@inproceedings{Odlyzko:1984a, key = "Odlyzko 1984a", author = "A. M. Odlyzko", title = "Discrete logarithms in finite fields and their cryptographic significance", booktitle = EUROCRYPT84, series = LNICS, volume = 209, publisher = SV, year = 1984, editor = "T. Beth and N. Cot and I. Ingemarsson", pages = "224-314"} @article{Pohlig&Hellman:1978, key = "Pohlig and Hellman 1978", author = "S. C. Pohlig and M. E. Hellman", title = "An improved algorithm for computing logarithms over {$GF(p)$} and its cryptographic significance", journal = IEEE-IT, volume = "IT-24", year = 1978, pages = "106-110"} @article{Wells:1984, key = "Wells 1984", author = "Wells, Jr., A. L.", title = "A polynomial form for logarithms modulo a prime", journal = IEEE-IT, volume = "IT-30", year = 1984, pages = "845-846"} @article{Mullen&White:1986, key = "Mullen and White 1986", author = "G. L. Mullen and D. White", title = "A polynomial representation for logarithms in {$GF(q)$}", journal = AA, volume = 47, year = 1986, pages = "255-261"} @article{Pollard:1978, key = "Pollard 1978", author = "J. M. Pollard", title = "{Monte Carlo} methods for index computation (mod $p$)", journal = MC, volume = 32, year = 1978, pages = "918--924"} @inproceedings{Hellman&Reyneri:1982, key = "Hellman and Reyneri 1982", author = "M. E. Hellman and J. M. Reyneri", title = "Fast computation of discrete logarithms in {$GF(q)$}", booktitle = CRYPTO82, publisher = "Plenum Press", year = 1982, pages = "3-13"} @article{Coppersmith&Odlyzko&Schroeppel:1986, key = "Coppersmith, Odlyzko, and Schroeppel 1986", author = "D. Coppersmith and A. M. Odlyzko and R. Schroeppel", title = "Discrete logarithms in {$GF(p)$}", journal = "Algorithmica", volume = 1, year = 1986, pages = "1-15"} @article{Coppersmith:1984, key = "Coppersmith 1984", author = "D. Coppersmith", title = "Fast evaluation of logarithms in fields of characteristic two", journal = IEEE-IT, volume = "IT-30", year = 1984, pages = "587-594"} @techreport{Bach:1984, key = "Bach 1984", author = "E. Bach", title = "Discrete logarithms and factoring", institution = "Computer Science Division, University of California, Berkeley", number = "UCB/CSD/84/186", year = 1984} @inproceedings{Adleman:1979, key = "Adleman 1979", author = "L. M. Adleman", title = "A subexponential algorithm for the discrete logarithm problem with applications to cryptography", booktitle = "Proc. 20th IEEE Conf. Found. Comp. Sci.", year = 1979, pages = "55-60"} @article{Blake&Fuji-Hara&Mullin&Vanstone:1984, key = "Blake, Fuji-Hara, Mullin, and Vanstone 1984", author = "I. F. Blake and R. Fuji-Hara and R. C. Mullin and S. A. Vanstone", title = "Computing logarithms in finite fields of characteristic two", journal = SIAMJADM, volume = 5, year = 1984, pages = "276-285"} @article{ElGamal:1985, key = "ElGamal 1985", author = "T. ElGamal", title = "A subexponential-time algorithm for computing discrete logarithms over {$GF(p^2)$}", journal = IEEE-IT, volume = "IT-31", year = 1985, pages = "473-481"} @article{Herlestam&Johannesson:1981a, key = "Herlestam and Johannesson 1981a", author = "T. Herlestam and R. Johannesson", title = "On computing logarithms over {$GF(2^p)$}", journal = BIT, volume = 21, year = 1981, pages = "326-334"} @article{Coppersmith&Davenport:1985, key = "Coppersmith and Davenport 1985", author = "D. Coppersmith and J. H. Davenport", title = "An application of factoring", journal = JSC, volume = 1, year = 1985, pages = "241-243"} @inproceedings{Long&Wigderson:1983, key = "Long and Wigderson 1983", author = "D. L. Long and A. Wigderson", title = "How discreet is the discrete log?", booktitle = STOC83, pages = "413-420", year = 1983} @article{Vanstone:1983, key = "Vanstone 1983", author = "S. A. Vanstone", title = "The discrete logarithm problem", journal = CN, volume = 37, year = 1983, pages = "119-133"} @article{Leopoldt:1961, key = "Leopoldt 1961", author = "H.