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Guide to Elliptic Curve Cryptography
, 2004
"... Elliptic curves have been intensively studied in number theory and algebraic geometry for over 100 years and there is an enormous amount of literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves. (This is not a threat.) Elliptic curves ..."
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Cited by 610 (18 self)
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Elliptic curves have been intensively studied in number theory and algebraic geometry for over 100 years and there is an enormous amount of literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves. (This is not a threat.) Elliptic curves also figured prominently in the recent proof of Fermat's Last Theorem by Andrew Wiles. Originally pursued for purely aesthetic reasons, elliptic curves have recently been utilized in devising algorithms for factoring integers, primality proving, and in publickey cryptography. In this article, we aim to give the reader an introduction to elliptic curve cryptosystems, and to demonstrate why these systems provide relatively small block sizes, highspeed software and hardware implementations, and offer the highest strengthperkeybit of any known publickey scheme.
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
, 1999
"... Differential Power Analysis, first introduced by Kocher et al. in [14], is a powerful technique allowing to recover secret smart card information by monitoring power signals. In [14] a specific DPA attack against smartcards running the DES algorithm was described. As few as 1000 encryptions were su ..."
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Cited by 250 (2 self)
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Differential Power Analysis, first introduced by Kocher et al. in [14], is a powerful technique allowing to recover secret smart card information by monitoring power signals. In [14] a specific DPA attack against smartcards running the DES algorithm was described. As few as 1000 encryptions were sufficient to recover the secret key. In this paper we generalize DPA attack to elliptic curve (EC) cryptosystems and describe a DPA on EC DiffieHellman key exchange and EC ElGamal type encryption. Those attacks enable to recover the private key stored inside the smartcard. Moreover, we suggest countermeasures that thwart our attack.
Digital Signcryption or How to Achieve Cost(Signature
, 1997
"... Abstract. Secure and authenticated message delivery/storage is one of the major aims of computer and communication security research. The current standard method to achieve this aim is “(digital) signature followed by encryption”. In this paper, we address a question on the cost of secure and authen ..."
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Cited by 205 (20 self)
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Abstract. Secure and authenticated message delivery/storage is one of the major aims of computer and communication security research. The current standard method to achieve this aim is “(digital) signature followed by encryption”. In this paper, we address a question on the cost of secure and authenticated message delivery/storage, namely, whether it is possible to transport/store messages of varying length in a secure and authenticated way with an expense less than that required by “signature followed by encryption”. This question seems to have never been addressed in the literature since the invention of public key cryptography. We then present a positive answer to the question. In particular, we discover a new cryptographic primitive termed as “signcryption ” which simultaneously fulfills both the functions of digital signature and public key encryption in a logically single step, and with a cost significantly lower than that required by “signature followed by encryption”. For typical security parameters for high level security applications (size of public moduli = 1536 bits), signcryption costs 50 % (31%, respectively) less in computation time and 85 % (91%, respectively) less in message expansion than does “signature followed by encryption ” based on the discrete logarithm problem (factorization problem, respectively).
Software Implementation of Elliptic Curve Cryptography Over Binary Fields
, 2000
"... This paper presents an extensive and careful study of the software implementation on workstations of the NISTrecommended elliptic curves over binary fields. We also present the results of our implementation in C on a Pentium II 400 MHz workstation. ..."
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Cited by 187 (10 self)
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This paper presents an extensive and careful study of the software implementation on workstations of the NISTrecommended elliptic curves over binary fields. We also present the results of our implementation in C on a Pentium II 400 MHz workstation.
The Elliptic Curve Digital Signature Algorithm (ECDSA)
, 1999
"... The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve analogue of the Digital Signature Algorithm (DSA). It was accepted in 1999 as an ANSI standard, and was accepted in 2000 as IEEE and NIST standards. It was also accepted in 1998 as an ISO standard, and is under consideratio ..."
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Cited by 183 (5 self)
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The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve analogue of the Digital Signature Algorithm (DSA). It was accepted in 1999 as an ANSI standard, and was accepted in 2000 as IEEE and NIST standards. It was also accepted in 1998 as an ISO standard, and is under consideration for inclusion in some other ISO standards. Unlike the ordinary discrete logarithm problem and the integer factorization problem, no subexponentialtime algorithm is known for the elliptic curve discrete logarithm problem. For this reason, the strengthperkeybit is substantially greater in an algorithm that uses elliptic curves. This paper describes the ANSI X9.62 ECDSA, and discusses related security, implementation, and interoperability issues. Keywords: Signature schemes, elliptic curve cryptography, DSA, ECDSA.
The gapproblems: a new class of problems for the security of cryptographic schemes
 Proceedings of PKC 2001, volume 1992 of LNCS
, 1992
"... Abstract. This paper introduces a novel class of computational problems, the gap problems, which can be considered as a dual to the class of the decision problems. We show the relationship among inverting problems, decision problems and gap problems. These problems find a nice and rich practical ins ..."
