메뉴 건너뛰기




Volumn 5677 LNCS, Issue , 2009, Pages 317-336

Batch binary Edwards

Author keywords

Batch throughput; Binary Edwards curves; Complete addition formulas; Differential addition; Diffie Hellman; Elliptic curves; Karatsuba; Scalar multiplication; Toom; Vectorization

Indexed keywords

BATCH THROUGHPUT; BINARY EDWARDS CURVES; COMPLETE ADDITION FORMULAS; DIFFERENTIAL ADDITION; DIFFIE-HELLMAN; ELLIPTIC CURVES; KARATSUBA; SCALAR MULTIPLICATION; TOOM; VECTORIZATION;

EID: 70350303858     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-03356-8_19     Document Type: Conference Paper
Times cited : (89)

References (70)
  • 1
    • 70350258317 scopus 로고    scopus 로고
    • Digital signature standard (DSS). Federal Information Processing Standard 186-2. National Institute of Standards and Technology (2000), http://csrc.nist.gov/ publications/fips/, Citations in this document: § 3
    • Digital signature standard (DSS). Federal Information Processing Standard 186-2. National Institute of Standards and Technology (2000), http://csrc.nist.gov/ publications/fips/, Citations in this document: § 3
  • 2
    • 70350299316 scopus 로고    scopus 로고
    • Standard specifications for public key cryptography. IEEE, Los Alamitos 2000, Citations in this document: §3
    • Standard specifications for public key cryptography. IEEE, Los Alamitos (2000); Citations in this document: §3
  • 3
    • 70350271778 scopus 로고    scopus 로고
    • Information theory workshop, ITW 2006, Chengdu. IEEE, Los Alamitos (2006), See [67]
    • Information theory workshop, ITW 2006, Chengdu. IEEE, Los Alamitos (2006), See [67]
  • 4
    • 70350299315 scopus 로고    scopus 로고
    • SPEED: software performance enhancement for encryption and decryption (2007), http://www.hyperelliptic.org/SPEED, See [35]
    • SPEED: software performance enhancement for encryption and decryption (2007), http://www.hyperelliptic.org/SPEED, See [35]
  • 5
    • 70350274940 scopus 로고    scopus 로고
    • Design, automation & test in Europe conference & exhibition, 2007. In: DATE 2007. IEEE, Los Alamitos (2007), See [57]
    • Design, automation & test in Europe conference & exhibition, 2007. In: DATE 2007. IEEE, Los Alamitos (2007), See [57]
  • 6
    • 70350271779 scopus 로고    scopus 로고
    • Fifth international conference on information technology: new generations (ITNG 2008), Las Vegas, Nevada, USA, April 7-8, 2008. IEEE, Los Alamitos (2008), See [37]
    • Fifth international conference on information technology: new generations (ITNG 2008), Las Vegas, Nevada, USA, April 7-8, 2008. IEEE, Los Alamitos (2008), See [37]
  • 7
    • 70350284965 scopus 로고    scopus 로고
    • Fifth workshop on fault diagnosis and tolerance in cryptography (FDTC 2008). IEEE, Los Alamitos (2008), See [31]
    • Fifth workshop on fault diagnosis and tolerance in cryptography (FDTC 2008). IEEE, Los Alamitos (2008), See [31]
  • 8
    • 84957001477 scopus 로고    scopus 로고
    • Aoki, K, Hoshino, F, Kobayashi, T, A cyclic window algorithm for ECC defined over extension fields. In: [58, pp. 62-73 2001, Citations in this document: §1
    • Aoki, K., Hoshino, F., Kobayashi, T.: A cyclic window algorithm for ECC defined over extension fields. In: [58], pp. 62-73 (2001); Citations in this document: §1
  • 9
    • 84947239944 scopus 로고    scopus 로고
    • Aoki, K, Hoshino, F, Kobayashi, T, Oguro, H, Elliptic curve arithmetic using SIMD. In: [27, pp. 235-247 2001, Citations in this document: §1, §1
