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The Block Cipher SQUARE
 FAST SOFTWARE ENCRYPTION (FSE) 1997
, 1997
"... In this paper we present a new 128bit block cipher called Square. The original design of Square concentrates on the resistance against differential and linear cryptanalysis. However, after the initial design a dedicated attack was mounted that forced us to augment the number of rounds. The goal of ..."
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Cited by 124 (19 self)
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In this paper we present a new 128bit block cipher called Square. The original design of Square concentrates on the resistance against differential and linear cryptanalysis. However, after the initial design a dedicated attack was mounted that forced us to augment the number of rounds. The goal of this paper is the publication of the resulting cipher for public scrutiny. A C implementation of Square is available that runs at 2.63 MByte/s on a 100 MHz Pentium. Our M68HC05 Smart Card implementation fits in 547 bytes and takes less than 2 msec. (4 MHz Clock). The high degree of parallellism allows hardware implementations in the Gbit/s range today.
New Multiparty Authentication Services and Key Agreement Protocols
 IEEE Journal on Selected Areas in Communications
, 2000
"... Many modern computing environments involve dynamic peer groups. Distributed simulation, multiuser games, conferencing applications and replicated servers are just a few examples. Given the openness of today's networks, communication among peers (group members) must be secure and, at the same t ..."
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Cited by 119 (4 self)
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Many modern computing environments involve dynamic peer groups. Distributed simulation, multiuser games, conferencing applications and replicated servers are just a few examples. Given the openness of today's networks, communication among peers (group members) must be secure and, at the same time, efficient. This paper studies the problem of authenticated key agreement in dynamic peer groups with the emphasis on efficient and provably secure key authentication, key confirmation and integrity. It begins by considering 2party authenticated key agreement and extends the results to Group DiffieHellman key agreement. In the process, some new security properties (unique to groups) are encountered and discussed.
Authenticated Group Key Agreement and Friends
, 1998
"... Many modern computing environments involve dynamic peer groups. Distributed simulation, multiuser games, conferencing and replicated servers are just a few examples. Given the openness of today's networks, communication among group members must be secure and, at the same time, efficient. This ..."
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Cited by 96 (6 self)
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Many modern computing environments involve dynamic peer groups. Distributed simulation, multiuser games, conferencing and replicated servers are just a few examples. Given the openness of today's networks, communication among group members must be secure and, at the same time, efficient. This paper studies the problem of authenticated key agreement in dynamic peer groups with the emphasis on efficient and provably secure key authentication, key confirmation and integrity. It begins by considering 2party authenticated key agreement and extends the results to Group DiffieHellman key agreement. In the process, some new security properties (unique to groups) are discussed. 1 Introduction This paper is concerned with security services in the context of dynamic peer groups (DPGs). Such groups are common in many network protocol layers and in many areas of modern computing and the solution to their security needs, in particular key management, are still open research challenges [19]. Exa...
Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance
, 2001
"... The number of steps any classical computer requires in order to find the prime factors of an ldigit integer N increases exponentially with l, at least using algorithms [1] known at present. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying th ..."
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Cited by 96 (4 self)
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The number of steps any classical computer requires in order to find the prime factors of an ldigit integer N increases exponentially with l, at least using algorithms [1] known at present. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying the security of widely used cryptographic codes [1, 2]. Quantum computers [3], however, could factor integers in only polynomial time, using Shor’s quantum factoring algorithm [4, 5, 6]. Although important for the study of quantum computers [7], experimental demonstration of this algorithm has proved elusive [8, 9, 10]. Here we report an implementation of the simplest instance of Shor’s algorithm: factorization of N=15 (whose prime factors are 3 and 5). We use seven spin1/2 nuclei in a molecule as quantum bits [11, 12], which can be manipulated with room temperature liquid state nuclear magnetic resonance techniques. This method of using nuclei to store quantum information is in principle scalable to many quantum bit systems [13], but such scalability is not implied by the present work. The significance of our work lies in the demonstration of experimental and theoretical techniques for precise control and modelling of complex quantum
Efficient arithmetic on Koblitz curves
 Designs, Codes, and Cryptography
, 2000
"... Abstract. It has become increasingly common to implement discretelogarithm based publickey protocols on elliptic curves over finite fields. The basic operation is scalar multiplication: taking a given integer multiple of a given point on the curve. The cost of the protocols depends on that of the ..."
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Cited by 85 (0 self)
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Abstract. It has become increasingly common to implement discretelogarithm based publickey protocols on elliptic curves over finite fields. The basic operation is scalar multiplication: taking a given integer multiple of a given point on the curve. The cost of the protocols depends on that of the elliptic scalar multiplication operation. Koblitz introduced a family of curves which admit especially fast elliptic scalar multiplication. His algorithm was later modified by Meier and Staffelbach. We give an improved version of the algorithm which runs 50 % faster than any previous version. It is based on a new kind of representation of an integer, analogous to certain kinds of binary expansions. We also outline further speedups using precomputation and storage.
Pairingbased Cryptography at High Security Levels
 Proceedings of Cryptography and Coding 2005, volume 3796 of LNCS
, 2005
"... Abstract. In recent years cryptographic protocols based on the Weil and Tate pairings on elliptic curves have attracted much attention. A notable success in this area was the elegant solution by Boneh and Franklin [7] of the problem of efficient identitybased encryption. At the same time, the secur ..."
