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On the Algebraic Immunity of Symmetric Boolean Functions
 In Indocrypt 2005, number 3797 in LNCS
, 2005
"... In this paper, we analyse the algebraic immunity of symmetric Boolean functions. ..."
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Cited by 28 (1 self)
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In this paper, we analyse the algebraic immunity of symmetric Boolean functions.
Efficient computation of algebraic immunity for algebraic and fast algebraic attacks
, 2006
"... Abstract. In this paper we propose several efficient algorithms for assessing the resistance of Boolean functions against algebraic and fast algebraic attacks when implemented in LFSRbased stream ciphers. An algorithm is described which permits to compute the algebraic immunity d of a Boolean functi ..."
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Cited by 22 (10 self)
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Abstract. In this paper we propose several efficient algorithms for assessing the resistance of Boolean functions against algebraic and fast algebraic attacks when implemented in LFSRbased stream ciphers. An algorithm is described which permits to compute the algebraic immunity d of a Boolean function with n variables in O(D 2) operations, for D ≈ � � n, rather d than in O(D 3) operations necessary in all previous algorithms. Our algorithm is based on multivariate polynomial interpolation. For assessing the vulnerability of arbitrary Boolean functions with respect to fast algebraic attacks, an efficient generic algorithm is presented that is not based on interpolation. This algorithm is demonstrated to be particularly efficient for symmetric Boolean functions. As an application it is shown that large classes of symmetric functions are very vulnerable to fast algebraic attacks despite their proven resistance against conventional algebraic attacks.
Dragon: A Fast Word Based Stream Cipher
, 2005
"... This paper presents Dragon, a new stream cipher constructed using a single word based nonlinear feedback shift register and a nonlinear filter function with memory. Dragon uses a variable length key and initialisation vector of 128 or 256 bits, and produces 64 bits of keystream per iteration. A ..."
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Cited by 11 (1 self)
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This paper presents Dragon, a new stream cipher constructed using a single word based nonlinear feedback shift register and a nonlinear filter function with memory. Dragon uses a variable length key and initialisation vector of 128 or 256 bits, and produces 64 bits of keystream per iteration. At the heart of Dragon are two highly optimised 8 sboxes. Dragon uses simple operations on 32bit words to provide a high degree of e#ciency in a wide variety of environments, making it highly competitive when compared with other word based stream ciphers. The components of Dragon are designed to resist all known attacks.
Sosemanuk, a fast softwareoriented stream cipher. eSTREAM, ECRYPT Stream Cipher
 ECRYPT  Network of Excellence in Cryptology, Call for stream Cipher Primitives  Phase 2 (2005), http://www.ecrypt.eu.org/stream/ F. Arnault et al
, 2005
"... Abstract. Sosemanuk is a new synchronous softwareoriented stream cipher, corresponding to Profile 1 of the ECRYPT call for stream cipher primitives. Its key length is variable between 128 and 256 bits. It accommodates a 128bit initial value. Any key length is claimed to achieve 128bit security. T ..."
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Cited by 10 (1 self)
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Abstract. Sosemanuk is a new synchronous softwareoriented stream cipher, corresponding to Profile 1 of the ECRYPT call for stream cipher primitives. Its key length is variable between 128 and 256 bits. It accommodates a 128bit initial value. Any key length is claimed to achieve 128bit security. The Sosemanuk cipher uses both some basic design principles from the stream cipher SNOW 2.0 and some transformations derived from the block cipher SERPENT. Sosemanuk aims at improving SNOW 2.0 both from the security and from the efficiency points of view. Most notably, it uses a faster IVsetup procedure. It also requires a reduced amount of static data, yielding better performance on several architectures. 1
Extending the Resynchronization Attack
 SAC 2004
, 2004
"... Synchronous stream ciphers need perfect synchronization between sender and receiver. In practice, this is ensured by a resync mechanism. Daemen et al first described attacks on ciphers using such a resync mechanism. In this paper we extend their attacks in several ways by combining the standard a ..."
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Cited by 8 (4 self)
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Synchronous stream ciphers need perfect synchronization between sender and receiver. In practice, this is ensured by a resync mechanism. Daemen et al first described attacks on ciphers using such a resync mechanism. In this paper we extend their attacks in several ways by combining the standard attack with cryptanalytic techniques such as algebraic attacks and linear cryptanalysis. Our results show that using linear resync mechanisms should be avoided, and provide lower bounds for the nonlinearity required from a secure resync mechanism.
Improving the Algebraic Immunity of Resilient and Nonlinear Functions and Constructing Bent Functions
, 2004
"... The currently known constructions of Boolean functions with high nonlinearities, high algebraic degrees and high resiliency orders do not seem to permit achieving su#ciently high algebraic immunities. We introduce a construction of Boolean functions, which builds a new function from three known ..."
