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Highspeed highsecurity signatures
"... Abstract. This paper shows that a $390 massmarket quadcore 2.4GHz Intel Westmere (Xeon E5620) CPU can create 109000 signatures per second and verify 71000 signatures per second on an elliptic curve at a 2 128 security level. Public keys are 32 bytes, and signatures are 64 bytes. These performance ..."
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Abstract. This paper shows that a $390 massmarket quadcore 2.4GHz Intel Westmere (Xeon E5620) CPU can create 109000 signatures per second and verify 71000 signatures per second on an elliptic curve at a 2 128 security level. Public keys are 32 bytes, and signatures are 64 bytes. These performance figures include strong defenses against software sidechannel attacks: there is no data flow from secret keys to array indices, and there is no data flow from secret keys to branch conditions.
INTRACTABLE PROBLEMS IN CRYPTOGRAPHY
"... Abstract. We examine several variants of the DiffieHellman and Discrete Log problems that are connected to the security of cryptographic protocols. We discuss the reductions that are known between them and the challenges in trying to assess the true level of difficulty of these problems, particular ..."
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Abstract. We examine several variants of the DiffieHellman and Discrete Log problems that are connected to the security of cryptographic protocols. We discuss the reductions that are known between them and the challenges in trying to assess the true level of difficulty of these problems, particularly if they are interactive or have complicated input. 1.
Summation polynomial algorithms for elliptic curves in characteristic two
"... Abstract. The paper is about the discrete logarithm problem for elliptic curves over characteristic 2 finite fields F2n of prime degree n. We consider practical issues about index calculus attacks using summation polynomials in this setting. The contributions of the paper include: a choice of variab ..."
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Abstract. The paper is about the discrete logarithm problem for elliptic curves over characteristic 2 finite fields F2n of prime degree n. We consider practical issues about index calculus attacks using summation polynomials in this setting. The contributions of the paper include: a choice of variables for binary Edwards curves (invariant under the action of a relatively large group) to lower the degree of the summation polynomials; a choice of factor base that “breaks symmetry ” and increases the probability of finding a relation; an experimental investigation of the use of SAT solvers rather than Gröbner basis methods for solving multivariate polynomial equations over F2. We show that our choice of variables gives a significant improvement to previous work in this case. The symmetrybreaking factor base and use of SAT solvers seem to give some benefits in practice, but our experimental results are not conclusive. Our work indicates that Pollard rho is still much faster than index calculus algorithms for the ECDLP (and even for variants such as the oracleassisted static DiffieHellman problem of Granger and JouxVitse) over prime extension fields F2n of reasonable size.
DOI 10.1007/s1338901200271 REGULAR PAPER Highspeed highsecurity signatures
"... © The Author(s) 2012. This article is published with open access at Springerlink.com Abstract This paper shows that a $390 massmarket quadcore 2.4GHz Intel Westmere (Xeon E5620) CPU can create 109000 signatures per second and verify 71000 signatures per second on an elliptic curve at a 2128 securit ..."
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© The Author(s) 2012. This article is published with open access at Springerlink.com Abstract This paper shows that a $390 massmarket quadcore 2.4GHz Intel Westmere (Xeon E5620) CPU can create 109000 signatures per second and verify 71000 signatures per second on an elliptic curve at a 2128 security level. Public keys are 32 bytes, and signatures are 64 bytes. These performance figures include strong defenses against software sidechannel attacks: there is no data flow from secret keys
On Efficient Pairings on Elliptic Curves over Extension Fields
"... Abstract. In implementation of elliptic curve cryptography, three kinds of finite fields have been widely studied, i.e. prime field, binary field and optimal extension field. In pairingbased cryptography, however, pairingfriendly curves are usually chosen among ordinary curves over prime fields and ..."
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Abstract. In implementation of elliptic curve cryptography, three kinds of finite fields have been widely studied, i.e. prime field, binary field and optimal extension field. In pairingbased cryptography, however, pairingfriendly curves are usually chosen among ordinary curves over prime fields and supersingular curves over extension fields with small characteristics. In this paper, we study pairings on elliptic curves over extension fields from the point of view of accelerating the Miller’s algorithm to present further advantage of pairingfriendly curves over extension fields, not relying on the much faster field arithmetic. We propose new pairings on elliptic curves over extension fields can make better use of the multipairing technique for the efficient implementation. By using some implementation skills, our new pairings could be implemented much more efficiently than the optimal ate pairing and the optimal twisted ate pairing on elliptic curves over extension fields. At last, we use the similar method to give more efficient pairings on Estibals’s supersingular curves over composite extension fields in parallel implementation.