@article{Stevenhagen:1987,
	key = "Stevenhagen 1987",
	author = "P. Stevenhagen",
	title = "On {Aurifeuillian} factorizations",
	journal = PKNAW,
	volume = 90,
	year = 1987,
	pages = "451-468",
	note = "(= {\it Indag. Math.} {\bf 49})"}

@article{Billingsley:1969,
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	pages = "132-139"}

@article{Knuth&Trabb.Pardo:1976,
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	author = "D. E. Knuth and L. Trabb Pardo",
	title = "Analysis of a simple factorization algorithm",
	journal = TCS,
	volume = 3,
	year = 1976,
	pages = "321-348"}

@article{Lehmer:1933a,
	key = "D. H. Lehmer 1933a",
	author = "D. H. Lehmer",
	title = "A photo-electric number sieve",
	journal = AMM,
	volume = 40,
	year = "{\noopsort{1933a}}1933",
	pages = "401-406"}

@article{DHLehmer:1932b,
	key = "D. H. Lehmer 1932b",
	author = "D. H. Lehmer",
	title = "A number theoretic machine",
	journal = BAMS,
	volume = 38,
	year = "{\noopsort{1932b}}1932",
	pages = "635"}

@article{DNLehmer:1932,
	key = "D. N. Lehmer 1932",
	author = "D. N. Lehmer",
	title = "Hunting big game in the theory of numbers",
	journal = SM,
	volume = 1,
	year = "1932-33",
	pages = "229-235"}

@incollection{Lehmer:1980,
	key = "D. H. Lehmer 1980",
	author = "D. H. Lehmer",
	title = "A history of the sieve process",
	booktitle = "A History of Computing in the Twentieth Century",
	publisher = AP,
	year = 1980,
	editor = "N. Metropolis and J. Howlett and Gian-Carlo Rota",
	pages = "445-456"}

@book{Brillhart&Lehmer&Selfridge&Tuckerman&Wagstaff:1983,
	key = "Brillhart, Lehmer, Selfridge, Tuckerman, and Wagstaff 1983",
	author = "J. Brillhart and D. H. Lehmer and J. L. Selfridge and
	B. Tuckerman and Wagstaff, Jr., S. S.",
	title = "Factorizations of $b^n \pm 1$, $b = 2,3,5,6,7,10,11,12$
	Up to High Powers",
	series = "Contemporary Mathematics",
	volume = 22,
	year = 1983,
	publisher = "American Mathematical Society" }

@book{Brillhart&Lehmer&Selfridge&Tuckerman&Wagstaff:1988,
	key = "Brillhart, Lehmer, Selfridge, Tuckerman, and Wagstaff 1988",
	author = "J. Brillhart and D. H. Lehmer and J. L. Selfridge and
	B. Tuckerman and Wagstaff, Jr., S. S.",
	title = "Factorizations of $b^n \pm 1$, $b = 2,3,5,6,7,10,11,12$
	Up to High Powers",
	series = "Contemporary Mathematics",
	volume = 22,
	year = 1988,
	publisher = "American Mathematical Society",
	note = "2nd edition"}

@article{Erdos&Kac:1939,
	key = "{Erd{\H{o}}s} and Kac 1939",
	author = {P. {Erd\H{o}s} and M. Kac},
	title = "On the {Gaussian} law of errors in the theory of
	additive functions",
	journal = PNAS,
	volume = 25,
	year = 1939,
	pages = "206-207"}

@article{Erdos&Kac:1940,
	key = "{Erd{\H{o}}s} and Kac 1940",
	author = {P. {Erd\H{o}s} and M. Kac},
	title = "The {Gaussian} law of errors in the theory of additive
	number theoretic functions",
	journal = AJM,
	volume = 62,
	year = 1940,
	pages = "738-742"}

@article{Hardy&Ramanujan:1920,
	key = "G. Hardy and Ramanujan 1920",
	author = "G. H. Hardy and S. Ramanujan",
	title = "The normal number of prime factors of a number $n$",
	journal = QJM,
	volume = 48,
	year = 1920,
	pages = "76-92",
	note = "Reprinted in {\it Collected Papers,} vol. II, pp. 100-113"
	}

