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Curves for the Elliptic Curves Cryptosystem
"... We use two methods to search for curves for the elliptic curve cryptosystem. The first method involves the definition of an elliptic curve over a number field and its reduction modulo prime ideals. The second method defines an elliptic curve over a small finite field and then considers it over exten ..."
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We use two methods to search for curves for the elliptic curve cryptosystem. The first method involves the definition of an elliptic curve over a number field and its reduction modulo prime ideals. The second method defines an elliptic curve over a small finite field and then considers it over
Multiplication in Elliptic Curve Cryptosystem
"... Abstract. The basic operation in elliptic curve cryptosystem is scalar multiplication. It is the computation of integer multiple of a given point on the curve. Computation of scalar multiple is faster by using signed binary representation as compared to binary representation. In this paper ‘Direct R ..."
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Abstract. The basic operation in elliptic curve cryptosystem is scalar multiplication. It is the computation of integer multiple of a given point on the curve. Computation of scalar multiple is faster by using signed binary representation as compared to binary representation. In this paper ‘Direct
Efficient Elliptic Curve Cryptosystem
"... Abstract — The concept of proxy multisignature scheme is first introduced by Yi et al. in 2000. In a proxy multisignature scheme a proxy signer can generate a proxy signature on behalf of two or more original signers. In this paper Elliptic Curve Cryptography is used to implement proxy multisigna ..."
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signature scheme. Hence it provides a secure signature scheme. Today, Elliptic curve cryptosystems are offering new opportunities for publickey cryptography. In the industry and the academic community, Elliptic Curve Cryptography (ECC) has gained increasing acceptance and has been the subject of several standards
Customizable elliptic curve cryptosystems
 IEEE Transactions on Very Large Scale Integration (VLSI) Systems
, 2005
"... Abstract—This paper presents a method for producing hardware designs for elliptic curve cryptography (ECC) systems over the finite field qp@P A, using the optimal normal basis for the representation of numbers. Our field multiplier design is based on a parallel architecture containing multiplebit s ..."
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Cited by 16 (2 self)
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Abstract—This paper presents a method for producing hardware designs for elliptic curve cryptography (ECC) systems over the finite field qp@P A, using the optimal normal basis for the representation of numbers. Our field multiplier design is based on a parallel architecture containing multiple
Elliptic Curve Cryptosystems
, 1997
"... The application of elliptic curves to the field of cryptography has been relatively recent. It has opened up a wealth of possibilities in terms of security, encryption, and realworld applications. In particular, we are interested in publickey cryptosystems that use the elliptic curve discrete loga ..."
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Cited by 4 (0 self)
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The application of elliptic curves to the field of cryptography has been relatively recent. It has opened up a wealth of possibilities in terms of security, encryption, and realworld applications. In particular, we are interested in publickey cryptosystems that use the elliptic curve discrete
Efficient Algorithms for Elliptic Curve Cryptosystems
, 1997
"... Elliptic curves are the basis for a relative new class of publickey schemes. It is predicted that elliptic curves will replace many existing schemes in the near future. It is thus of great interest to develop algorithms which allow efficient implementations of elliptic curve crypto systems. This th ..."
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Cited by 74 (9 self)
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implementations of elliptic curve cryptosystems. The first algorithm describes the application of the KaratsubaOfman Algorithm to multiplication in composite fields GF ((2 n ) m ). The second algorithm deals with efficient inversion in composite Galois fields of the form GF ((2 n ) m ). The third
Faster Attacks on Elliptic Curve Cryptosystems
 Selected Areas in Cryptography, LNCS 1556
, 1998
"... The previously best attack known on elliptic curve cryptosystems used in practice was the parallel collision search based on Pollard's aemethod. The complexity of this attack is the square root of the prime order of the generating point used. For arbitrary curves, typically defined over GF (p) ..."
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Cited by 78 (1 self)
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The previously best attack known on elliptic curve cryptosystems used in practice was the parallel collision search based on Pollard's aemethod. The complexity of this attack is the square root of the prime order of the generating point used. For arbitrary curves, typically defined over GF (p
Juxtaposition of RSA and Elliptic Curve Cryptosystem
, 2009
"... This paper presents an indepth juxtaposition of RSA and Elliptic Curve Cryptosystem (ECC) and provides an overview of the different tradeoff involved in choosing between cryptosystems based on them. We offer ECC as a suitable alternative to RSA. We also present experimental results quantifying the ..."
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Cited by 2 (0 self)
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This paper presents an indepth juxtaposition of RSA and Elliptic Curve Cryptosystem (ECC) and provides an overview of the different tradeoff involved in choosing between cryptosystems based on them. We offer ECC as a suitable alternative to RSA. We also present experimental results quantifying
Kleptographic Attacks on Elliptic Curve Cryptosystems
 International Journal of Computer Science and Network Security
, 2010
"... Summary This paper presents an approach to mount secretly embedded trapdoor with universal protection (SETUP) attacks on elliptic curve cryptosystems. The attacked cryptosystem used is the elliptic curve analog of ElGamal encryption. The attacker can obtain the user's confidential message cove ..."
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Cited by 1 (0 self)
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Summary This paper presents an approach to mount secretly embedded trapdoor with universal protection (SETUP) attacks on elliptic curve cryptosystems. The attacked cryptosystem used is the elliptic curve analog of ElGamal encryption. The attacker can obtain the user's confidential message
Polynomial interpolation in the elliptic curve cryptosystem
 J
, 2011
"... Abstract: Problem statement: In this research, we incorporate the polynomial interpolation method in the discrete logarithm problem based cryptosystem which is the elliptic curve cryptosystem. Approach: In this study, the polynomial interpolation method to be focused is the Lagrange polynomial inter ..."
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Cited by 2 (0 self)
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Abstract: Problem statement: In this research, we incorporate the polynomial interpolation method in the discrete logarithm problem based cryptosystem which is the elliptic curve cryptosystem. Approach: In this study, the polynomial interpolation method to be focused is the Lagrange polynomial
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