Filiol and Fontaine recently proposed a family of stream ciphers named COS. COS is based on nonlinear feedback shift registers and was claimed to be with high cryptographic strength. Babbage showed that COS $(2,128)$ Mode II is extremely weak. But Babbage's attack is too expensive to break the COS $(2,128)$ Mode I (the complexity is around $2^{52}$). In this paper, we show that the COS $(2,128)$ Mode I is too weak. With about $2^{16}$-bit known plaintext, the secret information could be recovered with small amount of memory and computation time (less than one second on a Pentium IV Processor).

A new family of very fast stream ciphers called COS (for “crossing over system”) has been proposed by Filiol and Fontaine, and seems to have been adopted for at least one commercial standard. COS(2,128) Mode I and COS(2,128) Mode II are particular members of this family for which the authors proposed a cryptanalysis challenge. The ciphers accept secret keys of 256, 192 or 128 bits. In this note we cryptanalyse both of these ciphers, using a small amount of known keystream — with negligible effort in the case of Mode II, and with effort well below that required for a single DES key search in the case of Mode I.

In this paper we estimate the period of the sequence generated by a clock-controlled LFSR with an irreducible feedback polynomial and an arbitrary structure of the control sequence, as well as some randomness properties of this sequence including element distribution and the autocorrelation function. Also we construct and analyze a specific key-stream generator that applies clock-control. Finally, we present a comprehensive survey of known correlation attacks on clock-controlled registers and their memoryless combiners.

HMAC is the internet standard for message authentication. What distinguishes HMAC from other MAC algorithms is that it provides proofs of security assuming that the underlying cryptographic hash (e.g. SHA-1) has some reasonable properties. HMAC is efficient for long messages, however, for short messages the nested construction results in a significant inefficiency. For example to MAC a message shorter than a block, HMAC requires at least two calls to the compression function rather than one. This inefficiency may be particularly high for some applications, like message authentication of signaling messages, where the individual messages may all fit within one or two blocks. Also for TCP/IP traffic it is well known that large number of packets (e.g. acknowledgment) have sizes around 40 bytes which fit within a block of most cryptographic hashes. We propose an enhancement that allows both short and long messages to be message authenticated more efficiently than HMAC while also providing proofs of security. In particular, for a message smaller than a block our MAC only requires one call to the compression function.

Many of the keystream generators which are used in practice are LFSR-based in the sense that they produce the keystream according to a rule $y=C(L(x))$, where $L(x)$ denotes an internal linear bitstream, produced by a small number of parallel linear feedback shift registers (LFSRs), and $C$ denotes some nonlinear compression function. We present an $n^{O(1)} 2^{(1-\alpha)/(1+\alpha)n}$ time bounded attack, the FBDD-attack, against LFSR-based generators, which computes the secret initial state $x\in\booln$ from $cn$ consecutive keystream bits, where $\alpha$ denotes the rate of information, which $C$ reveals about the internal bitstream, and $c$ denotes some small constant. The algorithm uses Free Binary Decision Diagrams (FBDDs), a data structure for minimizing and manipulating Boolean functions. The FBDD-attack yields better bounds on the effective key length for several keystream generators of practical use, so a $0.656n$ bound for the self-shrinking generator, a $0.6403 n$ bound for the A5/1 generator, used in the GSM standard, a $0.6n$ bound for the $E_0$ encryption standard in the one level mode, and a $0.8823n$ bound for the two-level $E_0$ generator used in the Bluetooth wireless LAN system.

In this note we discuss a novel but simple time-memory tradeoff attack against the stream cipher LILI-128. The attack defeats the security advantage of having an irregular stepping function. The attack requires $2^{46}$ bits of keystream, a lookup table of $2^{45}$ 89-bit words and computational effort which is roughly equivalent to $2^{48}$ DES operations.

In this paper we consider matrices of special form introduced in [11] and used for the constructing of resilient functions with cryptographically optimal parameters. For such matrices we establish lower bound ${1\over\log_2(\sqrt{5}+1)}=0.5902...$ for the important ratio ${t\over t+k}$ of its parameters and point out that there exists a sequence of matrices for which the limit of ratio of its parameters is equal to lower bound. By means of these matrices we construct $m$-resilient $n$-variable functions with maximum possible nonlinearity $2^{n-1}-2^{m+1}$ for $m=0.5902...n+O(\log_2 n)$. This result supersedes the previous record.