@article{Pollard:1975,
	key = "Pollard 1975",
	author = "J. M. Pollard",
	title = "A {Monte} {Carlo} method for factorization",
	journal = BIT,
	volume = 15,
	year = 1975,
	pages = "331-334"}

@article{Harris:1960,
	key = "B. Harris 1960",
	author = "B. Harris",
	title = "Probability distributions related to random mappings",
	journal = ANMS,
	volume = 31,
	year = 1960,
	pages = "1045-1062"}

@article{Brent&Pollard:1981,
	key = "Brent and Pollard 1981",
	author = "R. P. Brent and J. M. Pollard",
	title = "Factorization of the eighth {Fermat} number",
	journal = MC,
	volume = 36,
	year = 1981,
	pages = "627-630"}

@article{Brent:1980b,
	key = "Brent 1980b",
	author = "R. P. Brent",
	title = "An improved {Monte Carlo} factorization algorithm",
	journal = BIT,
	volume = 20,
	year = 1980,
	pages = "176-184"}

@article{Brillhart:1981,
	key = "Brillhart 1981",
	author = "J. Brillhart",
	title = "Fermat's factoring method and its variants",
	journal = CN,
	year = 1981,
	volume = 32,
	pages = "29-48"}

@article{Lang&Trotter:1972,
	key = "Lang and Trotter 1972",
	author = "S. Lang and H. Trotter",
	title = "Continued fractions for some algebraic numbers",
	journal = JFRAM,
	volume = 255,
	year = 1972,
	pages = "112-134",
	note = "Addendum, {\bf 267} (1974), 219-220"}

@article{Morrison&Brillhart:1975,
	key = "M. Morrison and Brillhart 1975",
	author = "M. A. Morrison and J. Brillhart",
	title = "A method of factoring and the factorization of {$F_7$}",
	journal = MC,
	volume = 29,
	year = 1975,
	pages = "183-205",
	note = "Corrigendum, {{\it Math. Comp.} {\bf 35} (1980), 1444}"}

@article{Lehmer&Powers:1931,
	key = "D. H. Lehmer and Powers 1931",
	author = "D. H. Lehmer and R. E. Powers",
	title = "On factoring large numbers",
	journal = BAMS,
	volume = 37,
	year = 1931,
	pages = "770-776"}

@article{Shamir:1979,
	key = "Shamir 1979",
	author = "A. Shamir",
	title = "Factoring numbers in {$O(\log n)$} arithmetic steps",
	journal = IPL,
	volume = 8,
	year = 1979,
	pages = "28-31"}

@article{Gerver:1983,
	key = "Gerver 1983",
	author = "J. L. Gerver",
	title = "Factoring large numbers with a quadratic sieve",
	journal = MC,
	volume = 41,
	year = 1983,
	pages = "287-294"}

@inproceedings{Davis&Holdridge:1983,
	key = "J. Davis and Holdridge 1983",
	author = "J. A. Davis and D. B. Holdridge",
	title = "Factorization using the quadratic sieve algorithm",
	booktitle = CRYPTO83,
	editor = "D. Chaum",
	year = 1983,
	publisher = "Plenum Press",
	pages = "103-113"}

@inproceedings{Davis&Holdridge&Simmons:1984,
	key = "J. Davis, Holdridge, and Simmons 1984",
	author = "J. A. Davis and D. B. Holdridge and G. J. Simmons",
	title = "Status report on factoring (at the {Sandia National
	Laboratories})",
	booktitle = EUROCRYPT84,
	editor = "T. Beth and N. Cot and I. Ingemarsson",
	year = 1984,
	publisher = SV,
	series = LNICS,
	volume = 209,
	pages = "183-215"}

@inproceedings{Pomerance&Smith&Wagstaff:1983,
	key = "Pomerance, Smith, and Wagstaff 1983",
	author = "C. Pomerance and J. W. Smith and Wagstaff, Jr., S. S.",
	title = "New ideas for factoring large integers",
	booktitle = CRYPTO83,
	editor = "D. Chaum",
	publisher = "Plenum Press",
	year = 1983,
	pages = "81-85"}

