[Show abstract][Hide abstract] ABSTRACT: RC4 has been the most popular stream cipher in the history of symmetric key cryptography. Its internal state contains a permutation over all possible bytes from 0 to 255, and it attempts to generate a pseudo-random sequence of bytes (called keystream) by extracting elements of this permutation. Over the last twenty years, numerous cryptanalytic results on RC4 stream cipher have been published, many of which are based on non-random (biased) events involving the secret key, the state variables, and the keystream of the cipher. Though biases based on the secret key are common in RC4 literature, none of the existing ones depends on the length of the secret key. In the first part of this paper, we investigate the effect of RC4 keylength on its keystream, and report significant biases involving the length of the secret key. In the process, we prove the two known empirical biases that were experimentally reported and used in recent attacks against WEP and WPA by Sepehrdad, Vaudenay and Vuagnoux in EUROCRYPT 2011. After our current work, there remains no bias in the literature of WEP and WPA attacks without a proof. In the second part of the paper, we present theoretical proofs of some significant initial-round empirical biases observed by Sepehrdad, Vaudenay and Vuagnoux in SAC 2010. In the third part, we present the derivation of the complete probability distribution of the first byte of RC4 keystream, a problem left open for a decade since the observation by Mironov in CRYPTO 2002. Further, the existence of positive biases towards zero for all the initial bytes 3 to 255 is proved and exploited towards a generalized broadcast attack on RC4. We also investigate for long-term non-randomness in the keystream, and prove a new long-term bias of RC4.
Journal of Cryptology 01/2014; 1(1). DOI:10.1007/s00145-012-9138-1 · 1.02 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The series of published works, related to differential fault attack (DFA) against the Grain family, require quite a large number (hundreds) of faults and also several assumptions on the locations and the timings of the faults 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 has to be re-keyed only a few times and faults 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.
[Show abstract][Hide abstract] ABSTRACT: Most of the existing conditional access-based systems (CAS) follow a standard methodology. The service provider shares two copies for single information (specifically image for this work). One copy is a low-resolution version which is shared in the public domain for preview purpose. The other one is a high-resolution version to be provided to the customers through a secure channel on demand (after payment). We propose a novel scheme that can be efficiently adapted in such a scenario. We analyze the images in the discrete cosine transform (DCT) domain and note that polynomials of suitable degree, representing the sorted DCT coefficients together with original index locations, can uniquely represent an image. We show that the arrangement of DCT index locations, after the actual coefficients have been sorted by magnitude, is significantly different for various images and we exploit this to design an efficient CAS-based scheme. We also show that the amount of private data, which a service provider needs to transmit through a secure channel to the customers on demand, is reduced significantly. This reduction in transmitted data makes the system apt for real-time secure applications.
[Show abstract][Hide abstract] ABSTRACT: In this paper we present a differential fault attack on the stream cipher MICKEY 2.0 which is in eStream's hardware portfolio. While fault attacks have already been reported against the other two eStream hardware candidates Trivium and Grain, no such analysis is known for MICKEY. Using the standard assumptions for fault attacks, we show that if the adversary can induce random single bit faults in the internal state of the cipher, then by injecting around 216.7 faults and performing 232.5 computations on an average, it is possible to recover the entire internal state of MICKEY at the beginning of the key-stream generation phase. We further consider the scenario where the fault may affect at most three neighbouring bits and in that case we require around 218.4 faults on an average.
Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems; 08/2013
[Show abstract][Hide abstract] ABSTRACT: Let a Boolean function be available as a black-box (oracle) and one likes to
devise an algorithm to test whether it has certain property or it is
$\epsilon$-far from having that property. The efficiency of the algorithm is
judged by the number of calls to the oracle so that one can decide, with high
probability, between these two alternatives. The best known quantum algorithm
for testing whether a function is linear or $\epsilon$-far $(0 < \epsilon <
\frac{1}{2})$ from linear functions requires $O(\epsilon^{-\frac{2}{3}})$ many
calls [Hillery and Andersson, Physical Review A 84, 062329 (2011)]. We show
that this can be improved to $O(\epsilon^{-\frac{1}{2}})$ by using the
Deutsch-Jozsa and the Grover Algorithms.
[Show abstract][Hide abstract] ABSTRACT: RC4 is the most popular stream cipher in the domain of cryptology. In this paper, we present a systematic study of the hardware implementation of RC4, and propose the fastest known architecture for the cipher. We combine the ideas of hardware pipeline and loop unrolling to design an architecture that produces 2 RC4 keystream bytes per clock cycle. We have optimized and implemented our proposed design using VHDL description, synthesized with 130, 90, and 65 nm fabrication technologies at clock frequencies 625 MHz, 1.37 GHz, and 1.92 GHz, respectively, to obtain a final RC4 keystream throughput of 10, 21.92, and 30.72 Gbps in the respective technologies.