This note summarizes the results of Babbage's cryptanalysis of COS ciphers and shows that in fact COS ciphers are not weak as claimed. These ciphers have been designed according a novel concept of encryption directly determined by the context of use. This concept is here more precisely defined.

A new family of very fast stream ciphers called COS (for "crossing over system") has been proposed by Filiol and Fontaine, and seems to have been adopted for at least one commercial standard. In this note we show that the COS ciphers are very weak indeed — it requires negligible effort to reconstruct the state of the keystream generator from a very small amount of known keystream.

In this article I analyze the function f(X) = A + X (mod 2**n) exclusive-or differential probability. The result, regarding differential cryptanalysis, is a better understanding of ciphers that use f(X) as a primitive operation. A simple O(n) algorithm to compute the probability is given.

Linear cryptanalysis remains the most powerful attack against DES at this time. Given $2^{43}$ known plaintext-ciphertext pairs, Matsui expected a complexity of less than $2^{43}$ DES evaluations in 85% of the cases for recovering the key. In this paper, we present a theoretical and experimental complexity analysis of this attack, which has been simulated 21 times using the idle time of several computers. The experimental results suggest a complexity upper-bounded by $2^{41}$ DES evaluations in 85% of the case, while more than the half of the experiments needed less than $2^{39}$ DES evaluations. In addition, we give a detailed theoretical analysis of the attack complexity.

This paper reports on variants of the Square attack applied to reduced-round versions of the PES and IDEA block ciphers. Attacks on 2.5 rounds of IDEA require $3\cdot 2^{16}$ chosen-plaintexts and recover 78 key bits. A new kind of attack, the Square related-key attack, is applied on 2.5 rounds of IDEA and recovers 32 key bits, with 2 chosen-plaintexts and $2^{17}$ related keys. Similar results hold for 2.5 rounds of PES. Implementations of the attacks on 32-bit block mini-versions of both ciphers confirmed the expected computational complexity. Although our attacks do not improve on previous approaches, this report shows new variants of the Square attack on word-oriented block ciphers like IDEA and PES.

The authors analyze the security of Hierocrypt-3(128-bit) and Hierocrypt-L1(64-bit) designed on the nested SPN(NSPN) structure against the differential and linear cryptanalysis, and found that they are sufficiently secure, e.g., the maximum average differential and linear hull probabilities (MACP and MALHP) are bounded by $2^{-96}$ for 4-round of Hierocrypt-3; those probabilities are bounded by $2^{-48}$ for 4-round of Hierocrypt-L1. The authors get these results by extending the provable security theorem by Hong et al.. Furthermore, the extended theory is applied to Rijndael, and found that MACP and MALHP of 4-round Rijndael are bounded by $2^{-96}$. This outperforms the best previous result by Keliher et al..

Stream ciphers are an important class of encryption algorithms, which are widely used in practice. In this paper the security of the WAKE stream cipher is investigated. We present two chosen plaintext attacks on this cipher. The complexities of these attacks can be estimated as 10^^19.2 and 10^^14.4.

Stream ciphers are often used in applications where high speed and low delay are a requirement. The ISAAC keystream generator is a fast software-oriented encryption algorithm. In this papers the security of the ISAAC keystream generator is investigated. Cryptanalytic algorithm is developed for a known plaintext attack where only a small segment of plaintext is assumed to be known. Keywords. ISAAC. Keystream generator. Cryptanalysis.

We address the problem of how to construct ideal cipher systems when the length of a key is much less than the length of an encrypted message. We suggest a new secret key cipher system in which firstly the message is transformed into two parts in such a way that the biggest part consists of independent and equiprobable letters. Secondly the relatively small second part is enciphered wholly by the Vernam cipher whereas only few bits from the biggest part are enciphered. This transformation is based on the fast version of the Elias construction of an unbiased random sequence. The time required for encoding and decoding and the memory size of the encoder and decoder are presented as functions of the ratio of the key length and the message length. The suggested scheme can be applied to sources with unknown statistics.

