National Institute of Standards and Technology (NIST), Recommended Elliptic Curves for Federal Government Use. NIST Special Publication, July  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Digital Signature Standard (DSS) to include ECC by incorporating content from X9.62. NIST is also including speci cations for ECC in its Minimum Interoperability Speci cation (MISPC) In addition, NIST has produced a document of recommended elliptic curves for United States federal government use [8, 38]. OTP 0.9. OTP, Open Trading Protocol, is a framework for encapsulating payment protocols. OTP seeks to provide a secure digital replication of the traditional paper based methods of trading, buying and selling. The speci cation provides a unifying framework within which SET (Secure Electronic ....

....strong. The test parameters contain RSA keys with public exponent 3 and with public exponent 2 1, because small public exponents make RSA a bit faster. There are no supersingular or anomalous elliptic curves in the test parameters. Many of the curves are from standards (NIST [38] and WAP WTLS [62] and those curves should be secure to use. Some of the curves are generated with curve generation software and they can not be considered secure without further analysis. As described in Chapter 5.2 the order of the curve E should be su ciently large, i.e. bits, to prevent ....

National Institute of Standards. Recommended Elliptic Curves for Federal Government Use, July 1999.

....p is the prime 2 390 3. The number of F p rational points on this curve is n = 2 390 2 195 7; this number has the form n = 63r, where r is a prime of approximately 384 bits. Thus the order r subgroup G of E(F p ) is similar in cryptographic strength to the curve P 384 presented in [8]. Let : 2 195 2) 3, and de ne 2 F p by 2 389 2 194 1 (mod p) then (x; y) x; y) for all (x; y) 2 G. It follows that (2 195 a b) x; y) 2a b) x; y) 3a (2 389 2 194 1) x; y for (x; y) 2 G. It follows that an element of G can be multiplied by ....

National Institute of Standards and Technology, FIPS PUB 186-2, Digital Signature Standard (DSS), Appendix 6, \Recommended Elliptic Curves for Federal Government Use," http://csrc.nist.gov/publications/fips/fips186-2/fips186-2.pdf

....field arithmetic is modular reduction. We chose the field GF (p) where p = 2 128 2 97 1, for the underlying arithmetic of our EC implementation. The first thing to notice is that p is a generalized Mersenne prime and that this type of fields allow for e#cient reduction as described in [28]. Following [28] we first notice that any number A # GF (p) such that A p 2 can be written as: A = i=15 X i=0 a i 2 16i 0 # a i # 2 16 1 (6) where we have chosen 2 16 1 to be the maximum digit value because of the MSP430 16 bit based architecture. Then, it is easy to ....

....is modular reduction. We chose the field GF (p) where p = 2 128 2 97 1, for the underlying arithmetic of our EC implementation. The first thing to notice is that p is a generalized Mersenne prime and that this type of fields allow for e#cient reduction as described in [28] Following [28], we first notice that any number A # GF (p) such that A p 2 can be written as: A = i=15 X i=0 a i 2 16i 0 # a i # 2 16 1 (6) where we have chosen 2 16 1 to be the maximum digit value because of the MSP430 16 bit based architecture. Then, it is easy to see that only the ....

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National Institute of Standard and Technology. Recommended elliptic curves for federal government use. available at http://csrc.nist.gov/encryption, May 1999.

....1998, FIPS 186 was revised to include both the DSA and RSA signature schemes (as specified in ANSI X9.31 [2] the revised standard was called FIPS 186 1 [61] Shortly after that, in June 1999, NIST presented a list of 15 elliptic curves that were recommended for U.S. Federal Government use [65]. These curves are compliant with the ANSI X9.62 formats (and therefore also with IEEE P1363 formats) and are discussed further in x10.2. In February 2000, FIPS 186 1 was revised to include ECDSA as specified in ANSI X9.62 with the choice of elliptic curves restricted to those in x10.2; the ....

....mobile devices such as cellular phones, personal device assistants, and pagers. ANSI X9.62 ECDSA is used for authentication. 10.2 NIST Recommended Curves This subsection presents the 15 elliptic curves that were recommended (but not mandated) by NIST in June 1999 for U.S. Federal Government use [65]. These curves are also recommended in the FIPS 186 2 standard. Recommended Finite Fields. There are 10 recommended finite fields: 1. The prime fields F p for p = 2 192 Gamma 2 64 Gamma 1, p = 2 224 Gamma 2 96 1, p = 2 256 Gamma 2 224 2 192 2 96 Gamma 1, p = 2 384 ....

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National Institute of Standards and Technology, Recommended Elliptic Curves for Federal Government Use, May 1999; revised July 1999. Available at http://csrc.nist.gov/encryption

....provided by NIST for the revised Digital Signature Algorithm [3] and using the fact that the best algorithms known for integer factorization and the (ordinary) discrete logarithm problems require approximately the same amount of resources. The estimates for ECC security were provided by NIST [12]. Table 1. Comparing ECC and RSA key lengths for same levels of security. Symmetric cipher Example ECC key length for Rough estimate of RSA key length algorithm equivalent security key length for equivalent security 80 SKIPJACK 160 1024 112 Triple DES 224 2048 128 128 bit AES 256 3072 192 ....

National Institute of Standards and Technology, Recommended Elliptic Curves for Federal Government Use, May 1999; revised July 1999. Available at http://csrc. nist.gov/encryption.

....to the different basis representations, a variety of algorithms and architectures for multiplication in GF( have been proposed. As an example, we refer to [1] for a report on a normal basis multiplier. However, in order to be compliant to well accepted standards for EC cryptography [6], the polynomial basis representation seems to be the best choice. From an architectural point of view, a polynomial basis multiplier can be realized in a bit serial, digit serial, or bit parallel fashion. For area restricted devices like smart cards, the bit serial architecture offers a fair ....

National Institute of Standards and Technology. Recommended Elliptic Curves for Federal Government Use, 1999.

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National Institute of Standards and Technology (NIST), Recommended Elliptic Curves for Federal Government Use. NIST Special Publication, July

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National Institute of Standards and Technology, Recommended Elliptic Curves for Federal Government Use, Appendix to FIPS 186-2, 2000.

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National Institute of Standards and Technology. Recommended elliptic curves for federal government use. http://csrc.nist.gov/CryptoToolkit/dss/ecdsa/NISTReCur.pdf, July 1999. 19

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National Institute of Standards and Technology, "Recommended Elliptic Curves For Federal Government Use," http://csrc.nist.gov/CryptoToolkit/ dss/ecdsa/NISTReCur.pdf, July 1999.

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National Institute of Standards and Technology. Recommended elliptic curves for federal government use. http://csrc.nist.gov/CryptoToolkit/dss/ecdsa/NISTReCur.pdf, July 1999. 19

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National Institute of Standard and Technology. Recommended elliptic curves for federal government use. available at http://csrc.nist.gov/encryption, May 1999.

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