    • Aoki, K., Hoshino, F., Kobayashi, T., Oguro, H.: Elliptic curve arithmetic using SIMD. In: [27], pp. 235-247 (2001), Citations in this document: §1, §1
  • 10
    • 0001224411 scopus 로고    scopus 로고
    • Bailey, D.V, Paar, C, Efficient arithmetic in finite field extensions with application in elliptic curve cryptography. Journal of Cryptology 14, 153-176 2001, ISSN 0933-2790, Citations in this document: §1
    • Bailey, D.V., Paar, C.: Efficient arithmetic in finite field extensions with application in elliptic curve cryptography. Journal of Cryptology 14, 153-176 (2001); ISSN 0933-2790, Citations in this document: §1
  • 11
    • 70350260249 scopus 로고    scopus 로고
    • Bernstein, D.J.: Fast multiplication (2000), http://cr.yp.to/talks. html#2000. 08.14, Citations in this document: §2
    • Bernstein, D.J.: Fast multiplication (2000), http://cr.yp.to/talks. html#2000. 08.14, Citations in this document: §2
  • 12
    • 33745965912 scopus 로고    scopus 로고
    • Bernstein, D.J.: Curve25519: new Diffie-Hellman speed records. In: [69], pp. 207-228 (2006), http://cr.yp.to/papers.html#curve25519, Citations in this document: §1, §1, §1, §3, §3
    • Bernstein, D.J.: Curve25519: new Diffie-Hellman speed records. In: [69], pp. 207-228 (2006), http://cr.yp.to/papers.html#curve25519, Citations in this document: §1, §1, §1, §3, §3
  • 13
    • 70350288136 scopus 로고    scopus 로고
    • Bernstein, D.J.: Can we avoid tests for zero in fast elliptic-curve arithmetic (2006), http://cr.yp.to/papers.html#curvezero, Citations in this document: §1
    • Bernstein, D.J.: Can we avoid tests for zero in fast elliptic-curve arithmetic (2006), http://cr.yp.to/papers.html#curvezero, Citations in this document: §1
  • 14
    • 38149061268 scopus 로고    scopus 로고
    • Bernstein, D.J., Lange, T.: Faster addition and doubling on elliptic curves. In: [49], pp. 29-50 (2007), http://cr.yp.to/papers.html#newelliptic, Citations in this document: §1
    • Bernstein, D.J., Lange, T.: Faster addition and doubling on elliptic curves. In: [49], pp. 29-50 (2007), http://cr.yp.to/papers.html#newelliptic, Citations in this document: §1
  • 15
    • 70350299312 scopus 로고    scopus 로고
    • Bernstein, D.J., Lange, T. (eds.): eBACS: ECRYPT Benchmarking of Cryptographic Systems (2009), http://bench.cr.yp.to (accessed June 3, 2009); Citations in this document: §1
    • Bernstein, D.J., Lange, T. (eds.): eBACS: ECRYPT Benchmarking of Cryptographic Systems (2009), http://bench.cr.yp.to (accessed June 3, 2009); Citations in this document: §1
  • 16
    • 51049085112 scopus 로고    scopus 로고
    • Bernstein, D.J., Lange, T., Farashahi, R. R.: Binary Edwards curves. In: [55], pp. 244-265 (2008), http://cr.yp.to/papers.html#edwards2, Citations in this document: §1, §1, §1, §3, §3, §3, §3, §3, §3, §3, §3
    • Bernstein, D.J., Lange, T., Farashahi, R. R.: Binary Edwards curves. In: [55], pp. 244-265 (2008), http://cr.yp.to/papers.html#edwards2, Citations in this document: §1, §1, §1, §3, §3, §3, §3, §3, §3, §3, §3
  • 17
    • 70350276857 scopus 로고    scopus 로고
    • Biham, E. (ed.): FSE 1997. LNCS, 1267. Springer, Heidelberg (1997); ISBN 3-540-63247-6, See [18]
    • Biham, E. (ed.): FSE 1997. LNCS, vol. 1267. Springer, Heidelberg (1997); ISBN 3-540-63247-6, See [18]
  • 18
    • 84947914301 scopus 로고    scopus 로고
