International Association for Cryptologic Research

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2013-06-12
15:26 [Job][New]

15:17 [Pub][ePrint]

The design and analysis of lightweight block ciphers has been a very active research area over the last couple of years, with many innovative proposals trying to optimize different performance figures. However, since these block ciphers are dedicated to low-cost embedded devices, their implementation is also a typical target for side-channel adversaries. As preventing such attacks with countermeasures usually implies significant performance overheads, a natural open problem is to propose new algorithms for which physical security is considered as an optimization criteria, hence allowing better performances again. We tackle this problem by studying how much we can tweak standard block ciphers such as the AES Rijndael in order to allow efficient masking (that is one of the most frequently considered solutions to improve security against side-channel attacks). For this purpose, we first investigate alternative S-boxes and round structures. We show that both approaches can be used separately in order to limit the total number of non-linear operations in the block cipher, hence allowing more efficient masking. We then combine these ideas into a concrete instance of block cipher called Zorro. We further provide a detailed security analysis of this new cipher taking its design specificities into account, leading us to exploit innovative techniques borrowed from hash function cryptanalysis (that are sometimes of independent interest). Eventually, we conclude the paper by evaluating the efficiency of masked Zorro implementations in an 8-bit microcontroller, and exhibit their interesting performance figures.

15:17 [Pub][ePrint]

Leakage-resilient cryptography aims at formally proving the security of cryptographic implementations against large classes of side-channel adversaries. One important challenge for such an approach to be relevant is to adequately connect the formal models used in the proofs with the practice of side-channel attacks. It raises the fundamental problem of finding reasonable restrictions of the leakage functions that can be empirically verified by evaluation laboratories. In this paper, we first argue that the previous bounded leakage\" requirements used in leakage-resilient cryptography are hard to fulfill by hardware engineers. We then introduce a new, more realistic and empirically verifiable assumption of simulatable leakage, under which security proofs in the standard model can be obtained. We finally illustrate our claims by analyzing the physical security of an efficient pseudorandom generator (for which security could only be proven under a random oracle based assumption so far). These positive results come at the cost of (algorithm-level) specialization, as our new assumption is specifically defined for block ciphers. Nevertheless, since block ciphers are the main building block of many leakage-resilient

cryptographic primitives, our results also open the way towards more realistic constructions and proofs for other pseudorandom objects.

15:17 [Pub][ePrint]

15:17 [Pub][ePrint]

Gentry\'s bootstrapping\'\' technique (STOC 2009) constructs a fully

homomorphic encryption (FHE) scheme from a somewhat homomorphic\'\'

one that is powerful enough to evaluate its own decryption function.

To date, it remains the only known way of obtaining unbounded FHE.

Unfortunately, bootstrapping is computationally very expensive,

despite the great deal of effort that has been spent on improving its

efficiency. The current state of the art, due to Gentry, Halevi, and

Smart (PKC 2012), is able to bootstrap packed\'\' ciphertexts (which

encrypt up to a linear number of bits) in time only \\emph{quasilinear}

$\\Otil(\\lambda) = \\lambda \\cdot \\log^{O(1)} \\lambda$ in the security

parameter. While this performance is \\emph{asymptotically} optimal up

to logarithmic factors, the practical import is less clear: the

procedure composes multiple layers of expensive and complex

operations, to the point where it appears very difficult to implement,

and its concrete runtime appears worse than those of prior methods

(all of which have quadratic or larger asymptotic runtimes).

In this work we give \\emph{simple}, \\emph{practical}, and entirely

\\emph{algebraic} algorithms for bootstrapping in quasilinear time, for

both packed\'\' and non-packed\'\' ciphertexts. Our methods are easy

to implement (especially in the non-packed case), and we believe that

they will be substantially more efficient in practice than all prior

realizations of bootstrapping. One of our main techniques is a

substantial enhancement of the ring-switching\'\' procedure of Gentry

et al.~(SCN 2012), which we extend to support switching between two

rings where neither is a subring of the other. Using this procedure,

we give a natural method for homomorphically evaluating a broad class

of structured linear transformations, including one that lets us

evaluate the decryption function efficiently.

15:17 [Pub][ePrint]

For a number of elliptic curve-based cryptographic protocols, it is useful and sometimes necessary to be able to encode a message (a bit string) as a point on an elliptic curve in such a way that the message can be efficiently and uniquely recovered from the point. This is for example the case if one wants to instantiate CPA-secure ElGamal encryption directly in the group of points of an elliptic curve. More practically relevant settings include Lindell\'s UC commitment scheme (EUROCRYPT 2011) or structure-preserving primitives.

