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Fast Cryptography in Genus 2 (Two is Greater than One)
"... Abstract. In this paper we highlight the benefits of using genus 2 curves in publickey cryptography. Compared to the standardized genus 1 curves, or elliptic curves, arithmetic on genus 2 curves is typically more involved but allows us to work with moduli of half the size. We give a taxonomy of the ..."
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of the best known techniques to realize genus 2 based cryptography, which includes fast formulas on the Kummer surface and efficient 4dimensional GLV decompositions. By studying different modular arithmetic approaches on these curves, we present a range of genus 2 implementations. On a single core
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a
A Security Architecture for Computational Grids
, 1998
"... Stateoftheart and emerging scientific applications require fast access to large quantities of data and commensurately fast computational resources. Both resources and data are often distributed in a widearea network with components administered locally and independently. Computations may involve ..."
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Cited by 569 (49 self)
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Stateoftheart and emerging scientific applications require fast access to large quantities of data and commensurately fast computational resources. Both resources and data are often distributed in a widearea network with components administered locally and independently. Computations may
A Digital Signature Scheme Secure Against Adaptive ChosenMessage Attacks
, 1995
"... We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a ..."
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Cited by 985 (43 self)
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is potentially practical: signing and verifying signatures are reasonably fast, and signatures are compact.
The Lifting Scheme: A Construction Of Second Generation Wavelets
, 1997
"... . We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to ..."
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Cited by 541 (16 self)
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. Essentially we can think of them as data building blocks. Their fundamental property is that they allow for representations which are efficient and which can be computed fast. In other words, wavelets are capable of quickly capturing the essence of a data set with only a small set of coefficients
Widearea cooperative storage with CFS
, 2001
"... The Cooperative File System (CFS) is a new peertopeer readonly storage system that provides provable guarantees for the efficiency, robustness, and loadbalance of file storage and retrieval. CFS does this with a completely decentralized architecture that can scale to large systems. CFS servers pr ..."
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Cited by 1009 (56 self)
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the Chord location protocol, which operates in time logarithmic in the number of servers. CFS is implemented using the SFS file system toolkit and runs on Linux, OpenBSD, and FreeBSD. Experience on a globally deployed prototype shows that CFS delivers data to clients as fast as FTP. Controlled tests show
Timing Attacks on Implementations of DiffieHellman, RSA, DSS, and Other Systems
, 1996
"... By carefully measuring the amount of time required to perform private key operations, attackers may be able to find fixed DiffieHellman exponents, factor RSA keys, and break other cryptosystems. Against a vulnerable system, the attack is computationally inexpensive and often requires only known cip ..."
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Cited by 644 (3 self)
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By carefully measuring the amount of time required to perform private key operations, attackers may be able to find fixed DiffieHellman exponents, factor RSA keys, and break other cryptosystems. Against a vulnerable system, the attack is computationally inexpensive and often requires only known ciphertext. Actual systems are potentially at risk, including cryptographic tokens, networkbased cryptosystems, and other applications where attackers can make reasonably accurate timing measurements. Techniques for preventing the attack for RSA and DiffieHellman are presented. Some cryptosystems will need to be revised to protect against the attack, and new protocols and algorithms may need to incorporate measures to prevent timing attacks.
Breaking and Fixing the NeedhamSchroeder PublicKey Protocol using FDR
, 1996
"... In this paper we analyse the well known NeedhamSchroeder PublicKey Protocol using FDR, a refinement checker for CSP. We use FDR to discover an attack upon the protocol, which allows an intruder to impersonate another agent. We adapt the protocol, and then use FDR to show that the new protocol is s ..."
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Cited by 716 (13 self)
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In this paper we analyse the well known NeedhamSchroeder PublicKey Protocol using FDR, a refinement checker for CSP. We use FDR to discover an attack upon the protocol, which allows an intruder to impersonate another agent. We adapt the protocol, and then use FDR to show that the new protocol is secure, at least for a small system. Finally we prove a result which tells us that if this small system is secure, then so is a system of arbitrary size. 1 Introduction In a distributed computer system, it is necessary to have some mechanism whereby a pair of agents can be assured of each other's identitythey should become sure that they really are talking to each other, rather than to an intruder impersonating the other agent. This is the role of an authentication protocol. In this paper we use the Failures Divergences Refinement Checker (FDR) [11, 5], a model checker for CSP, to analyse the NeedhamSchroeder PublicKey Authentication Protocol [8]. FDR takes as input two CSP processes, ...
A public key cryptosystem and a signature scheme based on discrete logarithms
 Adv. in Cryptology, SpringerVerlag
, 1985
"... AbstractA new signature scheme is proposed, together with an implementation of the DiffieHellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields. I. ..."
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Cited by 1520 (0 self)
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AbstractA new signature scheme is proposed, together with an implementation of the DiffieHellman key distribution scheme that achieves a public key cryptosystem. The security of both systems relies on the difficulty of computing discrete logarithms over finite fields. I.
Simulating Physics with Computers
 SIAM Journal on Computing
, 1982
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 601 (1 self)
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A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored. AMS subject classifications: 82P10, 11Y05, 68Q10. 1 Introduction One of the first results in the mathematics of computation, which underlies the subsequent development of much of theoretical computer science, was the distinction between computable and ...
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