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Volumn 1255, Issue , 1997, Pages 88-113

Exponentiation in finite fields: Theory and practice

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EID: 84957797971     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-63163-1_8     Document Type: Conference Paper
Times cited : (24)

References (42)
  • 3
    • 84966246609 scopus 로고
    • On addition chains
    • A. Brauer, On addition chains. Bull. Amer. Math. Soc. 45 (1939), 736-739.
    • (1939) Bull. Amer. Math. Soc , vol.45 , pp. 736-739
    • Brauer, A.1
  • 4
    • 0018019849 scopus 로고
    • Fast algorithms for manipulating formal power series
    • R. P. Brent and H. T. Kung, Fast algorithms for manipulating formal power series. J. Assoc. Comput. Mach. 25 (1978), 581-595.
    • (1978) J. Assoc. Comput. Mach , vol.25 , pp. 581-595
    • Brent, R.P.1    Kung, H.T.2
  • 5
    • 85027967075 scopus 로고
    • Fast exponentiation with precomputation
    • R. Rueppel, Lecture notes in computer science 658, Berlin, Springer
    • E. Brickell, D. Gordon, K. McCurley, and D. Wilson, Fast exponentiation with precomputation. In Advances in cryptology: Proceedings EUROCRYPT‘92, ed. R. Rueppel, Lecture notes in computer science 658, Berlin, 1993, Springer, 200-207
    • (1993) Advances in Cryptology: Proceedings EUROCRYPT‘92 , pp. 200-207
    • Brickell, E.1    Gordon, D.2    McCurley, K.3    Wilson, D.4
  • 6
    • 0010656780 scopus 로고
    • On arithmetical algorithms over finite fields
    • D. G. Cantor, On arithmetical algorithms over finite fields. Journal of Combinatorial Theory, Series A 50 (1989), 285-300.
    • (1989) Journal of Combinatorial Theory , vol.50 , Issue.A , pp. 285-300
    • Cantor, D.G.1
  • 7
    • 34249916280 scopus 로고
    • On fast multiplication of polynomials over arbitrary algebras
    • D. G. Cantor and E. Kaltofen, On fast multiplication of polynomials over arbitrary algebras. Acta. Inform. 28 (1991), 693-701.
    • (1991) Acta. Inform , vol.28 , pp. 693-701
    • Cantor, D.G.1    Kaltofen, E.2
  • 8
    • 85023205150 scopus 로고
    • Matrix multiplication via arithmetic progressions
    • D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progressions. J. Symb. Comp. 9 (1990), 251-280.
    • (1990) Bull. Amer. Math. Soc , vol.9 , pp. 251-280
    • Coppersmith, D.1    Winograd, S.2
  • 10
    • 0009399673 scopus 로고
    • Computing sequences with addition chains
    • P. Downey, B. Leong, and E. Sethi, Computing sequences with addition chains. SIAM J. Comput. 10(3) (1981), 638-646.
    • (1981) SIAM J. Comput , vol.10 , Issue.3 , pp. 638-646
    • Downey, P.1    Leong, B.2    Sethi, E.3
  • 11
    • 84874800178 scopus 로고
    • A public key cryptosystem and a signature scheme based on discrete logarithms
    • T. ElGamal, A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on information theory IT-31 (4) (1985), 469-472.
    • (1985) IEEE Transactions on information theory , vol.31 , Issue.4 , pp. 469-472
    • Elgamal, T.1
  • 14
    • 0003555072 scopus 로고
    • Efficient and optimal exponentiation in finite fields
    • J. von zur Gathen, Efficient and optimal exponentiation in finite fields. Comput complexity 1 (1991), 360-394.
    • (1991) Comput complexity , vol.1 , pp. 360-394
    • Von Zur Gathen, J.1
  • 15
  • 17
    • 0001605828 scopus 로고
    • Computing Frobenius maps and factoring polynomials
    • J. VON ZUR Gathen and V. Shoup, Computing Frobenius maps and factoring polynomials. Computational complexity 2 (1992), 187-224.
    • (1992) Computational complexity , vol.2 , pp. 187-224
    • Gathen, J.1    Shoup, V.2
  • 21
    • 0005395785 scopus 로고
    • Уmhoҗehиe MHoгo3Haчнx чиceл
    • Multiplication of multidigit numbers on automata, Soviet Physics-Doklady, (1963), 595-596
    • A. Karatsuba and Y. Ofman, Уmhoҗehиe MHoгo3Haчнx чиceл Ha aB- Tomatax. Dokl. Akad. Nauk USSR 145 (1962), 293-294. Multiplication of multidigit numbers on automata, Soviet Physics-Doklady 7 (1963), 595-596.
    • (1962) Dokl. Akad. Nauk USSR , vol.145-7 , pp. 293-294
    • Karatsuba, A.1    Ofman, Y.2
  • 23
    • 0002989263 scopus 로고
    • Euclid’s algorithm for large numbers
    • D. H. Lehmer, Euclid’s algorithm for large numbers. American Mathematical Monthly 45 (1938), 227-233.