-W. Leopoldt", title = "Zur {Approximation} des p-adischen {Logarithmus}", journal = "Abh. Math. Sem. Univ. Hamburg", volume = 25, year = 1961, pages = "77-81"} @book{Western&Miller:1968, key = "Western and Miller 1968", author = "A. E. Western and J. C. P. Miller", title = "Tables of Indices and Primitive Roots", publisher = "Royal Society", address = "Cambridge", year = 1968} @inproceedings{Herlestam&Johannesson:1981b, key = "Herlestam and Johannesson 1981b", author = "T. Herlestam and R. Johannesson", title = "On computing logarithms over {$GF(2^p)$} or an attempt to swindle {MITRE} {Corporation}", booktitle = "Proc. 1981 IEEE Int'l. Symp. Info. Theory", year = 1981, publisher = "IEEE", pages = "47"} @incollection{den.Boer:1990, key = "den Boer 1990", author = "Boer, B. den", title = "{Diffie-Hellman} is as strong as discrete log for certain primes", booktitle = CRYPTO88, editor = "S. Goldwasser", series = LNICS, publisher = SV, volume = 403, year = 1990, pages = "530-539"} @incollection{Goldreich&Kushilevitz:1990, key = "Goldreich and Kushilevitz 1990", author = "O. Goldreich and E. Kushilevitz", title = "A perfect zero-knowledge proof for a problem equivalent to discrete logarithm", booktitle = CRYPTO88, editor = "S. Goldwasser", series = LNICS, publisher = SV, volume = 403, year = 1990, pages = "57-70"} @incollection{Koblitz:1990, key = "Koblitz 1990", author = "N. Koblitz", title = "A family of {jacobians} suitable for discrete log cryptosystems", booktitle = CRYPTO88, editor = "S. Goldwasser", series = LNICS, publisher = SV, volume = 403, year = 1990, pages = "94-99"} @unpublished{McCurley:1990, key = "McCurley 1990", author = "K. McCurley", title = "The discrete logarithm problem", note = "Unpublished manuscript", year = "1990"} @article{Riesel:1988, key = "Riesel 1988", author = "H. Riesel", title = "Some soluble cases of the discrete logarithm problem", journal = BIT, volume = 28, year = 1988, pages = "839-851"} @incollection{Smeets:1987, key = "Smeets 1987", author = "B. J. M. Smeets", title = "Some results on the {Herlestam-Johannesson} algorithms for computing logarithms over ${GF(2^p)}$", booktitle = "Contributions to General Algebra 5", year = 1987, publisher = HPT, address = "Vienna", pages = "355-366"} @article{Niederreiter:1990, key = "Niederreiter 1990", author = "H. Niederreiter", title = "A short proof for explicit formulas for discrete logarithms in finite fields", journal = AAECC, volume = 1, year = 1990, pages = "55-57"} @unpublished{OConnor:1991, key = "O'Connor 1991", author = "L. O'Connor", title = "Every bit of the discrete logarithm is either hard or easy", note = "Manuscript", year = 1991} @article{LaMacchia&Odlyzko:1991a, key = "LaMacchia and Odlyzko 1991a", author = "B. A. LaMacchia and A. M. Odlyzko", title = "Computation of discrete logarithms in prime fields", journal = DCC, volume = 1, year = "{\noopsort{1991a}}1991", pages = "47-62"} @article{Cunningham:1900, key = "Cunningham 1900", author = "A. Cunningham", title = "Solution to problem 14327", journal = MQET, volume = 73, year = 1900, pages = "45-47"} @incollection{Shizuya&Itoh&Sakurai:1991, key = "Shizuya, Itoh, and Sakurai 1991", author = "H. Shizuya and T. Itoh and K. Sakurai", title = "On the complexity of hyperelliptic discrete logarithm problem", booktitle = EUROCRYPT91, series = LNICS, publisher = SV, volume = 547, editor = "D. W. Davies", year = 1991, pages = "337-351"} @incollection{Buchmann&Dullman:1991, key = "Buchmann and {D\"ullmann} 1991", author = "J. Buchmann and S. {D\"ullmann}", title = "On the computation of discrete logarithms in class groups", booktitle = CRYPTO90, editor = "A. J. Menezes and S. A. Vanstone", publisher = SV, year = 1991, series = LNICS, volume = 537, pages = "134-139"} @incollection{LaMacchia&Odlyzko:1991b, key = "LaMacchia and Odlyzko 1991b", author = "B. A. LaMacchia and A. M. Odlyzko", title = "Computation of discrete logarithms in prime fields", booktitle = CRYPTO90, editor = "A. J. Menezes and S. A. Vanstone", publisher = SV, year = "{\noopsort{1991b}}1991", series = LNICS, volume = 537, pages = "616-618"} @incollection{Yacobi:1991b, key = "Yacobi 1991b", author = "Y. Yacobi", title = "Discrete-log with compressible exponents", booktitle = CRYPTO90, editor = "A. J. Menezes and S. A. Vanstone", publisher = SV, year = "{\noopsort{1991b}}1991", series = LNICS, volume = 537, pages = "639-643"} @incollection{Massey:1983, key = "Massey 1983", author = "J. L. Massey", title = "Logarithms in finite cyclic groups -- cryptographic issues", booktitle = "Proc. 4th Annual IEEE Int'l Symp. Info. Theory in the Benelux", editor = "E. C. van der Meulen", publisher = IEEEPR, year = 1983, pages = "17-25"} @article{Bouniakowsky:1870, key = "Bouniakowsky 1870", author = "V. Bouniakowsky", title = "Sur les congruences {bin\^omes} exponentielles {\`a} base 3 et sur plusieurs nouveaux {th\'eor\`emes} relatifs aux {r\'esidus} et aux racines primitives", journal = BAIS, volume = 14, year = 1870, pages = "356-381"} @article{GordonD:1993, key = "D. Gordon 1993", author = "D. M. Gordon", title = "Discrete logarithms in {$GF(p)$} using the number field sieve", journal = SIAMJDM, volume = 6, year = 1993, pages = "124-138"} @incollection{Heiman:1993, key = "Heiman 1993", author = "R. Heiman", title = "A note on discrete logarithms with special structure", booktitle = EUROCRYPT92, editor = "R. A. Rueppel", series = LNICS, volume = 658, year = 1993, publisher = SV, pages = "454-457"} @incollection{Okamoto&Sakurai&Shizuya:1993, key = "Okamoto, Sakurai, and Shizuya 1993", author = "T. Okamoto and K. Sakurai and H. Shizuya", title = "How intractable is the discrete logarithm for a general finite group?", booktitle = EUROCRYPT92, editor = "R. A. Rueppel", series = LNICS, volume = 658, year = 1993, publisher = SV, pages = "420-428"} @inproceedings{Clark&Bannon&Keller:1988, key = "Clark, Bannon, and Keller 1988", author = "D. W. Clark and P. J. Bannon and J. B. Keller", title = "Measuring {VAX} 8800 performance with a histogram hardware monitor", booktitle = "Proc.\ 15th Ann. Intern. Symp. on Computer Architecture", year = 1988, pages = "176-185"} @article{Adleman&DeMarrais:1993, key = "Adleman and DeMarrais 1993", author = "L. M. Adleman and J. DeMarrais", title = "A subexponential algorithm for discrete logarithms over all finite fields", journal = MC, volume = 61, year = 1993, pages = "1-15"} @article{Schirokauer:1993, key = "Schirokauer 1993", author = "O. Schirokauer", title = "Discrete logarithms and local units", journal = PTRSA, volume = 345, year = 1993, pages = "409-423"} @article{Bouniakowsky:1841, key = "Bouniakowsky 1841", author = "V. Bouniakowsky", title = "Nouveaux theor{\` e}mes relatifs {\` a} la distinction des nombres premiers et {\` a} la d{\' e}composition des entiers en facteurs", journal = "", series = 6, volume = 2, year = 1841, pages = "447-469"} @article{Hastad&Schrift&Shamir:1993, key = "Hastad et. al 1993", author = "J. Hastad and A. W. Schrift and A. Shamir", title = "The discrete logarithm modulo a composite hides $O(n)$ bits", journal = JCSS, volume = 47, year = 1993, pages = "376-404"} @article{Meletiou&Mullen:1992, key = "Meletiou and Mullen 1992", author = "G. Meletiou and G. L. Mullen", title = "A note on discrete logarithms in finite fields", journal = AAECC, volume = 3, year = 1992, pages = "75-78"} @incollection{Odlyzko:1994, key = "Odlyzko 1994", author = "A. Odlyzko", title = "Discrete logarithms and smooth polynomials", booktitle = "Finite Fields: Theory, Applications, and Algorithms", series = "Contemporary Mathematics", volume = 168, publisher = AMS, year = 1994, editor = "G. L. Mullen and P. J.-S. Shiue", pages = "269-278"} @incollection{Adleman&DeMarrais&Huang:1994, key = "Adleman, DeMarrais, and Huang 1994", author = "L. M. Adleman and J. DeMarrais and M.-D. Huang", title = "A subexponential algorithm for discrete logarithms over the rational subgroup of the {Jacobians} of large genus hyperelliptic curves over finite fields", booktitle = ANTS1, editor = "L. M. Adleman and M.-D. Huang", series = LNICS, volume = 877, publisher = SV, year = 1994, pages = "28-40"}