    • Biham, E, A fast new DES implementation in software. In: [17, pp. 260-272 1997, Citations in this document: §1
    • Biham, E.: A fast new DES implementation in software. In: [17], pp. 260-272 (1997); Citations in this document: §1
  • 19
    • 70350263994 scopus 로고    scopus 로고
    • Bodrato, M.: Towards optimal Toom-Cook multiplication for univariate and multivariate polynomials in characteristic 2 and 0. In: [23], pp. 116-133 (2007), http:// bodrato.it/papers/#WAIFI2007, Citations in this document: §2
    • Bodrato, M.: Towards optimal Toom-Cook multiplication for univariate and multivariate polynomials in characteristic 2 and 0. In: [23], pp. 116-133 (2007), http:// bodrato.it/papers/#WAIFI2007, Citations in this document: §2
  • 20
    • 0031232428 scopus 로고    scopus 로고
    • Bosma, W, Cannon, J, Playoust, C, The Magma algebra system. I. The user language. Journal of Symbolic Computation 24, 235-265 1997, Citations in this document: §3
    • Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. Journal of Symbolic Computation 24, 235-265 (1997); Citations in this document: §3
  • 21
    • 84958760024 scopus 로고    scopus 로고
    • Boyd, C., Montague, P., Nguyen, K.: Elliptic curve based password authenticated key exchange protocols. In: [66], pp. 487-501 (2001), http://sky.fit.qut.edu. au/~boydc/papers/, Citations in this document: §3
    • Boyd, C., Montague, P., Nguyen, K.: Elliptic curve based password authenticated key exchange protocols. In: [66], pp. 487-501 (2001), http://sky.fit.qut.edu. au/~boydc/papers/, Citations in this document: §3
  • 22
    • 70350274939 scopus 로고    scopus 로고
    • Brent, R.P., Gaudry, P., Thomé, E., Zimmermann, P.: Faster multiplication in GF(2)[x]. In: [65], pp. 153-166, http://wwwmaths.anu.edu.au/ ~brent/pub/ pub232.html, Citations in this document: §1, §2
    • Brent, R.P., Gaudry, P., Thomé, E., Zimmermann, P.: Faster multiplication in GF(2)[x]. In: [65], pp. 153-166, http://wwwmaths.anu.edu.au/ ~brent/pub/ pub232.html, Citations in this document: §1, §2
  • 23
    • 70350260247 scopus 로고    scopus 로고
    • Carlet, C., Sunar, B. (eds.): WAIFI 2007. LNCS, 4547. Springer, Heidelberg (2007); ISBN 978-3-540-73073-6, See [19]
    • Carlet, C., Sunar, B. (eds.): WAIFI 2007. LNCS, vol. 4547. Springer, Heidelberg (2007); ISBN 978-3-540-73073-6, See [19]
  • 24
    • 33645985781 scopus 로고    scopus 로고
    • Chang, N.S, Kim, C.H, Park, Y.-H, Lim, J, A non-redundant and efficient architecture for Karatsuba-Ofman algorithm. In: [70, pp. 288-299 2005, Citations in this document: §2
    • Chang, N.S., Kim, C.H., Park, Y.-H., Lim, J.: A non-redundant and efficient architecture for Karatsuba-Ofman algorithm. In: [70], pp. 288-299 (2005); Citations in this document: §2
  • 25
    • 33745812321 scopus 로고    scopus 로고
    • Chevassut, O., Fouque, P.-A., Gaudry, P., Pointcheval, D.: The Twist-AUgmented technique for key exchange. In: [69], pp. 410-426 (2006), http://www.loria.fr/ ~gaudry/papers.en.html, Citations in this document: §3
    • Chevassut, O., Fouque, P.-A., Gaudry, P., Pointcheval, D.: The Twist-AUgmented technique for key exchange. In: [69], pp. 410-426 (2006), http://www.loria.fr/ ~gaudry/papers.en.html, Citations in this document: §3
  • 26
    • 0000267548 scopus 로고    scopus 로고
    • Chudnovsky, D.V, Chudnovsky, G.V, Sequences of numbers generated by addition in formal groups and new primality and factorization tests. Advances in Applied Mathematics 7, 385-434 1986, MR 88h:11094, Citations in this document: §3
