Results 1 
5 of
5
On Fast and Provably Secure Message Authentication Based on Universal Hashing
 In Advances in Cryptology – CRYPTO ’96
, 1996
"... There are wellknown techniques for message authentication using universal hash functions. This approach seems very promising, as it provides schemes that are both efficient and provably secure under reasonable assumptions. This paper contributes to this line of research in two ways. First, it analy ..."
Abstract

Cited by 67 (0 self)
 Add to MetaCart
There are wellknown techniques for message authentication using universal hash functions. This approach seems very promising, as it provides schemes that are both efficient and provably secure under reasonable assumptions. This paper contributes to this line of research in two ways. First, it analyzes the basic construction and some variants under more realistic and practical assumptions. Second, it shows how these schemes can be efficiently implemented, and it reports on the results of empirical performance tests that demonstrate that these schemes are competitive with other commonly employed schemes whose security is less wellestablished. 1 Introduction Message Authentication. Message authentication schemes are an important security tool. As more and more data is being transmitted over networks, the need for secure, highspeed, softwarebased message authentication is becoming more acute. The setting for message authentication is the following. Two parties A and B agree on a secre...
Efficient Computation of Minimal Polynomials in Algebraic Extensions of Finite Fields
 In Proceedings of the 1999 International Symposium on Symbolic and Algebraic Computation (Vancouver, BC
, 1999
"... New algorithms are presented for computing the minimal polynomial over a finite field K of a given element in an algebraic extension of K of the form K[ff] or K[ff][fi]. The new algorithms are explicit and can be implemented rather easily in terms of polynomial multiplication, and are much more effi ..."
Abstract

Cited by 31 (0 self)
 Add to MetaCart
New algorithms are presented for computing the minimal polynomial over a finite field K of a given element in an algebraic extension of K of the form K[ff] or K[ff][fi]. The new algorithms are explicit and can be implemented rather easily in terms of polynomial multiplication, and are much more efficient than other algorithms in the literature. 1 Introduction In this paper, we consider the problem of computing the minimal polynomial over a finite field K of a given element oe in an algebraic extension of K of the form K[ff] or K[ff][fi]. The minimal polynomial of oe is defined to be the unique monic polynomial OE oe=K 2 K[x] of least degree such that OE oe=K (oe) = 0. In the first case, we assume that the ring K[ff] is given as K[x]=(f) where f 2 K[x] is a monic polynomial of degree n, and that elements in K[ff] are represented in the natural way as elements of K[x] !n (the set of polynomials of degree less than n). Similarly, in the second case, we assume that K[ff] is given as a...
Faster Algorithms for String Matching Problems: Matching the Convolution Bound
 In Proceedings of the 39th Symposium on Foundations of Computer Science
, 1998
"... In this paper we give a randomized O(n log n)time algorithm for the string matching with don't cares problem. This improves the FischerPaterson bound [10] from 1974 and answers the open problem posed (among others) by Weiner [30] and Galil [11]. Using the same technique, we give an O(n log n)t ..."
Abstract

Cited by 30 (5 self)
 Add to MetaCart
In this paper we give a randomized O(n log n)time algorithm for the string matching with don't cares problem. This improves the FischerPaterson bound [10] from 1974 and answers the open problem posed (among others) by Weiner [30] and Galil [11]. Using the same technique, we give an O(n log n)time algorithm for other problems, including subset matching and tree pattern matching [15, 21, 9, 7, 17] and (general) approximate threshold matching [28, 17]. As this bound essentially matches the complexity of computing of the Fast Fourier Transform which is the only known technique for solving problems of this type, it is likely that the algorithms are in fact optimal. Additionally, the technique used for the threshold matching problem can be applied to the online version of this problem, in which we are allowed to preprocess the text and require to process the pattern in time sublinear in the text length. This result involves an interesting variant of the KarpRabin fingerprint m...
Normal Bases over Finite Fields
, 1993
"... Interest in normal bases over finite fields stems both from mathematical theory and practical applications. There has been a lot of literature dealing with various properties of normal bases (for finite fields and for Galois extension of arbitrary fields). The advantage of using normal bases to repr ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
Interest in normal bases over finite fields stems both from mathematical theory and practical applications. There has been a lot of literature dealing with various properties of normal bases (for finite fields and for Galois extension of arbitrary fields). The advantage of using normal bases to represent finite fields was noted by Hensel in 1888. With the introduction of optimal normal bases, large finite fields, that can be used in secure and e#cient implementation of several cryptosystems, have recently been realized in hardware. The present thesis studies various theoretical and practical aspects of normal bases in finite fields. We first give some characterizations of normal bases. Then by using linear algebra, we prove that F q n has a basis over F q such that any element in F q represented in this basis generates a normal basis if and only if some groups of coordinates are not simultaneously zero. We show how to construct an irreducible polynomial of degree 2 n with linearly i...
unknown title
"... The literature of cryptography has a curious history. Secrecy, of course, has always played a central role, but until the First World War, important developments appeared in print in a more or less timely fashion and the field moved forward in much the same way as other specialized disciplines. As l ..."
Abstract
 Add to MetaCart
The literature of cryptography has a curious history. Secrecy, of course, has always played a central role, but until the First World War, important developments appeared in print in a more or less timely fashion and the field moved forward in much the same way as other specialized disciplines. As late as 1918, one of the most influential cryptanalytic papers of the twentieth century, William F. Friedman’s monograph The Index of Coincidence and Its Applications in Cryptography, appeared as a research report of the private Riverbank Laboratories [577]. And this, despite the fact that the work had been done as part of the war effort. In the same year Edward H. Hebern of Oakland, California filed the first patent for a rotor machine [710], the device destined to be a mainstay of military cryptography for nearly 50 years. After the First World War, however, things began to change. U.S. Army and Navy organizations, working entirely in secret, began to make fundamental advances in cryptography. During the thirties and forties a few basic papers did appear in the open literature and several treatises on the subject were published, but the latter were farther and farther behind the state of the art. By the end of the war the transition was complete. With one notable exception, the public literature had died. That exception was Claude Shannon’s paper “The Communication Theory of Secrecy Systems, ” which