    • (1938) American Mathematical Monthly , vol.45 , pp. 227-233
    • Lehmer, D.H.1
  • 28
    • 84957014368 scopus 로고
    • Discrete logarithms and their cryptographic significance
    • Springer-Verlag
    • A. Odlyzko, Discrete logarithms and their cryptographic significance. In Advances in Cryptology, Proceedings of Eurocrypt 1984. Springer-Verlag, 1985, 224-314.
    • (1985) Advances in Cryptology, Proceedings of Eurocrypt 1984 , pp. 224-314
    • Odlyzko, A.1
  • 29
    • 0017930809 scopus 로고
    • A method for obtaining digital signatures and public-key cryptosystems
    • R. L. Rivest, A. Shamir, and L. M. Adleman, A method for obtaining digital signatures and public-key cryptosystems. Comm. ACM 21 (1978), 120-126.
    • (1978) Comm. ACM , vol.21 , pp. 120-126
    • Rivest, R.L.1    Shamir, A.2    Adleman, L.M.3
  • 30
    • 84948971456 scopus 로고
    • Efficient exponentiation using precomputation and vector addition chains
    • A., Lecture notes in computer science 950, Berlin, Springer
    • P. de Rooij, Efficient exponentiation using precomputation and vector addition chains. In Advances in cryptology: Proceedings EUROCRYPT‘94, ed. A. DeSantis, Lecture notes in computer science 950, Berlin, 1995, Springer, 389-399.
    • (1995) Advances in cryptology: Proceedings EUROCRYPT‘94 , pp. 389-399
    • De Rooij, P.1
  • 31
    • 0015197550 scopus 로고
    • Schnelle Berechnung von Kettenbruchentwicklungen
    • A. Schönhage, Schnelle Berechnung von Kettenbruchentwicklungen. Acta Informatica 1 (1971), 139-144.
    • (1971) Acta Informatica , pp. 139-144
    • Schönhage, A.1
  • 32
    • 0012680953 scopus 로고
    • Lower bound for the length of addition chains
    • A. Schönhage, A lower bound for the length of addition chains. Theor. Computer Science 1 (1975), 1-12.
    • (1975) Theor. Computer Science , vol.1 , pp. 1-12
    • Schönhage, A.1
  • 33
    • 0000256895 scopus 로고
    • Schnelle Multiplikation von Polynomen über Korpern der Charakteristik 2
    • A. Schonhage, Schnelle Multiplikation von Polynomen über Korpern der Charakteristik 2. Acta Inf. 7 (1977), 395-398.
    • (1977) Acta Inf , pp. 395-398
    • Schonhage, A.1
  • 34
    • 34250459760 scopus 로고
    • Schnelle Multiplikation grofier Zahlen
    • A. Schonhage and V. Strassen, Schnelle Multiplikation grofier Zahlen. Computing (1971), 281-292.
    • (1971) Acta Inf , pp. 281-292
    • Schonhage, A.1    Strassen, V.2
  • 36
    • 0025476342 scopus 로고
    • Some observations on parallel algorithms for fast exponentiation in
    • n). SIAM J. Comput. 19 (1990), 711-717.
    • (1990) SIAM J. Comput , vol.19 , pp. 711-717
    • Stinson, D.R.1
  • 37
    • 34250487811 scopus 로고
    • Gaussian elimination is not optimal
    • V. Strassen, Gaussian elimination is not optimal. Ntimer. Mathematik 13 (1969), 354-356.
    • (1969) Ntimer. Mathematik , vol.13 , pp. 354-356
    • Strassen, V.1
  • 38
    • 0001977576 scopus 로고
    • The computational complexity of continued fractions
    • V. Strassen, The computational complexity of continued fractions. SIAMJ. Comput. 12 (1983), 1-27.
    • (1983) SIAMJ. Comput , vol.12 , pp. 1-27
    • Strassen, V.1
  • 40
    • 0040557251 scopus 로고
    • Zur Arithmetik in endliehen Korpern
    • A. Wassermann, Zur Arithmetik in endliehen Korpern. Bayreuther Math. Schriften 44 (1993), 147-251.
    • (1993) Bayreuther Math. Schriften , vol.44 , pp. 147-251
    • Wassermann, A.1
  • 41
    • 85043760127 scopus 로고
    • Exponentiating faster with addition chains
    • I. Damgard, Lecture notes in computer science 473, Berlin, Springer
    • Y. Yacobi, Exponentiating faster with addition chains. In Advances in cryptology: Proceedings EUROCRYPT‘90, ed. I. Damgard, Lecture notes in computer science 473, Berlin, 1991, Springer, 222-229.
    • (1991) Advances in cryptology: Proceedings EUROCRYPT‘90 , pp. 222-229
    • Yacobi, Y.1
  • 42
    • 0018019231 scopus 로고
    • Compression of individual sequences via variable-rate coding
    • J. Ziv and A. Lempel, Compression of individual sequences via variable-rate coding. IEEE Trans. Inform. Theory IT-24(5) (1978), 530-536.
    • (1978) IEEE Trans. Inform. Theory , vol.24 , Issue.5 , pp. 530-536
    • Ziv, J.1    Lempel, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.