexity of Winograd\'s variant to $(5n^{2.81}+0.5n^{2.59}+2n^{2.32}-6.5n^2)$ for $n=2^k$. It is also shown that the total arithmetic complexity can be improved to $(3.55n^{2.81}+0.148n^{2.59}+1.02n^{2.32}-6.5n^2)$ for $n=8\\cdot 2^k$, which, to the best of our knowledge, improves the best-known bound for a Strassen-like matrix multiplication algorithm.

19:17 [Pub][ePrint]

We present a constant-round unconditional black-box compiler, that transforms any ideal straight- line extractable commitment scheme, into an extractable and equivocal commitment scheme, therefore yielding to UC-security [Can01]. We exemplify the usefulness of our compiler providing two (constant- round) instantiations of ideal straight-line extractable commitment using (malicious) PUFs [OSVW13] and stateless tamper-proof hardware tokens [Kat07]. This allows us to achieve the first unconditionally UC-secure commitment with malicious PUFs and the first unconditionally UC-secure commitment with stateless tokens. Our constructions are secure for adversaries creating arbitrarily malicious stateful PUFs/tokens.

Previous results with malicious PUFs used either computational assumptions to achieve UC-secure commitments or were unconditionally secure but only in the indistinguishability sense [OSVW13]. Similarly, with stateless tokens, UC-secure commitments are known only under computational assumptions [CGS08, GIS+10, CKS+11], while the (not UC) unconditional commitment scheme of [GIMS10] is secure only in a weaker model in which the adversary is not allowed to create stateful tokens.

Besides allowing us to prove feasibility of unconditional UC-security with (malicious) PUFs and stateless tokens, our compiler can be instantiated with any ideal straight-line extractable commitment scheme, thus allowing the use of various setup assumptions which may better fit the application or the technology available.

19:17 [Pub][ePrint]

We define a novel notion of quasi-adaptive non-interactive zero knowledge (NIZK) proofs for probability distributions on parametrized languages. It is quasi-adaptive in the sense that the common reference string (CRS) generator can generate the CRS depending on the language parameters. However, the simulation is required to be uniform, i.e., a single efficient simulator should work for the whole class of parametrized languages. For distributions on languages that are linear subspaces of vector spaces over bilinear groups, we give quasi-adaptive NIZKs that are shorter and more efficient than Groth-Sahai NIZKs. For many cryptographic applications quasi-adaptive NIZKs suffice, and our constructions can lead to significant improvements in the standard model. Our construction can be based on any $k$-linear assumption, and in particular under the Symmetric eXternal Diffie Hellman (SXDH) assumption our proofs are even competitive with Random-Oracle based $\\Sigma$-protocol NIZK proofs.

We also show that our system can be extended to include integer tags in the defining equations, where the tags are provided adaptively by the adversary. This leads to applicability of our system to many applications that use tags, e.g. applications using Cramer-Shoup projective hash proofs. Our techniques also lead to the shortest known (ciphertext) fully secure identity based encryption (IBE) scheme under standard static assumptions (SXDH).

19:17 [Pub][ePrint]

It is well known that it is impossible for two parties to toss a coin fairly (Cleve, STOC 1986). This result implies that it is impossible to securely compute with fairness any function that can be used to toss a coin fairly. In this paper, we focus on the class of deterministic Boolean functions with finite domain, and we ask for which functions in this class is it possible to information-theoretically toss an unbiased coin, given a protocol for securely computing the function with fairness. We provide a \\emph{complete characterization} of the functions in this class that imply and do not imply fair coin tossing. This characterization extends our knowledge of which functions cannot be securely computed with fairness. In addition, it provides a focus as to which functions may potentially be securely computed with fairness, since a function that cannot be used to fairly toss a coin is not ruled out by the impossibility result of Cleve (which is the \\emph{only} known impossibility result for fairness). In addition to the above, we draw corollaries to the feasibility of achieving fairness in two possible fail-stop models.