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Cited by 143 (11 self)
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Abstract. This paper introduces a novel class of computational problems, the gap problems, which can be considered as a dual to the class of the decision problems. We show the relationship among inverting problems, decision problems and gap problems. These problems find a nice and rich practical instantiation with the DiffieHellman problems. Then, we see how the gap problems find natural applications in cryptography, namely for proving the security of very efficient schemes, but also for solving a more than 10year old open security problem: the Chaum’s undeniable signature.
Global Intrusion Detection in the DOMINO Overlay System
 In Proceedings of Network and Distributed System Security Symposium (NDSS
, 2004
"... Sharing data between widely distributed intrusion detection systems offers the possibility of significant improvements in speed and accuracy over isolated systems. In this paper, we describe and evaluate DOMINO (Distributed Overlay for Monitoring InterNet Outbreaks); an architecture for a distribute ..."
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Cited by 127 (4 self)
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Sharing data between widely distributed intrusion detection systems offers the possibility of significant improvements in speed and accuracy over isolated systems. In this paper, we describe and evaluate DOMINO (Distributed Overlay for Monitoring InterNet Outbreaks); an architecture for a distributed intrusion detection system that fosters collaboration among heterogeneous nodes organized as an overlay network. The overlay design enables DOMINO to be heterogeneous, scalable, and robust to attacks and failures. An important component of DOMINO’s design is the use of active sink nodes which respond to and measure connections to unused IP addresses. This enables efficient detection of attacks from spoofed IP sources, reduces false positives, enables attack classification and production of timely blacklists. We evaluate the capabilities and performance of DOMINO using a large set of intrusion logs collected from over 1600 providers across the Internet. Our analysis demonstrates the significant marginal benefit obtained from distributed intrusion data sources coordinated through a system like DOMINO. We also evaluate how to configure DOMINO in order to maximize performance gains from the perspectives of blacklist length, blacklist freshness and IP proximity. We perform a retrospective analysis on the 2002 SQLSnake and 2003 SQLSlammer epidemics that highlights how information exchange through DOMINO would have reduced the reaction time and falsealarm rates during outbreaks. Finally, we provide preliminary results from our prototype active sink deployment that illustrates the limited variability in the sink traffic and the feasibility of efficient classification and discrimination of attack types. 1
The Discrete Logarithm Problem On Elliptic Curves Of Trace One
 JOURNAL OF CRYPTOLOGY
, 1999
"... In this short note we describe an elementary technique which leads to a linear algorithm for solving the discrete logarithm problem on elliptic curves of trace one. In practice the method described means that when choosing elliptic curves to use in cryptography one has to eliminate all curves who ..."
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Cited by 117 (2 self)
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In this short note we describe an elementary technique which leads to a linear algorithm for solving the discrete logarithm problem on elliptic curves of trace one. In practice the method described means that when choosing elliptic curves to use in cryptography one has to eliminate all curves whose group orders are equal to the order of the finite field.
Fast Key Exchange with Elliptic Curve Systems
, 1995
"... The DiffieHellman key exchange algorithm can be implemented using the group of points on an elliptic curve over the field F 2 n . A software version of this using n = 155 can be optimized to achieve computation rates that are significantly faster than nonelliptic curve versions with a similar leve ..."
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Cited by 110 (2 self)
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The DiffieHellman key exchange algorithm can be implemented using the group of points on an elliptic curve over the field F 2 n . A software version of this using n = 155 can be optimized to achieve computation rates that are significantly faster than nonelliptic curve versions with a similar level of security. The fast computation of reciprocals in F 2 n is the key to the highly efficient implementation described here. March 31, 1995 Department of Computer Science The University of Arizona Tucson, AZ 1 Introduction The DiffieHellman key exchange algorithm [10] is a very useful method for initiating a conversation between two previously unintroduced parties. It relies on exponentiation in a large group, and the software implementation of the group operation is usually computationally intensive. The algorithm has been proposed as an Internet standard [13], and the benefit of an efficient implementation would be that it could be widely deployed across a variety of platforms, greatl...
A survey of security issues in wireless sensor networks
 IEEE Communications Surveys & Tutorials
"... Advances in wireless communication and electronics have enabled the development of lowcost, lowpower, multifunctional sensor nodes. These tiny sensor nodes, consisting of sensing, data processing, and communication components, make it possible to deploy Wireless Sensor Networks (WSNs), which repres ..."
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Cited by 108 (4 self)
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Advances in wireless communication and electronics have enabled the development of lowcost, lowpower, multifunctional sensor nodes. These tiny sensor nodes, consisting of sensing, data processing, and communication components, make it possible to deploy Wireless Sensor Networks (WSNs), which represent a significant improvement over traditional wired sensor networks. WSNs can greatly simplify system design and operation, as the environment being monitored does not require the communication or energy infrastructure associated with wired networks [1]. WSNs are expected to be solutions to many applications, such as detecting and tracking the passage of troops and tanks on a battlefield, monitoring environmental pollutants, measuring traffic flows on roads, and tracking the location of personnel in a building. Many sensor networks have missioncritical tasks and thus require that security be considered [2, 3]. Improper use of information or using forged information may cause unwanted information leakage and provide inaccurate results. While some aspects of WSNs are similar to traditional wireless ad hoc networks, important distinctions exist which greatly affect how security is achieved. The differences