[Show abstract][Hide abstract] ABSTRACT: Ultra-low power dissipation for nanoscale circuits
and future technologies such as quantum computing require
reversible logic. Existing methods of reversible logic synthesis
attempt to minimize gate count, quantum cost, garbage count
and try to achieve scalability for large Boolean functions.
Several notable heuristics for reversible logic synthesis employ
a method based on repeated transformation, demonstrating
excellent performance compared to available optimal results. In
this paper, we suggest two novel techniques to the transformationbased
synthesis flow for improving synthesis outcome. The first
technique is based on properties of Boolean functions and the
second technique incorporates generalized Fredkin gates during
synthesis flow. We present theoretical results and experimental
evidence in support of our strategies.
Proceedings of The International Symposium on Multiple-Valued Logic 01/2013; DOI:10.1109/ISMVL.2013.14
[Show abstract][Hide abstract] ABSTRACT: In this paper we study weaknesses of two variants of RSA: Dual RSA and Common Prime RSA. Several schemes under the framework of Dual RSA have been proposed by Sun et al. (IEEE Trans Inf Theory 53(8):2922–2933, 2007). We here concentrate on the Dual CRT-RSA scheme and present certain range of parameters where it is insecure. As a corollary of our work, we prove that the Dual Generalized Rebalanced-RSA (Scheme III of Sun et al.) can be efficiently broken for a significant region where the scheme has been claimed to be secure. Next we consider the Common Prime RSA as proposed by Wiener (IEEE Trans. Inf. Theory 36:553–558, 1990). We present new range of parameters in Common Prime RSA where it is not secure. We use lattice based techniques for the attacks.
[Show abstract][Hide abstract] ABSTRACT: The first known result on RC4 cryptanalysis (presented by Roos in 1995) points out that the most likely value of the y-th element of the permutation after the key scheduling algorithm (KSA) for the first few values of y is given by S N [y]=f y , some linear combinations of the secret keys. While it should have been quite natural to study the association S N [y]=f y ±t for small positive integers t (e.g., t≤4), surprisingly that had never been tried before. In this paper, we study that problem for the first time and show that though the event S N [y]=f y +t occurs with random association, there is a significantly high probability for the event S N [y]=f y -t. We also present several related non-randomness behaviour for the event S N [S N [y]]=f y -t of RC4 KSA in this direction. Further, we investigate near-colliding keys that lead to related states after the KSA and related keystream bytes. Our investigation reveals that near-colliding states do not necessarily lead to near-colliding keystreams. From this motivation, we present a heuristic to find a related key pair with differences in two bytes, that lead to significant matches in the initial keystream. In the process, we discover a class of related key distinguishers for RC4. The best one of these shows that given a random key and a related one to that (the last two bytes increased and decreased by 1 respectively), the first pair of bytes corresponding to the related keys are same with very high probability (e.g., approximately 0.011 for 16-byte keys to 0.044 for 30-byte keys).
[Show abstract][Hide abstract] ABSTRACT: The 32-bit MAC of Grain-128a is a linear combination of the first 64 and then the alternative keystream bits. In this paper we describe a successful differential fault attack on Grain-128a, in which we recover the Secret Key by observing the correct and faulty MACs of certain chosen messages. The attack works due to certain properties of the Boolean functions and corresponding choices of the taps from the LFSR. We present methods to identify the fault locations and then construct a set of linear equations to obtain the contents of the LFSR and the NFSR. Our attack requires less than 211 fault injections and invocations of less than 212 MAC generation routines.
Proceedings of the Second international conference on Security, Privacy, and Applied Cryptography Engineering; 11/2012
[Show abstract][Hide abstract] ABSTRACT: In this paper we explain how one can obtain Key-IV pairs for Grain family of stream ciphers that can generate output key-streams which are either (i) almost similar in the initial part or (ii) exact shifts of each other throughout the generation of the stream. Let lP be the size of the pad used during the key loading of Grain. For the first case, we show that in expected $2^{l_P}$ many invocations of the Key Scheduling Algorithm and its reverse routine, one can obtain two related Key-IV pairs that can produce same output bits in 75 (respectively 112 and 115) selected positions among the initial 96 (respectively 160 and 160) bits for Grain v1 (respectively Grain-128 and Grain-128a). Similar idea works for the second case in showing that given any Key-IV, one can obtain another related Key-IV in expected $2^{l_P}$ many trials such that the related Key-IV pairs produce shifted key-streams. We also provide an efficient strategy to obtain related Key-IV pairs that produce exactly i-bit shifted key-streams for small i. Our technique pre-computes certain equations that help in obtaining such related Key-IV pairs in 2i many expected trials.
Proceedings of the Second international conference on Security, Privacy, and Applied Cryptography Engineering; 11/2012
[Show abstract][Hide abstract] ABSTRACT: In this paper, we study efficient algorithms towards the construction of any
arbitrary Dicke state. Our contribution is to use proper symmetric Boolean
functions that involve manipulations with Krawtchouk polynomials. Deutsch-Jozsa
algorithm, Grover algorithm and the parity measurement technique are stitched
together to devise the complete algorithm. Further, motivated by the work of
Childs et al (2002), we explore how one can plug the biased Hadamard
transformation in our strategy. Our work compares fairly with the results of
Childs et al (2002).
