International Association for Cryptologic Research

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2013-08-15
09:17 [Pub][ePrint]

In this paper, we present a new class of semi-bent quadratic Boolean functions of the form $f(x)=\\sum_{i=1}^{\\lfloor\\frac{m-1}{2}\\rfloor}Tr^n_1(c_ix^{1+4^{i}})$ $~(c_i\\in \\mathbb{F}_4$,$n=2m)$. We first characterize the semi-bentness of these quadratic Boolean functions. There exists semi-bent functions only when $m$ is odd. For the case: $m=p^r$, where $p$ is an odd prime with some conditions, we enumerate the semi-bent functions. Further, we give a simple characterization of semi-bentness for these functions with linear properties of $c_i$. In particular, for

a special case of $p$, any quadratic Boolean function $f(x)=\\sum_{i=1}^{\\frac{p-1}{2}}Tr^{2p}_1(c_ix^{1+4^{i}})$ over $\\mathbb{F}_{2^{2p}}$ is a semi-bent function.

09:17 [Pub][ePrint]

The series of published works, related to Differential Fault Attack

(DFA) against the Grain family, require (i) quite a large number (hundreds) of faults (around $n \\ln n$, where $n = 80$ for Grain v1 and $n = 128$ for Grain-128, Grain-128a) and also (ii) several assumptions on location and timing of the fault injected. In this paper we present a significantly improved scenario from the adversarial point of view for DFA against the Grain family of stream ciphers. Our model is the most realistic one so far as it considers that the cipher to be re-keyed a very few times and fault can be injected at any random location and at any random point of time, i.e., no precise control is needed over the location and timing

of fault injections. We construct equations based on the algebraic description of the cipher by introducing new variables so that the degrees of the equations do not increase. In line of algebraic cryptanalysis, we accumulate such equations based on the fault-free and faulty key-stream bits and solve them using the SAT Solver

Cryptominisat-2.9.5 installed with SAGE 5.7. In a few minutes we can recover the state of Grain v1, Grain-128 and Grain-128a with as little as 10, 4 and 10 faults respectively (and may be improved further with more computational efforts).

09:17 [Pub][ePrint]

Identity-based encryption (IBE) has been regarded as an attractive alternative to more conventional certificate-based public key systems.

It has recently attracted not only considerable research from the academic community, but also interest from the industry and standardization bodies. However, while key revocation is a fundamental requirement to any public key systems, not much work has been done in the identity-based setting. In this paper, we continue the study of revocable IBE (RIBE) initiated by Boldyreva, Goyal, and Kumar. Their proposal of a selective secure RIBE scheme, and a subsequent construction by Libert and Vergnaud in a stronger adaptive security model are based on a binary tree approach, such that their key update size is logarithmic in the number of users. We ask the question of whether or not the key update size could be further reduced by using a cryptographic accumulator. We show that, indeed, the key update material can be made constant with some small amount of auxiliary information, through a novel combination of the Lewko and Waters IBE scheme and the Camenisch, Kohlweiss, and Soriente pairing-based dynamic accumulator.

09:17 [Pub][ePrint]

Existing work on \"rational cryptographic protocols\" treats each party (or coalition of parties) running the protocol as a selfish agent trying to maximize its utility. In this work we propose a fundamentally different approach that is better suited to modeling a protocol under attack from an external entity. Specifically, we consider a two-party game between an protocol designer and an external attacker. The goal of the attacker is to break security properties such as correctness or privacy, possibly by corrupting protocol participants; the goal of the protocol designer is to prevent the attacker from succeeding.

We lay the theoretical groundwork for a study of cryptographic protocol design in this setting by providing a methodology for defining the problem within the traditional simulation paradigm. Our framework provides ways of reasoning about important cryptographic concepts (e.g., adaptive corruptions or attacks on communication resources) not handled by previous game-theoretic treatments of cryptography. We also prove composition theorems that--for the first time--provide a sound way to design rational protocols assuming \"ideal communication resources\" (such as broadcast or authenticated channels) and then instantiate these resources using standard cryptographic tools.