@article{Pomerance&Wagstaff:1983,
	key = "Pomerance and Wagstaff 1983",
	author = "C. Pomerance and Wagstaff, Jr., S. S.",
	title = "Implementation of the continued fraction integer factoring
	algorithm",
	journal = CN,
	volume = 37,
	year = 1983,
	pages = "99-118"}

@article{Dixon:1981,
	key = "Dixon 1981",
	author = "J. D. Dixon",
	title = "Asymptotically fast factorization of integers",
	journal = MC,
	volume = 36,
	year = 1981,
	pages = "255-260"}

@inproceedings{Pomerance:1984b,
	key = "Pomerance 1984b",
	author = "C. Pomerance",
	title = "The quadratic sieve factoring algorithm",
	booktitle = EUROCRYPT84,
	editor = "T. Beth and N. Cot and I. Ingemarsson",
	series = LNICS,
	volume = 209,
	year = 1984,
	pages = "169--182"}

@article{Silverman:1987,
	key = "Silverman 1987",
	author = "R. D. Silverman",
	title = "The multiple polynomial quadratic sieve",
	journal = MC,
	volume = 48,
	year = 1987,
	pages = "329-339"}

@article{Schnorr&Lenstra:1984,
	key = "Schnorr and Lenstra 1984",
	author = "C. P. Schnorr and Lenstra, Jr., H. W.",
	title = "A {Monte Carlo} factoring algorithm with linear storage",
	journal = MC,
	volume = 43,
	year = 1984,
	pages = "289-311"}

@article{Lehmer:1933b,
	key = "D. H. Lehmer 1933b",
	author = "D. H. Lehmer",
	title = "Some new factorizations of $2^n \pm 1$",
	journal = BAMS,
	volume = 39,
	year = "{\noopsort{1933b}}1933",
	pages = "105-108"}

@article{Lehmer&Lehmer:1974,
	key = "D. H. Lehmer and E. Lehmer 1974",
	author = "D. H. Lehmer and E. Lehmer",
	title = "A new factorization technique using quadratic forms",
	journal = MC,
	volume = 28,
	year = 1974,
	pages = "625-635"}

@article{Lehman:1974,
	key = "Lehman 1974",
	author = "R. S. Lehman",
	title = "Factoring large integers",
	journal = MC,
	volume = 28,
	year = 1974,
	pages = "637-646"}

@incollection{Schoof:1982,
	key = "Schoof 1982",
	author = "R. J. Schoof",
	title = "Quadratic fields and factorization",
	editor = "Lenstra, Jr., H. W. and R. Tijdeman",
	booktitle = "Computational Methods in Number Theory",
	publisher = "Mathematisch Centrum",
	address = "Amsterdam",
	year = 1982,
	pages = "235-286"}

@incollection{Pomerance:1982a,
	key = "Pomerance 1982a",
	author = "C. Pomerance",
	title = "Analysis and comparison of some integer factoring algorithms",
	editor = "Lenstra, Jr., H. W. and R. Tijdeman",
	booktitle = "Computational Methods in Number Theory",
	publisher = "Mathematisch Centrum",
	address = "Amsterdam",
	year = "{\noopsort{1982a}}1982",
	pages = "89-139"}

@article{Schnorr:1982,
	key = "Schnorr 1982",
	author = "C. P. Schnorr",
	title = "Refined analysis and improvements on some factoring
	algorithms",
	journal = JA,
	volume = 3,
	year = 1982,
	pages = "101-127"}

@article{AKLenstra:1988,
	key = "A. K. Lenstra 1988",
	author = "A. K. Lenstra",
	title = "Fast and rigorous factorization under the generalized
{Riemann} hypothesis",
	journal = PKNAW,
	volume = 91,
	year = 1988,
	pages = "443-454",
	note = "(= {\it Indag. Math.} {\bf 50})"}