19:17 [Pub][ePrint]

Message Authentication Code (MAC) is one of most basic primitives in cryptography. After Biham (EUROCRYPT 1993) proposed related-key attacks (RKAs), RKAs have damaged MAC\'s security. To relieve MAC of RKA distress, Bellare and Cash proposed pseudo-random functions (PRFs) secure against multiplicative RKAs (EUROCRYPT 2010). They also proposed PRFs secure against additive RKAs, but their reduction requires sub-exponential time. Since PRF directly implies Fixed-Input Length (FIL) MAC, their PRFs result in MACs secure against multiplicative RKAs.

In this paper, we proposed Variable-Input Length (VIL) MAC secure against \\emph{additive} RKAs, whose reductions are polynomial time in the security parameter. Our construction stems from MACs from number-theoretic assumptions proposed by Dodis, Kiltz, Pietrzak, Wichs (EUROCRYPT 2012) and public-key encryption schemes secure against additive RKAs proposed by Wee (PKC 2012).

19:17 [Pub][ePrint]

We show in this paper how several proposed Strong

Physical Unclonable Functions (PUFs) can be broken by numerical

modeling attacks. Given a set of challenge-response pairs

(CRPs) of a Strong PUF, our attacks construct a computer

algorithm which behaves indistinguishably from the original PUF

on almost all CRPs. This algorithm can subsequently impersonate

the PUF, and can be cloned and distributed arbitrarily. This

breaks the security of almost all applications and protocols that

are based on the respective PUF.

The PUFs we attacked successfully include standard Arbiter

PUFs and Ring Oscillator PUFs of arbitrary sizes, and XOR

Arbiter PUFs, Lightweight Secure PUFs, and Feed-Forward

Arbiter PUFs of up to a given size and complexity. The attacks

are based upon various machine learning techniques, including

a specially tailored variant of Logistic Regression and Evolution

Strategies.

Our results were obtained on a large number of CRPs

coming from numerical simulations, as well as four million CRPs

collected from FPGAs and ASICs. The performance on silicon

CRPs is very close to simulated CRPs, confirming a conjecture

from earlier versions of this work. Our findings lead to new

design requirements for secure electrical PUFs, and will be useful

to PUF designers and attackers alike.

19:17 [Pub][ePrint]

The cryptographic hash functions BLAKE and Skein are built from the ChaCha stream cipher and the tweakable Threefish block cipher, respectively. Interestingly enough, they are based on the same arithmetic operations, and the same design philosophy allows one to design lightweight coprocessors for hashing and encryption. The key element of our approach is to take advantage of the parallelism of the algorithms to deeply pipeline our Arithmetic an Logic Units, and to avoid data dependencies by interleaving independent tasks. We show for instance that a fully autonomous implementation of BLAKE and ChaCha on a Xilinx Virtex-6 device occupies 144 slices and three memory blocks, and achieves competitive throughputs. In order to offer the same features, a coprocessor implementing Skein and Threefish requires a substantial higher slice count.

19:17 [Pub][ePrint]

We offer a public key exchange protocol in the spirit of Diffie-Hellman, but we use (small) matrices over a group ring of a (small) symmetric group as the platform. This nested structure\" of the platform makes computation very efficient for legitimate parties. We discuss security of this scheme by addressing the Decision Diffie-Hellman (DDH) and Computational Diffie-Hellman (CDH) problems for our platform.

19:17 [Pub][ePrint]

To allow a delegator not only to delegate the keyword-controlled decryption rights of a broadcast encryption to a set of specified recipients, but also to control when the decryption rights will be delegated, in this paper, for the first time, we introduce a new notion called timed-release conditional proxy broadcast re-encryption (TR-CPBRE). We also propose a concrete construction for TR-CPBRE which can be proven selective identity adaptive CCA secure under the (P,Q,f)-GDDHE assumption, and chosen-time period chosen-ciphertext secure under the BDH assumption. When compared with the existing CPBRE and TR-PRE schemes, our scheme achieves better efficiency, and enables the delegator to make a fine-grained delegation of decryption rights to multiple delegatees.