It turns out that constructing such an encoding function is not easy in general, especially if one wishes to encode points whose length is large relative to the size of the curve. There is a probabilistic, folklore\'\' method for doing so, but it only provably works for messages of length less than half the size of the curve.

In this paper, we investigate several approaches to injective encoding to elliptic curves, and in particular, we propose a new, essentially optimal geometric construction for a large class of curves, including Edwards curves; the resulting algorithm is also quite efficient, requiring only one exponentiation in the base field and simple arithmetic operations (however, the curves for which the map can be constructed have a point of order two, which may be a limiting factor for possible applications). The new approach is based on the existence of a covering curve of genus 2 for which a bijective encoding is known.

15:17 [Pub][ePrint]

Authentication and key agreement protocols play an important role in wireless sensor communication networks. Recently Xue et al\'. suggested a key agreement protocols for WSN which in this paper we show that the protocol has some security flaws. Also we introduce an enhanced authentication and key agreement protocol for WSN satisfying all the security requirements.

15:17 [Pub][ePrint]

This paper presents first results of the Networking and Cryptography library (NaCl) on the 8-bit AVR family of microcontrollers. We show that NaCl, which has so far been optimized mainly for different desktop and server platforms, is feasible on resource-constrained devices while being very fast and memory efficient. Our implementation shows that encryption using Salsa20 requires 268 cycles/byte, authentication using Poly1305 needs 195 cycles/byte, a Curve25519 scalar multiplication needs 22,791,579 cycles, signing of data using Ed25519 needs 23,216,241 cycles, and verification can be done within 32,634,713 cycles. All implemented primitives provide at least 128-bit security, run in constant time, do not use secret-data-dependent branch conditions, and are open to the public domain (no usage restrictions).

15:17 [Pub][ePrint]

The power of an accurate model for describing a physical process or designing a physical system is beyond doubt. The currently used reliability model for physically unclonable functions (PUFs) assumes an equally likely error for every evaluation of every PUF response bit. This limits an accurate description since experiments show that certain responses are more error-prone than others, but this fixed error rate model only captures average case behavior. We introduce a new PUF reliability model taking this observed heterogeneous nature of PUF cells into account. An extensive experimental validation demonstrates that the new predicted distributions describe the empirically observed data statistics almost perfectly, even considering sensitivity to operational temperature. This allows studying PUF reliability behavior in full detail, including average and worst case probabilities, and is an invaluable tool for designing more efficient and better adapted PUFs and PUF-based systems.

15:17 [Pub][ePrint]

We put forward a new algebraic framework to generalize and

analyze Diffie-Hellman like Decisional Assumptions which allows

us to argue about security and applications by considering only algebraic properties.

Our $D_{\\ell,k}-MDDH$ assumption states that it is hard to decide whether

a vector in $G^\\ell$ is linearly dependent of the columns of some matrix in $G^{\\ell\\times k}$ sampled according to distribution $D_{\\ell,k}$.

It covers known assumptions such as $DDH$, $2-Lin$ (linear assumption), and $k-Lin$ (the $k$-linear assumption).

Using our algebraic viewpoint, we can relate the generic hardness of our assumptions in $m$-linear groups to the irreducibility of certain polynomials which describe the output of $D_{\\ell,k}$.

We use the hardness results to find new distributions for which the $D_{\\ell,k}-MDDH$-Assumption holds generically in $m$-linear groups.

In particular, our new assumptions $2-SCasc$ and $2-ILin$ are generically hard in bilinear groups and, compared to $2-Lin$, have shorter description size, which is a relevant parameter for efficiency in many applications.

These results support using our new assumptions as natural replacements for the $2-Lin$ Assumption which was already used in a large number of applications.

To illustrate the conceptual advantages of our algebraic framework, we construct several fundamental primitives based on any $MDDH$-Assumption. In particular, we can give many instantiations of a primitive in a compact way, including public-key encryption, hash-proof systems, pseudo-random functions, and Groth-Sahai NIZK and NIWI proofs.

As an independent contribution we give more efficient NIZK and NIWI proofs for membership in a subgroup of $G^\\ell$, for validity of ciphertexts and for equality of plaintexts. The results imply very significant efficiency improvements for a large number of schemes, most notably Naor-Yung type of constructions.

15:17 [Pub][ePrint]

In a basic related-key attack against a block cipher, the adversary has access to encryptions under keys that differ from the target key by bit-flips. In this short note we show that for a quantum adversary such attacks are quite powerful: if the secret key is (i) uniquely determined by a small number of plaintext-ciphertext pairs, (ii) the block cipher can be evaluated efficiently, and (iii) a superposition of related keys can be queried, then the key can be extracted efficiently.