    • Chudnovsky, D.V., Chudnovsky, G.V.: Sequences of numbers generated by addition in formal groups and new primality and factorization tests. Advances in Applied Mathematics 7, 385-434 (1986); MR 88h:11094, Citations in this document: §3
  • 27
    • 70350258316 scopus 로고    scopus 로고
    • Davida, G.I., Frankel, Y. (eds.): ISC 2001. LNCS, 2200. Springer, Heidelberg (2001); ISBN 978-3-540-42662-2, See [9]
    • Davida, G.I., Frankel, Y. (eds.): ISC 2001. LNCS, vol. 2200. Springer, Heidelberg (2001); ISBN 978-3-540-42662-2, See [9]
  • 28
    • 38349097522 scopus 로고    scopus 로고
    • Edwards, H.M.: A normal form for elliptic curves. Bulletin of the American Mathematical Society 44, 393-422 (2007), http://www.ams.org/bull/2007- 44-03/ S0273-0979-07-01153-6/home.html, Citations in this document: §3
    • Edwards, H.M.: A normal form for elliptic curves. Bulletin of the American Mathematical Society 44, 393-422 (2007), http://www.ams.org/bull/2007- 44-03/ S0273-0979-07-01153-6/home.html, Citations in this document: §3
  • 29
    • 70350268727 scopus 로고    scopus 로고
    • Fan, H., Sun, J., Gu, M., Lam., K.-Y.: Overlap-free Karatsuba-Ofman polynomial multiplication algorithms for hardware implementations (October 7, 2008), http://eprint.iacr.org/2007/393, Citations in this document: §2
    • Fan, H., Sun, J., Gu, M., Lam., K.-Y.: Overlap-free Karatsuba-Ofman polynomial multiplication algorithms for hardware implementations (October 7, 2008), http://eprint.iacr.org/2007/393, Citations in this document: §2
  • 30
    • 3242670828 scopus 로고    scopus 로고
    • Fong, K., Hankerson, D., López, J., Menezes, A.: Field inversion and point halving revisited. IEEE Transactions on Computers 53, 1047-1059 (2004), http://www.cacr.math.uwaterloo.ca/techreports/2003/tech-reports2003. html, ISSN 0018-9340, Citations in this document: §1
    • Fong, K., Hankerson, D., López, J., Menezes, A.: Field inversion and point halving revisited. IEEE Transactions on Computers 53, 1047-1059 (2004), http://www.cacr.math.uwaterloo.ca/techreports/2003/tech-reports2003. html, ISSN 0018-9340, Citations in this document: §1
  • 31
    • 52949099582 scopus 로고    scopus 로고
    • Fouque, P.-A., Lercier, R., Réal, D., Valette, F.: Fault attack on elliptic curve with Montgomery ladder implementation. In: [7], pp. 92-98 (2008), http://www.di. ens.fr/~fouque/index-pub.html, Citations in this document: §3
    • Fouque, P.-A., Lercier, R., Réal, D., Valette, F.: Fault attack on elliptic curve with Montgomery ladder implementation. In: [7], pp. 92-98 (2008), http://www.di. ens.fr/~fouque/index-pub.html, Citations in this document: §3
  • 32
    • 35448968883 scopus 로고    scopus 로고
    • Fürer, M.: Faster integer multiplication. In: [42], pp. 57-66 (2007), http://www. cse.psu.edu/~furer/, Citations in this document: §2
    • Fürer, M.: Faster integer multiplication. In: [42], pp. 57-66 (2007), http://www. cse.psu.edu/~furer/, Citations in this document: §2
  • 33
    • 70350262138 scopus 로고    scopus 로고
    • Galbraith, S., Lin, X., Scott, M.: Endomorphisms for faster elliptic curve cryptography on a large class of curves. In: [43], pp. 518-535 (2009), http://eprint. iacr.org/2008/194, Citations in this document: §1, §3
    • Galbraith, S., Lin, X., Scott, M.: Endomorphisms for faster elliptic curve cryptography on a large class of curves. In: [43], pp. 518-535 (2009), http://eprint. iacr.org/2008/194, Citations in this document: §1, §3