@article{Brillhart&Selfridge:1967,
	key = "Brillhart and Selfridge 1967",
	author = "J. Brillhart and J. L. Selfridge",
	title = "Some factorizations of {$2^n \pm 1$} and related results",
	journal = MC,
	volume = 21,
	year = 1967,
	pages = "87-96",
	note = "Corrigendum, {\it Math. Comp.} {\bf 21} (1967) 751"}

@incollection{Shanks:1969,
	key = "Shanks 1969",
	author = "D. Shanks",
	title = "Class Number, a Theory of Factorization, and Genera",
	booktitle = "Number Theory Institute, 1969",
	series = "Proceedings of Symposia in Pure Mathematics",
	volume = 20,
	year = 1969,
	publisher = AMS,
	pages = "415-440"}

@inproceedings{Wunderlich:1984,
	key = "Wunderlich 1984",
	author = "M. C. Wunderlich",
	title = "Factoring numbers on the massively parallel computer",
	booktitle = CRYPTO83,
	editor = "D. Chaum",
	publisher = "Plenum Press",
	year = 1984,
	pages = "87-102"}

@inproceedings{Wunderlich:1983b,
	key = "Wunderlich 1983b",
	author = "M. C. Wunderlich",
	title = "Recent advances in the design and implementation of large
	integer factoring algorithms",
	booktitle = "1983 IEEE Symposium on Security and Privacy,
Preproceedings",
	year = "{\noopsort{1983b}}1983",
	pages = "2401-2405"}

@inproceedings{Wunderlich:1979,
	key = "Wunderlich 1979",
	author = "M. C. Wunderlich",
	title = "A running time analysis of {Brillhart's} continued
	fraction factoring method",
	booktitle = "Number Theory: Carbondale 1979",
	editor = "M. B. Nathanson",
	series = LNIM,
	volume = 751,
	year = 1979,
	pages = "328-342"}

@inproceedings{Smith&Wagstaff:1983,
	key = "J. Smith and Wagstaff 1983",
	author = "J. W. Smith and Wagstaff, Jr., S. S.",
	title = "An extended precision operand computer",
	booktitle = "Proc. 21st Southeast Region ACM Conference",
	year = 1983,
	pages = "209-216"}

@article{Buell:1984,
	key = "Buell 1984",
	author = "D. A. Buell",
	title = "The expectation of success using a {Monte} {Carlo}
	factoring method--some statistics on quadratic class numbers",
	journal = MC,
	volume = 43,
	year = 1984,
	pages = "313-327"}

@article{Riesel:1985b,
	key = "Riesel 1985b",
	author = "H. Riesel",
	title = "Modern factorization methods",
	journal = BIT,
	volume = 25,
	year = "{\noopsort{1985b}}1985",
	pages = "205-222"}

@inproceedings{Bach:1983,
	key = "Bach 1983",
	author = "E. Bach",
	title = "How to generate random integers with known factorization",
	booktitle = STOC83,
	year = 1983,
	pages = "184-188"}

@inproceedings{Rivest&Shamir:1985,
	key = "Rivest and Shamir 1985",
	author = "R. L. Rivest and A. Shamir",
	title = "Efficient factoring based on partial information",
	booktitle = CRYPTO85,
	editor = "F. Pichler",
	series = LNICS,
	volume = 219,
	year = 1985,
	pages = "31-34"}

@article{Pomerance&Smith&Tuler:1988,
	key = "Pomerance, Smith, and Tuler 1988",
	author = "C. Pomerance and J. W. Smith and R. Tuler",
	title = "A pipeline architecture for factoring large integers with
the quadratic sieve algorithm",
	journal = SIAMJC,
	volume = 17,
	year = 1988,
	pages = "387-403"}

@article{Williams:1984,
	key = "H. Williams 1984",
	author = "H. C. Williams",
	title = "Factoring on a computer",
	journal = MI,
	volume = 6,
	year = 1984,
	number = 3,
	pages = "29-36"}