Quantum Information Processing 09/2012; 13(9). DOI:10.1007/s11128-014-0797-8 · 1.92 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Towards the cold boot attack (a kind of side channel attack), the problems of reconstructing RSA parameters when (i) certain bits are unknown (Heninger and Shacham, Crypto 2009) and (ii) the bits are available but with some error probability (Henecka, May and Meurer, Crypto 2010) have been considered very recently. In this paper we exploit the error correction heuristic proposed by Henecka et al to show that CRT-RSA schemes having low Hamming weight decryption exponents are insecure given small encryption exponents (e.g., e=216+1). In particular, we show that the CRT-RSA schemes presented by Lim and Lee (SAC 1996) and Galbraith, Heneghan and McKee (ACISP 2005) with low weight decryption exponents can be broken in a few minutes in certain cases. Further, the scheme of Maitra and Sarkar (CT-RSA 2010), where the decryption exponents are not of low weight but they have large low weight factors, can also be cryptanalysed. We also identify a few modifications of the error correction strategy that provides significantly improved experimental outcome towards the cold boot attack.
Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems; 09/2012
[Show abstract][Hide abstract] ABSTRACT: Parker considered a new type of discrete Fourier transform, called nega-Hadamard transform. We prove several results regarding its behavior on combinations of Boolean functions and use this theory to derive several results on negabentness (that is, flat nega-spectrum) of concatenations, and partially symmetric functions. We derive the upper bound $\lceil {{ n}\over { 2}} \rceil $ for the algebraic degree of a negabent function on $n$ variables. Further, a characterization of bent–negabent functions is obtained within a subclass of the Maiorana–McFarland set. We develop a technique to construct bent–negabent Boolean functions by using complete mapping polynomials. Using this technique, we demonstrate that for each $\ell \geq 2$, there exist bent–negabent functions on $n = 12\ell $ variables with algebraic degree $ {{ n}\over { 4}}+1 = 3\ell + 1$. It is also demonstrated that there exist bent–negabent functions on eight variables with algebraic degrees 2, 3, and 4. Simple proofs of several previously known facts are obtained as immediate consequences of our work.
IEEE Transactions on Information Theory 06/2012; 58(6):4064-4072. DOI:10.1109/TIT.2012.2186785 · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This paper discusses the factorization of the RSA modulus when some 'partial information' about the bits of the RSA secret param-eters are known. Heninger and Shacham (Crypto 2009) considered the reconstruction of RSA secret parameters from a few randomly known bits, and Henecka, May and Meurer (Crypto 2010) studied the recon-struction of secret parameters when all the bits are known with some probability of error. Both the approaches attempted reconstruction from the least significant side of the parameters. In this paper we provide two new techniques for reconstruction and error correction that work from the most significant side of the parameters. Our idea uses adaptive fil-tering using a 'sliding window' technique. We provide theoretical as well as experimental results that are competitive with the existing works.
[Show abstract][Hide abstract] ABSTRACT: Let N = pq be the product of two large primes. Consider CRT-RSA with the public encryption exponent e and private decryption exponents dp, dq. It is well known that given any one of dp or dq (or both) one can factorize N in probabilistic poly(log N) time with success probability almost equal to 1. Though this serves all the practical purposes, from theoretical point of view, this is not a deterministic polynomial time algorithm. In this paper, we present a lattice based deterministic poly(log N) time algorithm that uses both dp, dq (in addition to the public information e, N) to factorize N for certain ranges of dp, dq. We like to stress that proving the equivalence for all the values of dp, dq may be a nontrivial task. Keywords: CRT-RSA, Cryptanalysis, Factorization, LLL Algorithm, RSA. 1
[Show abstract][Hide abstract] ABSTRACT: In-network data aggregation in Wireless Sensor Networks (WSNs) provides
efficient bandwidth utilization and energy-efficient computing.Supporting
efficient in-network data aggregation while preserving the privacy of the data
of individual sensor nodes has emerged as an important requirement in numerous
WSN applications. For privacy-preserving data aggregation in WSNs, He et al.
(INFOCOM 2007) have proposed a Cluster-based Private Data Aggregation (CPDA)
that uses a clustering protocol and a well-known key distribution scheme for
computing an additive aggregation function in a privacy-preserving manner. In
spite of the wide popularity of CPDA, it has been observed that the protocol is
not secure and it is also possible to enhance its efficiency. In this paper, we
first identify a security vulnerability in the existing CPDA scheme, wherein we
show how a malicious participant node can launch an attack on the privacy
protocol so as to get access to the private data of its neighboring sensor
nodes. Next it is shown how the existing CPDA scheme can be made more efficient
by suitable modification of the protocol. Further, suitable modifications in
the existing protocol have been proposed so as to plug the vulnerability of the
protocol.