  • 34
    • 79957797091 scopus 로고    scopus 로고
    • Gallant, R.P, Lambert, R.J, Vanstone, S.A, Faster point multiplication on elliptic curves with efficient endomorphisms. In: [46, pp. 190-200 2001, MR 2003h:14043, Citations in this document: §3
    • Gallant, R.P., Lambert, R.J., Vanstone, S.A.: Faster point multiplication on elliptic curves with efficient endomorphisms. In: [46], pp. 190-200 (2001), MR 2003h:14043, Citations in this document: §3
  • 35
    • 70350256342 scopus 로고    scopus 로고
    • Gaudry, P., Thomé, E.: The mpFq library and implementing curve-based key exchanges. In: [4], pp. 49-64 (2007), http://www.loria.fr/ ~gaudry/papers.en. html, Citations in this document: §1, §1, §1
    • Gaudry, P., Thomé, E.: The mpFq library and implementing curve-based key exchanges. In: [4], pp. 49-64 (2007), http://www.loria.fr/ ~gaudry/papers.en. html, Citations in this document: §1, §1, §1
  • 36
    • 51049102787 scopus 로고    scopus 로고
    • Güneysu, T, Paar, C, Ultra high performance ECC over NIST primes on commercial FPGAs. In: [55, pp. 62-78 2008, Citations in this document: §1, §1
    • Güneysu, T., Paar, C.: Ultra high performance ECC over NIST primes on commercial FPGAs. In: [55], pp. 62-78 (2008); Citations in this document: §1, §1
  • 37
    • 44049086563 scopus 로고    scopus 로고
    • Gueron, S, Kounavis, M.E, A technique for accelerating characteristic 2 elliptic curve cryptography. In: [6, pp. 265-272 2008, Citations in this document: §1
    • Gueron, S., Kounavis, M.E.: A technique for accelerating characteristic 2 elliptic curve cryptography. In: [6], pp. 265-272 (2008); Citations in this document: §1
  • 38
    • 85099427145 scopus 로고    scopus 로고
    • Hankerson, D., Hernandez, J.L., Menezes, A.: Software implementation of elliptic curve cryptography over binary fields. In: [48], pp. 1-24 (2000), http://www. cacr.math.uwaterloo.ca/techreports/2000/corr2000-42.ps, Citations in this document: §1, §1
    • Hankerson, D., Hernandez, J.L., Menezes, A.: Software implementation of elliptic curve cryptography over binary fields. In: [48], pp. 1-24 (2000), http://www. cacr.math.uwaterloo.ca/techreports/2000/corr2000-42.ps, Citations in this document: §1, §1
  • 39
    • 70350258315 scopus 로고    scopus 로고
    • Hankerson, D., Karabina, K., Menezes., A.: Analyzing the Galbraith-Lin-Scott point multiplication method for elliptic curves over binary fields (2008), http:// eprint.iacr.org/2008/334, Citations in this document: §1, §3
    • Hankerson, D., Karabina, K., Menezes., A.: Analyzing the Galbraith-Lin-Scott point multiplication method for elliptic curves over binary fields (2008), http:// eprint.iacr.org/2008/334, Citations in this document: §1, §3
  • 40
    • 70350296192 scopus 로고    scopus 로고
    • Intel Corporation, Carry-less multiplication and its usage for computing the GCM mode (2008), http://software.intel.com/en-us/articles/ carry-less-multiplication-and-its-usage-for-computing-the-gcm-mode, Citations in this document: §1
    • Intel Corporation, Carry-less multiplication and its usage for computing the GCM mode (2008), http://software.intel.com/en-us/articles/ carry-less-multiplication-and-its-usage-for-computing-the-gcm-mode, Citations in this document: §1
  • 41
    • 70350288135 scopus 로고    scopus 로고