@inproceedings{Pomerance:1986,
	key = "Pomerance 1986",
	author = "C. Pomerance",
	title = "Fast, rigorous factorization and discrete
logarithm algorithms",
	booktitle = "Discrete Algorithms and Complexity",
	organization = "Proc. of the Japan-US Joint Seminar",
	publisher = "Academic Press",
	editor = "{Johnson et al.}, D. S.",
	year = 1986,
	pages = "119-143"}

@article{Williams&Wunderlich:1987,
	key = "H. Williams and Wunderlich 1987",
	author = "H. C. Williams and M. C. Wunderlich",
	title = "On the parallel generation of the residues for the
continued fraction factoring algorithm",
	journal = MC,
	volume = 48,
	year = 1987,
	pages = "405-423"}

@article{Lehmer:1925,
	key = "D. N. Lehmer 1925",
	author = "D. N. Lehmer",
	title = "On a new method of factorization",
	journal = PNAS,
	volume = 11,
	year = 1925,
	pages = "97-98"}

@book{DNLehmer:1929,
	key = "D. N. Lehmer 1929",
	author = "D. N. Lehmer",
	title = "Factor Stencils",
	publisher = "Carnegie Institute of Washington",
	address = "Washington, D. C.",
	year = 1929,
	note = "Revised and extended by J. D. Elder, 1939.  Factor
stencil errata can be found in Elder [1937]"}

@article{Elder:1937,
	key = "Elder 1937",
	author = "J. D. Elder",
	title = "Errata in the {Lehmer} factor stencils",
	journal = BAMS,
	volume = 43,
	year = 1937,
	pages = "253-255"}

@article{Cole:1903,
	key = "Cole 1903",
	author = "F. N. Cole",
	title = "On the factoring of large numbers",
	journal = BAMS,
	volume = 10,
	year = 1903,
	pages = "134-137"}

@article{Glaisher:1878a,
	key = "Glaisher 1878a",
	author = "J. W. L. Glaisher",
	title = "On factor tables, with an account of the mode of formation
of the factor table for the fourth million",
	journal = PCPS,
	volume = 3,
	year = 1878,
	pages = "99-138"}

@article{Buell:1987,
	key = "Buell 1987",
	author = "D. A. Buell",
	title = "Factoring:  algorithms, computations, and computers",
	journal = JS,
	volume = 1,
	year = 1987,
	pages = "191-216"}

@article{Lehmer:1918,
	key = "D. N. Lehmer 1918",
	author = "D. N. Lehmer",
	title = "On the history of the problem of separating a number
into its prime factors",
	journal = SCIM,
	volume = 7,
	year = 1918,
	pages = "227-234"}

@unpublished{Wagstaff&Smith:1986,
	key = "Wagstaff and Smith 1986",
	author = "Wagstaff, Jr., S. S. and J. W. Smith",
	title = "Methods of factoring large integers",
	note = "unpublished",
	year = 1986}

@article{Lawrence:1895,
	key = "Lawrence 1895",
	author = "F. W. Lawrence",
	title = "Factorisation of numbers",
	journal = MESSM,
	volume = 24,
	year = 1895,
	pages = "100-109"}

@article{Lawrence:1896,
	key = "Lawrence 1896",
	author = "F. W. Lawrence",
	title = "Factorisation of numbers",
	journal = QJPAM,
	volume = 28,
	year = 1896,
	pages = "285-311"}

@article{teRiele&Lioen&Winter:1989,
	key = "te Riele, Lioen and Winter 1989",
	author = "Riele, H. te and W. Lioen and D. Winter",
	title = "Factoring with the quadratic sieve on large vector
computers",
	journal = JCAM,
	volume = 27,
	year = 1989,
	pages = "267-278"}

@article{Lioen&teRiele&Winter:1988,
	key = "Lioen, te Riele and Winter 1988",
	author = "W. Lioen and H. te Riele and D. Winter",
	title = "Optimization of the {MPQS-factoring} algorithm on the
{Cyber 205} and the {NEC SX-2}",
	journal = "Supercomputer",
	volume = 26,
	year = 1988,
	pages = "42-50"}