Constructing highly nonlinear balanced Boolean functions with very good autocorrelation property is an interesting open question. In this direction we use the measure $\Delta_f$ for a function $f$ proposed by Zhang and Zheng (1995). We provide balanced functions $f$ with currently best known nonlinearity and $\Delta_f$ values together. Our results for 15-variable functions disprove the conjecture proposed by Zhang and Zheng (1995), where our constructions are based on modifications of Patterson-Wiedemann (1983) functions. Also we propose a simple bent based construction technique to get functions with very good $\Delta_f$ values for odd number of variables. This construction has a root in Kerdock Codes. Moreover, our construction on even number of variables is a recursive one and we conjecture (similar to Dobbertin's conjecture (1994) with respect to nonlinearity) that this provides minimum possible value of $\Delta_f$ for a function $f$ on even number of variables.

In this paper the security of the stream cipher Vesta-2M is investigated. Cryptanalytic algorithm is developed for a known plaintext attack where only a small segment of plaintext is assumed to be known. The complexity the attack is estimated the time of searching through the square root of all possible initial states.

In this paper we systematically study the differential properties of addition modulo $2^n$. We derive $\Theta(\log n)$-time algorithms for most of the properties, including differential probability of addition. We also present log-time algorithms for finding good differentials. Despite the apparent simplicity of modular addition, the best known algorithms require naive exhaustive computation. Our results represent a significant improvement over them. In the most extreme case, we present a complexity reduction from $\Omega(2^{4n})$ to $\Theta(\log n)$.

This paper is motivated by some results presented by Knudsen, Robshaw and Wagner at Crypto'99, that described many attacks of reduced versions of Skipjack, some of them being erroneous. Differential cryptanalysis is based on distinguishers, any attack should prove that the events that triggers the analysis has not the same probability for the cipher than for a random function. In particular, the composition of differential for successive parts of a cipher should be done very carefully to lead to an attack. This revised version of the paper includes the exact computations of some probabilities and repairs the attack of the first half of Skipjack.

In [3], we present a new algorithm for computing an upper bound on the maximum average linear hull probability (MALHP) for the SPN symmetric cipher structure, a value required to make claims about provable security against linear cryptanalysis. This algorithm improves on existing work in that the resulting upper bound is a function of the number of encryption rounds (other upper bounds known to the authors are not), and moreover, it can be computed for an SPN with any linear transformation layer (the best previous result, that of Hong et.al [4], applies only to SPNs with highly diffusive linear transformations). It is well known that there exists a duality between linear cryptanalysis and differential cryptanalysis which allows certain results related to one of the attacks to be translated into the corresponding results for the other attack [1,5]. Since this duality applies to our work in [3], we immediately obtain an algorithm for upper bounding the maximum average differential probability (MADP) for SPNs (required to make claims about provable security against differential cryptanalysis). Note: In what follows, we assume familiarity with the notation and results of [3].

This paper was prepared for NIST, which is considering new block-cipher modes of operation. It describes a parallelizable mode of operation that simultaneously provides both privacy and authenticity. "OCB mode" encrypts-and-authenticates an arbitrary message $M\in\bits^*$ using only $\lceil |M|/n\rceil + 2$ block-cipher invocations, where $n$ is the block length of the underlying block cipher. Additional overhead is small. OCB refines a scheme, IAPM, suggested by Jutla [IACR-2000/39], who was the first to devise an authenticated-encryption mode with minimal overhead compared to standard modes. Desirable new properties of OCB include: very cheap offset calculations; operating on an arbitrary message $M\in\bits^*$; producing ciphertexts of minimal length; using a single underlying cryptographic key; making a nearly optimal number of block-cipher calls; avoiding the need for a random IV; and rendering it infeasible for an adversary to find "pretag collisions". The paper provides a full proof of security for OCB.

Recently, Jutla suggested two new modes of operation for block ciphers. These modes build on traditional CBC and ECB modes, respectively, but add to them masking of the outputs and inputs. Jutla proved that these masking operations considerably strengthen CBC and ECB modes. In particular, together with a simple checksum, the modified modes ensure not only confidentiality, but also authenticity. Similar modes were also suggested by Gligor and Donsecu and by Rogaway. In Jutla's proposal (as well as in some of the other proposals), the masks themselves are derived from an IV via the same block cipher as used for the encryption (perhaps with a different key). In this work we note, however, that the function for deriving these masks need not be cryptographic at all. In particular, we prove that a universal hash function (a-la-Carter-Wegman) is sufficient for this purpose.