    • Intel Corporation, Intel Advanced Vector Extensions programming reference (2008), http://softwarecommunity.intel.com/isn/downloads/intelavx/ Intel-AVX-Programming-Reference-31943302.pdf, Citations in this document: §1
    • Intel Corporation, Intel Advanced Vector Extensions programming reference (2008), http://softwarecommunity.intel.com/isn/downloads/intelavx/ Intel-AVX-Programming-Reference-31943302.pdf, Citations in this document: §1
  • 43
    • 70350281858 scopus 로고    scopus 로고
    • Joux, A. (ed.): EUROCRYPT 2009. LNCS, 5479. Springer, Heidelberg (2009); ISBN 978-3-642-01000-2, See [33]
    • Joux, A. (ed.): EUROCRYPT 2009. LNCS, vol. 5479. Springer, Heidelberg (2009); ISBN 978-3-642-01000-2, See [33]
  • 44
    • 0025790774 scopus 로고    scopus 로고
    • Kaliski Jr, B.S, One-way permutations on elliptic curves. Journal of Cryptology 3, 187-199 1991, Citations in this document: §3
    • Kaliski Jr., B.S.: One-way permutations on elliptic curves. Journal of Cryptology 3, 187-199 (1991), Citations in this document: §3
  • 45
    • 70350276855 scopus 로고    scopus 로고
    • Karatsuba, A.A., Ofman, Y.: Multiplication of multidigit numbers on automata. Soviet Physics Doklady 7, 595-596 (1963), http://cr.yp.to/bib/entries. html# 1963/karatsuba, ISSN 0038-5689, Citations in this document: §2, §2
    • Karatsuba, A.A., Ofman, Y.: Multiplication of multidigit numbers on automata. Soviet Physics Doklady 7, 595-596 (1963), http://cr.yp.to/bib/entries. html# 1963/karatsuba, ISSN 0038-5689, Citations in this document: §2, §2
  • 46
    • 70350284963 scopus 로고    scopus 로고
    • Kilian, J. (ed.): CRYPTO 2001. LNCS, 2139. Springer, Heidelberg (2001); ISBN 3-540-42456-3. MR 2003d:94002, See [34]
    • Kilian, J. (ed.): CRYPTO 2001. LNCS, vol. 2139. Springer, Heidelberg (2001); ISBN 3-540-42456-3. MR 2003d:94002, See [34]
  • 47
    • 70350256341 scopus 로고    scopus 로고
    • Koblitz, A.H., Koblitz, N., Menezes, A.: Elliptic curve cryptography: the serpentine course of a paradigm shift (2008), http://eprint.iacr.org/2008/390, Citations in this document: §3
    • Koblitz, A.H., Koblitz, N., Menezes, A.: Elliptic curve cryptography: the serpentine course of a paradigm shift (2008), http://eprint.iacr.org/2008/390, Citations in this document: §3
  • 48
    • 70350276856 scopus 로고    scopus 로고
    • Koç, Ç.K., Paar, C. (eds.): CHES 2000. LNCS, 1965. Springer, Heidelberg (2000); ISBN 3-540-42521-7, See [38]
    • Koç, Ç.K., Paar, C. (eds.): CHES 2000. LNCS, vol. 1965. Springer, Heidelberg (2000); ISBN 3-540-42521-7, See [38]
  • 49
    • 70350298072 scopus 로고    scopus 로고
    • Kurosawa, K. (ed.): ASIACRYPT 2007. LNCS, 4833. Springer, Heidelberg (2007); ISBN 978-3-540-76899-9, See [14]
    • Kurosawa, K. (ed.): ASIACRYPT 2007. LNCS, vol. 4833. Springer, Heidelberg (2007); ISBN 978-3-540-76899-9, See [14]
  • 50
    • 38049060653 scopus 로고    scopus 로고
    • Matsui, M, Nakajima, J, On the power of bitslice implementation on Intel Core2 processor. In: [56, pp. 121-134 2007, Citations in this document: §1
    • Matsui, M., Nakajima, J.: On the power of bitslice implementation on Intel Core2 processor. In: [56], pp. 121-134 (2007), Citations in this document: §1
  • 51
    • 33847320580 scopus 로고    scopus 로고
    • Menezes, A, Qu, M, Analysis of the Weil descent attack of Gaudry, Hess and Smart. In: [54, pp. 308-318 2001, Citations in this document: §3