Finally, we investigate the problem of secure function evaluation in our framework, where the attacker has to pay for each party it corrupts. Our results demonstrate how knowledge of the attacker\'s incentives can be used to

09:17 [Pub][ePrint]

In 2007, Camenisch, Neven and Shelat proposed an adaptive oblivious transfer (OT) in which a sender has $N$ messages, of which a receiver can adaptively choose to receive $k$ one-after-the-other.

In this paper, we show that the scheme has a drawback that the sender can only serve a single receiver only once. The drawback results from the deterministic encryption used. To fix it, we suggest to replace the deterministic encryption with a probabilistic encryption. The OT scheme adopts the paradigm of encryption and proof of knowledge\" in order to force the sender to keep the consistency of the transferred messages. We remark that the paradigm is unnecessary. In most reasonable applications of OT, the transferred messages must be recognizable for the receiver or the sender is willing to disclose some messages to the receiver. This property has been explicitly specified in the earlier works by Rabin, Even, Goldreich and Lempel.

09:17 [Pub][ePrint]

We construct an efficient information-theoretically non-mall\\-eable code in the split-state model for one-bit messages. Non-malleable codes were introduced recently by Dziembowski, Pietrzak and Wichs (ICS 2010), as a general tool for storing messages securely on hardware that can be subject to tampering attacks. Informally, a code $(Enc : \\cal M \\rightarrow \\cal L \\times \\cal R, Dec : \\cal L \\times \\cal R \\rightarrow \\cal M)$ is {\\em non-malleable in the split-state model} if any adversary, by manipulating {\\em independently} $L$ and $R$ (where $(L,R)$ is an encoding of some message $M$), cannot obtain an encoding of a message $M\'$ that is not equal to $M$ but is related\'\' $M$ in some way. Until now it was unknown how to construct an information-theoretically secure code with such a property, even for $\\cal M = \\{0,1\\}$. Our construction solves this problem. Additionally, it is leakage-resilient, and the amount of leakage that we can tolerate can be an arbitrary fraction $\\xi < {1}/{4}$ of the length of the codeword. Our code is based on the inner-product two-source extractor, but in general it can be instantiated by any two-source extractor that has large output and has the property of being {\\em flexible}, which is a new notion that we define.

We also show that the non-malleable codes for one-bit messages have an equivalent, perhaps simpler characterization, namely such codes can be defined as follows: if $M$ is chosen uniformly from $\\{0,1\\}$ then the probability (in the experiment described above) that the output message $M\'$ is not equal to $M$ can be at most $1/2 + \\epsilon$.

09:17 [Pub][ePrint]

We revisit the question of whether cryptographic protocols can replace correlated equilibria mediators in two-player strategic games. This problem was first addressed by Dodis, Halevi and Rabin (CRYPTO 2000), who suggested replacing the mediator with a secure protocol and proved that their solution is stable in the Nash equilibrium (NE) sense, provided that the players are computationally bounded.

We show that there exist two-player games for which no cryptographic protocol can implement the mediator in a sequentially rational way; that is, without introducing empty threats. This explains why all solutions so far were either sequentially unstable, or were restricted to a limited class of correlated equilibria (specifically, those that do not dominate any NE, and hence playing them does not offer a clear advantage over playing any NE).

In the context of computational NE, we classify necessary and sufficient cryptographic assumptions for implementing a mediator that allows to achieve a given utility profile of a correlated equilibrium. The picture that emerges is somewhat different than the one arising in semi-honest secure two-party computation. Specifically, while in the latter case every functionality is either \"complete\" (i.e., implies Oblivious Transfer) or \"trivial\" (i.e., can be securely computed unconditionally), in the former there exist some \"intermediate\" utility profiles whose implementation is equivalent to the existence of one-way functions.