Serpent is one of the 5 AES finalists. The best attack published so far analyzes up to 9 rounds. In this paper we present attacks on 7-round, 8-round, and 10-round variants of Serpent. We attack 7-round variant of Serpent with all key lengths, and 8- and 10-round variants wih 256-bit keys. The 10-roun attack on the 256-bit keys variants is the best published attack on the cipher. The attack enhances the amplified boomerang attack and uses better differentials. We also present the best 3-round, 4-round, 5-round and 6-round differential characteristics of Serpent.

In this paper a preliminary version of the NTRU signature scheme is cryptanalyzed. The attack exploits a correlation between some bits of a signature and coefficients of a secret random polynomial. The attack does not apply to the next version of the signature scheme.

In this paper we develop a technique that allows to obtain new effective constructions of highly resilient Boolean functions with high nonlinearity. In particular, we prove that the upper bound $2^{n-1}-2^{m+1}$ on nonlinearity of m-resilient n-variable Boolean functions is achieved for $0.6n-1\le m\le n-2$.

Here we provide a construction method for unbalanced, first order correlation immune Boolean functions on even number of variables $n \geq 6$. These functions achieve the currently best known nonlinearity $2^{n-1} - 2^{\frac{n}{2}} + 2^{\frac{n}{2} - 2}$ . Then we provide a simple modification of these functions to get unbalanced correlation immune Boolean functions on even number of variables $n$, with nonlinearity $2^{n-1} - 2^{\frac{n}{2}} + 2^{\frac{n}{2} - 2} - 2$ and maximum possible algebraic degree $n-1$. Moreover, we present a detailed study on the Walsh spectra of these functions.

We use the recent results on the spectral structure of correlation immune and resilient Boolean functions for the investigations of high order correlation immune functions. At first, we give simple proofs of some theorems where only long proofs were known. Next, we introduce the matrix of nonzero Walsh coefficients and establish important properties of this matrix. We use these properties to prove the nonexistence of some high order correlation immune functions. Finally, we establish the order of magnitude for the number of (n-4)th order correlation immune functions of n variables.

An attack on the A5/2 stream cipher algorithm is described, that determines the linear relations among the output sequence bits. The vast majority of the unknown output bits can be reconstructed. The time complexity of the attack is proportional to 2**17.

In this paper we prove a general result on the Walsh Transform of an arbitrary Boolean function. As a consequence, we obtain several divisibility results on the Walsh Transform of correlation immune and resilient Boolean functions. This allows us to improve upper bounds on the nonlinearity of correlation immune and resilient Boolean functions. Also we provide new necessary conditions on the algebraic normal form of correlation immune/resilient functions attaining the maximum possible nonlinearity.

Recently weight divisibility results on resilient and correlation immune Boolean functions have received a lot of attention. These results have direct consequences towards the upper bound on nonlinearity of resilient and correlation immune Boolean functions of certain order. Now the clear benchmark in the design of resilient Boolean functions (which optimizes Sigenthaler's inequality) is to provide results which attain the upper bound on nonlinearity. Here we construct a 7-variable, 2-resilient Boolean function with nonlinearity 56. This solves the maximum nonlinearity issue for 7-variable functions with any order of resiliency. Using this 7-variable function, we also construct a 10-variable, 4-resilient Boolean function with nonlinearity 480. Construction of these two functions were justified as important open questions in Crypto 2000. Also we provide methods to generate an infinite sequence of Boolean functions on $n = 7 + 3i$ variables $(i \geq 0)$ with order of resiliency $m = 2 + 2i$, algebraic degree $4 + i$ and nonlinearity $2^{n-1} - 2^{m+1}$, which were not known earlier. We conclude with a few interesting construction results on unbalanced correlation immune functions of 5 and 6 variables.

This paper presents a new attack called {\em Decimation Attack} of most stream ciphers. It exploits the property that multiple clocking (or equivalently $d$-th decimation) of a LFSR can simulate the behavior of many other LFSRs of possible shorter length. It yields then significqnt improvements of all the previous known correlation and fast correlation attacks provided a new criterion is satisfied. This criterion on the length of the feedback polynomial is then defined to resist the decimation attack. Simulation results and complexity comparison are detailed for ciphertext only attack.

We introduce the notion of a saturation attack and present attacks on reduced-round versions of the Twofish block cipher. Our attack for all generic key sizes of Twofish (i.e., for 128-bit, 192-bit and 256-bit keys) improves on exhaustive key search for seven rounds of Twofish with full whitening, and for eight rounds of Twofish without whitening at the end. The core of the attack is a a key-independent distinguisher for six rounds of Twofish. The distinguisher is used to attack up to 7 rounds of Twofish with full whitening and and 8 rounds of Twofish with prewhitening only - half of the cipher. The attacks take up to 2^127 chosen plaintexts (half of the codebook!) and are 2-4 times faster than exhaustive search.

