D. V. Bailey and C. Paar, "Efficient Arithmetic in Finite Field Extensions with Application in Elliptic Curve Cryptography," To appear in Journal of Cryptology. Home/Search Document Details and Download
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A Comparison Of Different Finite Fields For Use In Elliptic Curve.. - Smart (2000) (Correct)
....and for implementors due to the advantages that they offer in hardware and on some RISC processors. The literature on these is quite extensive so we just refer the reader to [7] or [13] for more details. Optimized Extension Fields These fields have been proposed by Bailey and Paar in [5] and [6]. They appear to offer a number of advantages which we shall outline below. An Optimized Extension Field (OEF) is one of the form ffl p = 2 k Sigma c is a pseudo Mersenne prime with log 2 c k=2 and such that p fits into a computer word. ffl f(x) x n Gamma is irreducible. For ....
....which even provides a performance advantage for polynomial multiplication for very small degree polynomials. Finally inversion is particularly easy since one can use a technique due to Itoh and Tsujii [12] combined with an efficient method to compute the action of the Frobenius mapping, see [6] for more details on this. It should be noted that the technique of Weil descent which is described in [10] could be applied to curves defined over OEFs, since n is typcially small. However the resulting curve does not seem to have the nice properties that one observes in the even characteristic ....
D.V. Bailey and C. Paar. Efficient arithmetic in finite field extensions with applications in elliptic curve cryptography. To appear J. Cryptology.
Efficient GF(p m) Arithmetic Architectures for.. - Bertoni.. (2003) Self-citation (Paar) (Correct)
....by the logical values 0 and 1 . For these types of fields, both software implementations and hardware architectures have been studied extensively. In recent years, GF(p TM) fields, where p is odd, have gained interest in the research community. MihElescu [28] and independently Bailey and Paar [3, 4] introduced the concept of Optimal Extension Fields (OEFs) in the context of elliptic curve cryptography. OEFs are fields GF(p TM) where 9 is odd and both 9 and m are chosen to match the particular hardware used to perform the arithmetic, thus allowing for efficient field arithmetic. The treatment ....
....the concept of Optimal Extension Fields (OEFs) in the context of elliptic curve cryptography. OEFs are fields GF(p TM) where 9 is odd and both 9 and m are chosen to match the particular hardware used to perform the arithmetic, thus allowing for efficient field arithmetic. The treatment in [4, 28] and that of other works based on OEFs has only been concerned with efficient software implementations. In [21, 32] GF(p TM) fields are proposed for cryptographic purposes where 9 is relatively small. 21] describes an implementation of ECDSA over fields of characteristic 3 and 7. The author in ....
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D. V. Bailey and C. Paar. Efficient arithmetic in finite field extensions with appli- cation in elliptic curve cryptography. Journal of Cryptology, 14(3):153 176, 2001.
Elliptic Curve Cryptography On Smart Cards Without.. - Woodbury, Bailey, Paar (2000) (3 citations) Self-citation (Bailey Paar) (Correct)
....the authors achieve an ECC performance of 1.95 msec on a 400 MHz Pentium II. A rump session presentation in [20] introduces an efficient algorithm for exponentiation in an OEF which leads to efficient implementation of cryptosystems based on the finite field discrete logarithm problem. Reference [3] introduces the Itoh Tsujii inversion algorithm for OEFs which is used in this contribution. In [21] Naccache and M Rahi provide an overview of smart cards with cryptographic capabilities, including a discussion of general implementation concerns on various types of smart cards. In [22] a ....
....is reduced to 242h. As this is still a 10 bit number, the next reduction steps would be identical to their multiplication counterparts, and therefore the same reduction code is used. 4.3. INVERSION Inversion in the OEF is performed via a modification of the Itoh Tsujii algorithm [14] as shown in [3], which reduces the problem of extension field inversion to subfield inversion. The algorithm computes an inverse in GF (p 17 ) as A 1 = A r ) 1 A r 1 where r = p 17 1) p 1) 11 . 10 p . Algorithm 1.3 shows the details of this method. A key point is that A r # GF (p) ....
Daniel V. Bailey and Christof Paar. Efficient Arithmetic in Finite Field Extensions with Application in Elliptic Curve Cryptography. Journal of Cryptology, to appear.
High Performance ECDSA over F(2^n) based on Java with.. - Ernst, Henhapl (Correct)
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D. V. Bailey and C. Paar, "Efficient Arithmetic in Finite Field Extensions with Application in Elliptic Curve Cryptography," To appear in Journal of Cryptology.
Hardware and Software Normal Basis Arithmetic for Pairing.. - Granger, Page, Stam (2004) (1 citation) (Correct)
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D. Bailey and C. Paar. Efficient Arithmetic in Finite Field Extensions with Application in Elliptic Curve Cryptography. In Journal of Cryptology, 14 (3), 153--176, 2001.
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