    • Menezes, A., Qu, M.: Analysis of the Weil descent attack of Gaudry, Hess and Smart. In: [54], pp. 308-318 (2001), Citations in this document: §3
  • 52
    • 84968484435 scopus 로고    scopus 로고
    • Montgomery, P.L.: Speeding the Pollard and elliptic curve methods of factorization. Mathematics of Computation 48, 243-264 (1987), http://links.jstor.org/sici? sici=0025-5718(198701)48:177lang;243:STPAEC〉2. 0.CO;2-3; ISSN 0025-5718. MR 88e:11130, Citations in this document: §1, §3, §3, §3, §3
    • Montgomery, P.L.: Speeding the Pollard and elliptic curve methods of factorization. Mathematics of Computation 48, 243-264 (1987), http://links.jstor.org/sici? sici=0025-5718(198701)48:177lang;243:STPAEC〉2. 0.CO;2-3; ISSN 0025-5718. MR 88e:11130, Citations in this document: §1, §3, §3, §3, §3
  • 53
    • 14844351609 scopus 로고    scopus 로고
    • Montgomery, P.L, Five, six, and seven-term Karatsuba-like formulae. IEEE Transactions on Computers 54, 362-369 2005, Citations in this document: §2
    • Montgomery, P.L.: Five, six, and seven-term Karatsuba-like formulae. IEEE Transactions on Computers 54, 362-369 (2005); Citations in this document: §2
  • 54
    • 70350270669 scopus 로고    scopus 로고
    • Naccache, D. (ed.): CT-RSA 2008. LNCS, 4964. Springer, Heidelberg (2008); ISBN 3-540-41898-9. MR 2003a:94039, See [51]
    • Naccache, D. (ed.): CT-RSA 2008. LNCS, vol. 4964. Springer, Heidelberg (2008); ISBN 3-540-41898-9. MR 2003a:94039, See [51]
  • 55
    • 70350258306 scopus 로고    scopus 로고
    • Oswald, E., Rohatgi, P. (eds.): CHES 2008. LNCS, 5154. Springer, Heidelberg (2008); ISBN 978-3-540-85052-6, See [16], [36]
    • Oswald, E., Rohatgi, P. (eds.): CHES 2008. LNCS, vol. 5154. Springer, Heidelberg (2008); ISBN 978-3-540-85052-6, See [16], [36]
  • 56
    • 70350270668 scopus 로고    scopus 로고
    • Paillier, P., Verbauwhede, I. (eds.): CHES 2007. LNCS, 4727. Springer, Heidelberg (2007); ISBN 978-3-540-74734-5, See [50]
    • Paillier, P., Verbauwhede, I. (eds.): CHES 2007. LNCS, vol. 4727. Springer, Heidelberg (2007); ISBN 978-3-540-74734-5, See [50]
  • 57
    • 70350284959 scopus 로고    scopus 로고
    • m) and its application to ECC designs. In: [5] (2007), http://ieeexplore.ieee.org/xpl/ freeabs-all.jsp?isnumber=4211749&arnumber= 4211979&count=305&index=229, Citations in this document: §2
    • m) and its application to ECC designs. In: [5] (2007), http://ieeexplore.ieee.org/xpl/ freeabs-all.jsp?isnumber=4211749&arnumber= 4211979&count=305&index=229, Citations in this document: §2
  • 58
    • 70350270671 scopus 로고    scopus 로고
    • Qing, S., Okamoto, T., Zhou, J. (eds.): ICICS 2001. LNCS, 2229. Springer, Heidelberg (2001); ISBN 3-540-42880-1, See [8]
    • Qing, S., Okamoto, T., Zhou, J. (eds.): ICICS 2001. LNCS, vol. 2229. Springer, Heidelberg (2001); ISBN 3-540-42880-1, See [8]
  • 59
    • 1542643573 scopus 로고    scopus 로고
    • Rodríguez-Henríquez, F, Koç, Ç.K, On fully parallel Karatsuba multipliers for GF(2m, In: [60, pp. 405-410 2003, Citations in this document: §2, §2
    • m). In: [60], pp. 405-410 (2003); Citations in this document: §2, §2
  • 61
    • 0000256895 scopus 로고    scopus 로고
    • Schönhage, A.: Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2. Acta Informatica 7, 395-398 (1977), http://cr.yp.to/bib/entries. html#1977/schoenhage, ISSN 0001-5903. MR 55:9604, Citations in this document: §2
    • Schönhage, A.: Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2. Acta Informatica 7, 395-398 (1977), http://cr.yp.to/bib/entries. html#1977/schoenhage, ISSN 0001-5903. MR 55:9604, Citations in this document: §2