We show how to construct pseudo-random permutations that satisfy a certain cycle restriction, for example that the permutation be cyclic (consisting of one cycle containing all the elements) or an involution (a self-inverse permutation) with no fixed points. The construction can be based on any (unrestricted) pseudo-random permutation. The resulting permutations are defined succinctly and their evaluation at a given point is efficient. Furthermore, they enjoy a {\em fast forward} property, i.e. it is possible to iterate them at a very small cost.

We investigate, in a concrete security setting, several alternate characterizations of pseudorandom functions (PRFs) and pseudorandom permutations (PRPs). By analyzing the concrete complexity of the reductions between the standard notions and the alternate ones, we show that the latter, while equivalent under polynomial-time reductions, are weaker in the concrete security sense. With these alternate notions, we argue that it is possible to get better concrete security bounds for certain PRF/PRP-based schemes. As an example, we show how using an alternate characterization of a PRF could result in tighter security bounds for a certain class of message authentication codes. We also apply these techniques to give a simple concrete security analysis of the counter mode of encryption. In addition, our results provide some insight into how injectivity impacts pseudorandomness.

This paper takes a closer look at Rivest's chaffing-and-winnowing paradigm for data privacy. We begin with a \textit{definition} which enables one to determine clearly whether a given scheme qualifies as ``chaffing-and-winnowing.'' We then analyze Rivest's schemes to see what quality of data privacy they provide. His simplest scheme is easily proven secure but is ineffient. The security of his more efficient scheme ---based on all-or-nothing transforms (AONTs)--- is however more problematic. It can be attacked under Rivest's definition of security of an AONT, and even under stronger notions does not appear provable. We show however that by using a OAEP as the AONT one can prove security. We also present a different scheme, still using AONTs, that is equally efficient and easily proven secure even under the original weak notion of security of AONTs.

There has been a recent upsurge of research in the design of resilient Boolean functions for use in stream cipher systems. The existing research concentrates on maximum degree resilient functions and tries to obtain as high nonlinearity as possible. In sharp contrast to this approach we identify the class of functions with {\em provably best} possible trade-off among the parameters: number of variables, resiliency, nonlinearity and algebraic degree. We first prove a sharper version of McEliece theorem for Reed-Muller codes as applied to resilient functions, which also generalizes the well known Xiao-Massey characterization. As a consequence a nontrivial upper bound on the nonlinearity of resilient functions is obtained. This result coupled with Siegenthaler's inequality naturally leads to the notion of provably best resilient functions. We further show that such best functions can be constructed by the Maiorana-McFarland like technique. In cases where this method fails, we provide new ideas to construct best functions. We also briefly discuss efficient implementation of these functions in hardware.

This paper proposes an algorithm to encipher the Chinese plaintext message written in Big-5/GB Chinese character internal codes. Unlike the ordinary ciphers, the Crypto-key of our proposed algorithm consists of a pair of formulas and a set of parameter values. The senders can formulate and compose their own unique formulas and parameters for encryption. According to the character internal code structure, we apply the formulas in a Key-stream generator to encipher the Chinese plaintext message. Since the proposed stream generator does not contain permanent encryption and decryption operations, the opponents are inadequate to predict the forms of its output (ciphertext). Experiment results show that the proposed algorithm achieves the data secrecy.

It is proved that the maximal possible nonlinearity of $n$-variable $m$-resilient Boolean function is $2^{n-1}-2^{m+1}$ for ${2n-7\over 3}\le m\le n-2$. This value can be achieved only for optimized functions (i.~e. functions with an algebraic degree $n-m-1$). For ${2n-7\over 3}\le m\le n-\log_2{n-2\over 3}-2$ it is suggested a method to construct an $n$-variable $m$-resilient function with maximal possible nonlinearity $2^{n-1}-2^{m+1}$ such that each variable presents in ANF of this function in some term of maximal possible length $n-m-1$. For $n\equiv 2\pmod 3$, $m={2n-7\over 3}$, it is given a scheme of hardware implementation for such function that demands approximately $2n$ gates EXOR and $(2/3)n$ gates AND.