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Efficient elliptic curve exponentiation (1997).
| Content Provider | CiteSeerX |
|---|---|
| Author | Miyaji, Atsuko Ono, Takatoshi Cohen, Henri |
| Abstract | Elliptic curve cryptosystems, proposed by Koblitz([8]) and Miller([11]), can be constructed over a smaller definition field than the ElGamal cryptosystems([5]) or the RSA cryptosystems([16]). This is why elliptic curve cryptosystems have be un to attract notice. There are mainly two types in elliptic curve cryptosystems, elliptic curves E over IF 2 r and E over IFp . Some current systems based on ElGamal or RSA may often use modulo arithmetic over IFp . Therefore it is convenient to construct fast elliptic curve cryptosystems over IFp . In this paper, we investi ate how to implement elliptic curve cryptosystems on E/IF p . 1 Introdu1 Koblitz ([8])a8 Miller ([11]) proposeda method by which public key cryptosystemsca be constructed on the groupof points on a elliptic curve over a finite fieldinstea ofa finite field. If elliptic curve cryptosystemsa void the Menezes-Okaeneze aeneze reduction ([13]), then the only knownapGS ks ap the PollaS #-method ([15]) ap the Pohlig-Hellma method ([14]). So upto the present, weca construct elliptic curve cryptosystems overa smaE// definition field tha the discrete-loga6paEGpaEGpap////p// cryptosystems likeElGa ma cryptosystems([5]) or DSA([3])aA the RSA cryptosystems([16]). Elliptic curve cryptosystems with 160-bit key ha ve the sap securitya s bothElGaD/ cryptosystemsar RSA with 1,024-bit key. This is why elliptic curve cryptosystemsha ve been discussed in ISO/IEC CD 14883-3, ISO/IEC DIS 11770-3, ANSI ASC X.9, X.9.62,a9 IEEE P1363([7]). AsstaS0LpPL6/0Sp is apapE/E faEimplementalem of elliptic curve cryptosystemsha been reported([6, 20, 22]). Thereae marep two types in elliptic curve cryptosystems, elliptic curves over IF 2 raD elliptic curves over IF p . U to the resent, the study on im lementapDE ha been often atena elli tic cur... |
| File Format | |
| Publisher Date | 1997-01-01 |
| Publisher Institution | Université Bordeaux |
| Access Restriction | Open |
| Subject Keyword | Elliptic Curve Cryptosystems Elliptic Curve Efficient Elliptic Curve Exponentiation Rsa Cryptosystems Knownapgs K Pohlig-hellma Method Introdu1 Koblitz Discrete-loga6paegpaegpap Cryptosystems Pollas Method Current System Elgamal Cryptosystems A9 Ieee P1363 Sap Securitya Bothelgad Cryptosystemsar Rsa Atena Elli Tic Cur Smae Definition Field Rad Elliptic Curve Finite Fieldinstea Weca Construct Elliptic Curve Cryptosystems Ansi Asc 160-bit Key Ha Im Lementapde Ha Elliptic Curve Cryptosystemsa Proposeda Method Public Key Cryptosystemsca Apape Faeimplementalem Definition Field Iso Iec Cd Ma Cryptosystems Elliptic Curve Cryptosystemsha Finite Field Iso Iec Dis Elliptic Curve Cryptosystemsha Ve Groupof Point Menezes-okaeneze Aeneze Reduction 024-bit Key |
| Content Type | Text |