09:17 [Pub][ePrint]

We show that the class of polynomial-size branching programs can be obfuscated according to a virtual black-box notion akin to that of Barak et al. [Crypto 01], in an idealized black-box group model

over pseudo-free groups. This class is known to lie between $NC^1$ and $P$ and includes most interesting cryptographic algorithms. The construction is rather simple and is based on Kilian\'s randomization

technique for Barrington\'s branching programs.

The black-box group model over pseudo-free groups is a strong idealization. In particular, in a pseudo-free group, the group operation can be efficiently performed, while finding surprising relations between group elements is intractable.

%inverses or linking between different representations of the same group element are infeasible. A black-box representation of the group provides an ideal interface which permits prescribed group operations, and nothing else. Still, the algebraic structure and security requirements appear natural and potentially realizable. They are also unrelated to the specific function to be obfuscated.

Our modeling should be compared with the recent breakthrough obfuscation scheme of Garg et al. [FOCS 2013]: While the high level structure is similar, some important details differ. It should be stressed however that, unlike Garg et al., we do not provide a candidate concrete instantiation of our abstract structure.

09:17 [Pub][ePrint]

The Trusted Platform Module (TPM) is designed to enable trustworthy computation and communication over open networks. The TPM provides a way to store cryptographic keys and other sensitive values in its shielded memory and act as \\emph{Root of Trust for Storage} (RTS). The TPM interacts with applications via a predefined set of commands (an API). In this paper, we give an abstraction model for the TPM 2.0 specification concentrating on Protected Storage part. With identification and formalization of their secrecy properties, we devise a type system with asymmetric cryptographic primitives to statically enforce and prove their security.

09:17 [Pub][ePrint]

After a series of works on RC4 cryptanalysis in last few years (published in flagship cryptology conferences and journals), the most significant (and also very recent) attack on the cipher has been the discovery of vulnerabilities in the SSL/TLS protocol, by AlFardan, Bernstein, Paterson, Poettering and Schuldt. They ran extensive computations to identify significant short-term single-byte keystream biases of RC4, and utilized that knowledge in the attack. The biases identified by AlFardan et al. consist of earlier known biases of RC4, as well as some newly discovered ones.

In this paper, we attempt at proving the new, unproved or partially proved biases amongst the above-mentioned ones. The theoretical proofs of these biases not only assert a scientific justification, but also discover intricate patterns and operations of the cipher associated with these biases. For example, while attempting the proof of a bias of the first output byte towards 129, we observe that this bias occurs prominently only for certain lengths of the secret key of RC4. In addition, our findings reveal that this bias may be related to the old and unsolved problem of anomalies\'\' in the distribution of the state array after the Key Scheduling Algorithm. In this connection, we prove the anomaly in $S_0[128] = 127$, a problem open for more than a decade.

Other than proving the new biases, we also complete the proof for the extended keylength dependent biases in RC4, a problem attempted and partially solved by Isobe, Ohigashi, Watanabe and Morii in FSE 2013. Our new proofs and observations in this paper, along with the connection to the older results, provide a comprehensive view on the state-of-the-art literature in RC4 cryptanalysis.

2013-08-14
15:17 [Pub][ePrint]

We present an efficient algorithm that can distinguish the keystream of WPA from that of a generic instance of RC4 with a packet complexity of $O(N^2)$, where $N$ denotes the size of the internal permutation of RC4. In practice, our distinguisher requires approximately $2^{19}$ packets; thus making it the best known distinguisher of WPA to date. This is a significantly improved distinguisher than the previous WPA distinguisher identified by Sepehrdad, Vaudenay and Vuagnoux in Eurocrypt 2011, which requires more than $2^{40}$ packets in practice. The motivation of our distinguisher arises from the recent observations on WPA by AlFardan, Bernstein, Paterson, Poettering and Schuldt, and this work puts forward an example how an experimental bias may lead to an efficient theoretical distinguisher.