  • 62
    • 34250459760 scopus 로고    scopus 로고
    • Schönhage, A., Strassen, V.: Schnelle Multiplikation großer Zahlen. Computing 7, 281-292 (1971), http://cr.yp.to/bib/entries.html#1971/ schoenhage-mult, ISSN 0010-485X. MR 45:1431. Citations in this document: §2
    • Schönhage, A., Strassen, V.: Schnelle Multiplikation großer Zahlen. Computing 7, 281-292 (1971), http://cr.yp.to/bib/entries.html#1971/ schoenhage-mult, ISSN 0010-485X. MR 45:1431. Citations in this document: §2
  • 63
    • 70350299306 scopus 로고    scopus 로고
    • Stein,W, ed, Sage Mathematics Software (Version 3.2.3) The Sage Group 2009, Citations in this document: §1
    • Stein,W. (ed.): Sage Mathematics Software (Version 3.2.3) The Sage Group (2009), http://www.sagemath.org, Citations in this document: §1
  • 64
    • 70350258307 scopus 로고    scopus 로고
    • Toom, A.L, The complexity of a scheme of functional elements realizing the multiplication of integers. Soviet Mathematics Doklady 3, 714-716 1963, ISSN 0197-6788. Citations in this document: §2
    • Toom, A.L.: The complexity of a scheme of functional elements realizing the multiplication of integers. Soviet Mathematics Doklady 3, 714-716 (1963); ISSN 0197-6788. Citations in this document: §2
  • 65
    • 70350284958 scopus 로고    scopus 로고
    • van der Poorten, A.J., Stein, A. (eds.): ANTS-VIII 2008. LNCS, 5011. Springer, Heidelberg (2008); ISBN 978-3-540-79455-4, See [22]
    • van der Poorten, A.J., Stein, A. (eds.): ANTS-VIII 2008. LNCS, vol. 5011. Springer, Heidelberg (2008); ISBN 978-3-540-79455-4, See [22]
  • 66
    • 70350299305 scopus 로고    scopus 로고
    • Varadharajan, V., Mu, Y. (eds.): ACISP 2001. LNCS, 2119. Springer, Heidelberg (2001); ISBN 978-3-540-42300-3, See [21]
    • Varadharajan, V., Mu, Y. (eds.): ACISP 2001. LNCS, vol. 2119. Springer, Heidelberg (2001); ISBN 978-3-540-42300-3, See [21]
  • 67
    • 33751061273 scopus 로고    scopus 로고
    • von zur Gathen, J, Shokrollahi, J, Fast arithmetic for polynomials over F2 in hardware. In: [3, pp. 107-111 2006, Citations in this document: §2, §2, §2
    • 2 in hardware. In: [3], pp. 107-111 (2006); Citations in this document: §2, §2, §2
  • 68
    • 70350299304 scopus 로고    scopus 로고
    • Weimerskirch, A., Paar, C.: Generalizations of the Karatsuba algorithm for ef-ficient implementations (2006), http://eprint.iacr.org/2006/224, Citations in this document: §2
    • Weimerskirch, A., Paar, C.: Generalizations of the Karatsuba algorithm for ef-ficient implementations (2006), http://eprint.iacr.org/2006/224, Citations in this document: §2
  • 69
    • 70350273704 scopus 로고    scopus 로고
    • Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.): PKC 2006. LNCS, 3958. Springer, Heidelberg (2006); ISBN 978-3-540-33851-2, See [12], [25]
    • Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.): PKC 2006. LNCS, vol. 3958. Springer, Heidelberg (2006); ISBN 978-3-540-33851-2, See [12], [25]
  • 70
    • 70350270667 scopus 로고    scopus 로고
    • Zhou, J., López, J., Deng, R.H., Bao, F. (eds.): ISC 2005. LNCS, 3650. Springer, Heidelberg (2005); ISBN 3-540-29001-X, See [24]
    • Zhou, J., López, J., Deng, R.H., Bao, F. (eds.): ISC 2005. LNCS, vol. 3650. Springer, Heidelberg (2005); ISBN 3-540-29001-X, See [24]


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.