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Cited by 6 (0 self)
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The currently known constructions of Boolean functions with high nonlinearities, high algebraic degrees and high resiliency orders do not seem to permit achieving su#ciently high algebraic immunities. We introduce a construction of Boolean functions, which builds a new function from three known ones. Assuming that the three functions have some resiliency order, nonlinearity and algebraic degree, as well as their sum modulo 2, the constructed function has the same resiliency order and can have the same nonlinearity, but has potentially better algebraic degree and algebraic immunity. The set of classical constructions together with this new one (and with a simpler derived one, having the same advantages) permit now to obtain functions achieving all necessary criteria for being used in the pseudorandom generators in stream ciphers.
FURTHER PROPERTIES OF SEVERAL CLASSES OF BOOLEAN FUNCTIONS WITH OPTIMUM ALGEBRAIC IMMUNITY
"... Abstract. Thanks to a method proposed by Carlet, several classes of balanced Boolean functions with optimum algebraic immunity are obtained. By choosing suitable parameters, for even n ≥ 8, the balanced nvariable functions can have nonlinearity 2 n−1 − ` ´ ` ´ n−1 n−2 n + 2 −1 n /(n − 2), −2 ..."
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Cited by 6 (2 self)
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Abstract. Thanks to a method proposed by Carlet, several classes of balanced Boolean functions with optimum algebraic immunity are obtained. By choosing suitable parameters, for even n ≥ 8, the balanced nvariable functions can have nonlinearity 2 n−1 − ` ´ ` ´ n−1 n−2 n + 2 −1 n /(n − 2), −2
Improving the lower bound on the higher order nonlinearity of Boolean functions with prescribed algebraic immunity
, 2007
"... The recent algebraic attacks have received a lot of attention in cryptographic literature. The algebraic immunity of a Boolean function quantifies its resistance to the standard algebraic attacks of the pseudorandom generators using it as a nonlinear filtering or combining function. Very few result ..."
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Cited by 5 (0 self)
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The recent algebraic attacks have received a lot of attention in cryptographic literature. The algebraic immunity of a Boolean function quantifies its resistance to the standard algebraic attacks of the pseudorandom generators using it as a nonlinear filtering or combining function. Very few results have been found concerning its relation with the other cryptographic parameters or with the rth order nonlinearity. As recalled by Carlet at Crypto’06, many papers have illustrated the importance of the rthorder nonlinearity profile (which includes the firstorder nonlinearity). The role of this parameter relatively to the currently known attacks has been also shown for block ciphers. Recently, two lower bounds involving the algebraic immunity on the rthorder nonlinearity have been shown by Carlet et al. None of them improves upon the other one in all situations. In this paper, we prove a new lower bound on the rthorder nonlinearity profile of Boolean functions, given their algebraic immunity, that improves significantly upon one of these lower bounds for all orders and upon the other one for low orders.
Classes of Plateaued Rotation Symmetric Boolean functions under Transformation of Walsh Spectra
 In WCC 2005, Pages 325–334. See also IACR eprint server
, 2005
"... Abstract. Construction methods of Boolean functions with cryptographically significant properties is an important and difficult problem. In this work we investigate the class of rotation symmetric Boolean functions (RSBFs). These functions are invariant under circular translation of indices and were ..."
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Cited by 4 (1 self)
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Abstract. Construction methods of Boolean functions with cryptographically significant properties is an important and difficult problem. In this work we investigate the class of rotation symmetric Boolean functions (RSBFs). These functions are invariant under circular translation of indices and were mainly introduced for efficient implementation purposes. First, we derive general results on these functions. Afterwards, we concentrate on plateaued RSBFs on odd number of variables, which have three valued Walsh Spectra (0, ±λ), and can have maximum nonlinearity. We consider both cases when the number of variables n is composite and prime. When n is odd and prime, we derive the constructive relation between balanced/unbalanced plateaued RSBFs and show how from one given such function the complete sub class can be generated. As long as search for one plateaued RSBF is of high complexity, our proposed manipulation technique with Walsh spectra imediately give us the way to construct many such functions without time consuming. Since the most important properties of a function are determined via the values of Walsh spectra, then such transformation technique is important to create new function with, possible, better properties. The application of our transformation technique construct a class of�(2 n−1 2 + 1)/n�! ·�2 n−1 2 − 1� balanced/unbalanced plateaued RSBFs. In our practical implementation of this technique, given one balanced PRSBF on n = 11 variables we could construct 185 new such functions. To find the first function took us several days, whereas to construct new 185 functions took us just a second. However, this technique can be applied only when the Legendre symbol