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Cited by 80 (3 self)
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Abstract. In recent years cryptographic protocols based on the Weil and Tate pairings on elliptic curves have attracted much attention. A notable success in this area was the elegant solution by Boneh and Franklin [7] of the problem of efficient identitybased encryption. At the same time, the security standards for public key cryptosystems are expected to increase, so that in the future they will be capable of providing security equivalent to 128, 192, or 256bit AES keys. In this paper we examine the implications of heightened security needs for pairingbased cryptosystems. We first describe three different reasons why highsecurity users might have concerns about the longterm viability of these systems. However, in our view none of the risks inherent in pairingbased systems are sufficiently serious to warrant pulling them from the shelves. We next discuss two families of elliptic curves E for use in pairingbased cryptosystems. The first has the property that the pairing takes values in the prime field Fp over which the curve is defined; the second family consists of supersingular curves with embedding degree k = 2. Finally, we examine the efficiency of the Weil pairing as opposed to the Tate pairing and compare a range of choices of embedding degree k, including k = 1 and k = 24. Let E be the elliptic curve 1.
Another Look at “Provable Security"
, 2004
"... We give an informal analysis and critique of several typical “provable security” results. In some cases there are intuitive but convincing arguments for rejecting the conclusions suggested by the formal terminology and “proofs,” whereas in other cases the formalism seems to be consistent with common ..."
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Cited by 63 (12 self)
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We give an informal analysis and critique of several typical “provable security” results. In some cases there are intuitive but convincing arguments for rejecting the conclusions suggested by the formal terminology and “proofs,” whereas in other cases the formalism seems to be consistent with common sense. We discuss the reasons why the search for mathematically convincing theoretical evidence to support the security of publickey systems has been an important theme of researchers. But we argue that the theoremproof paradigm of theoretical mathematics is often of limited relevance here and frequently leads to papers that are confusing and misleading. Because our paper is aimed at the general mathematical public, it is selfcontained and as jargonfree as possible.
Speeding Up Pollard's Rho Method For Computing Discrete Logarithms
, 1998
"... . In Pollard's rho method, an iterating function f is used to define a sequence (y i ) by y i+1 = f(y i ) for i = 0; 1; 2; : : : , with some starting value y 0 . In this paper, we define and discuss new iterating functions for computing discrete logarithms with the rho method. We compare the ..."
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Cited by 48 (7 self)
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. In Pollard's rho method, an iterating function f is used to define a sequence (y i ) by y i+1 = f(y i ) for i = 0; 1; 2; : : : , with some starting value y 0 . In this paper, we define and discuss new iterating functions for computing discrete logarithms with the rho method. We compare their performances in experiments with elliptic curve groups. Our experiments show that one of our newly defined functions is expected to reduce the number of steps by a factor of approximately 0:8, in comparison with Pollard's originally used function, and we show that this holds independently of the size of the group order. For group orders large enough such that the run time for precomputation can be neglected, this means a realtime speedup of more than 1:2. 1. Introduction Let G be a finite cyclic group, written multiplicatively, and generated by the group element g. Given an element h in G, we wish to find the least nonnegative number x such that g x = h. This problem is the discre...
New PublicKey Schemes Based on Elliptic Curves over the Ring Z_n
, 1991
"... Three new trapdoor oneway functions are proposed that are based on elliptic curves over the ring Z_n. The first class of functions is a naive construction, which can be used only in a digital signature scheme, and not in a publickey cryptosystem. The second, preferred class of function, does not s ..."
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Cited by 46 (0 self)
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Three new trapdoor oneway functions are proposed that are based on elliptic curves over the ring Z_n. The first class of functions is a naive construction, which can be used only in a digital signature scheme, and not in a publickey cryptosystem. The second, preferred class of function, does not suffer from this problem and can be used for the same applications as the RSA trapdoor oneway function, including zeroknowledge identification protocols. The third class of functions has similar properties to the Rabin trapdoor oneway functions. Although the security of these proposed schemes is based on the difficulty of factoring n, like the RSA and Rabin schemes, these schemes seem to be more secure than those schemes from the viewpoint of attacks without factoring such as low multiplier attacks.
Parallel Algorithms for Integer Factorisation
"... The problem of finding the prime factors of large composite numbers has always been of mathematical interest. With the advent of public key cryptosystems it is also of practical importance, because the security of some of these cryptosystems, such as the RivestShamirAdelman (RSA) system, depends o ..."
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Cited by 42 (17 self)
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The problem of finding the prime factors of large composite numbers has always been of mathematical interest. With the advent of public key cryptosystems it is also of practical importance, because the security of some of these cryptosystems, such as the RivestShamirAdelman (RSA) system, depends on the difficulty of factoring the public keys. In recent years the best known integer factorisation algorithms have improved greatly, to the point where it is now easy to factor a 60decimal digit number, and possible to factor numbers larger than 120 decimal digits, given the availability of enough computing power. We describe several algorithms, including the elliptic curve method (ECM), and the multiplepolynomial quadratic sieve (MPQS) algorithm, and discuss their parallel implementation. It turns out that some of the algorithms are very well suited to parallel implementation. Doubling the degree of parallelism (i.e. the amount of hardware devoted to the problem) roughly increases the size of a number which can be factored in a fixed time by 3 decimal digits. Some recent computational results are mentioned – for example, the complete factorisation of the 617decimal digit Fermat number F11 = 2211 + 1 which was accomplished using ECM.