@article{Brethouwer:1973a,
	key = "Brethouwer 1973a",
	author = "Brethouwer, Sr., D. H. G.",
	title = "Factorizing large numbers. {I}",
	journal = PKNAW,
	volume = 76,
	year = 1973,
	pages = "410-423",
	note = "(= {\it Indag. Math.} {\bf 35})"}

@article{Brethouwer:1973b,
	key = "Brethouwer 1973b",
	author = "Brethouwer, Sr., D. H. G.",
	title = "Factorizing large numbers. {II}",
	journal = PKNAW,
	volume = 76,
	year = 1973,
	pages = "424-433",
	note = "(= {\it Indag. Math.} {\bf 35})"}

@article{Davis&Holdridge:1985,
	key = "J. Davis and Holdridge 1985",
	author = "J. A. Davis and D. B. Holdridge",
	title = "New results on integer factorizations",
	journal = CN,
	volume = 46,
	year = 1985,
	pages = "65-78"}

@article{Brillhart&Montgomery&Silverman:1988,
	key = "Brillhart, Montgomery, and Silverman 1988",
	author = "J. Brillhart and P. L. Montgomery and R. D. Silverman",
	title = "Tables of {Fibonacci} and {Lucas} factorizations",
	journal = MC,
	volume = 50,
	year = 1988,
	pages = "251-260"}

@article{deBruijn:1951a,
	key = "de Bruijn 1951a",
	author = "Bruijn, N. G. de",
	title = "The asymptotic behaviour of a function occurring in the
theory of primes",
	journal = JIMS,
	volume = 15,
	year = 1951,
	pages = "25-32"}

@article{deBruijn:1951b,
	key = "de Bruijn 1951b",
	author = "Bruijn, N. G. de",
	title = "On the number of positive integers $\leq x$ and free
of prime factors $>y$",
	journal = PKNAW,
	volume = 54,
	year = 1951,
	pages = "50-60",
	note = "(= {\it Indag. Math.} {\bf 13})"}

@article{deBruijn:1966,
	key = "de Bruijn 1966",
	author = "Bruijn, N. G. de",
	title = "On the number of positive integers $\leq x$ and free
of prime factors $>y$, {II}",
	journal = PKNAW,
	volume = 69,
	year = 1966,
	pages = "239-247",
	note = "(= {\it Indag. Math.} {\bf 28})"}

@article{Canfield&Erdos&Pomerance:1983,
	key = "Canfield, {Erd{\H{o}}s}, and Pomerance 1983",
	author = "E. R. Canfield and P. {Erd{\H{o}}s} and C. Pomerance",
	title = {On a problem of {Oppenheim} concerning
{``Factorisatio Numerorum"}},
	journal = JNT,
	volume = 17,
	year = 1983,
	pages = "1-28"}

@article{Dickman:1930,
	key = "Dickman 1930",
	author = "K. Dickman",
	title = "On the frequency of numbers containing prime factors of
a certain magnitude",
	journal = "Arkiv for Mathematik, Astronomi oc Fysik",
	volume = "22A",
	year = 1930,
	pages = "1-14"}

@inproceedings{Guy:1976,
	key = "Guy 1976",
	author = "R. K. Guy",
	title = "How to factor a number",
	booktitle = "Proc. 5th Manitoba Conf. on Numerical Math.",
	address = "Winnipeg",
	year = 1976,
	pages = "49-89"}

@article{Hildebrand:1984,
	key = "Hildebrand 1984",
	author = "A. Hildebrand",
	title = "Integers free of large prime factors and the {Riemann}
hypothesis",
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	volume = 31,
	year = 1984,
	pages = "258-271"}

@article{Lagarias:1980,
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	author = "J. C. Lagarias",
	title = "Worst-case complexity bounds for algorithms in the theory of integral
quadratic forms",
	journal = JA,
	volume = 1,
	year = 1980,
	pages = "142-186"}

@article{Miller:1975,
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	author = "J. C. P. Miller",
	title = "On factorisation, with a suggested new approach",
	journal = MC,
	volume = 29,
	year = 1975,
	pages = "155-172"}

@article{Narkiewicz:1967,
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	author = "W. Narkiewicz",
	title = "Class number and factorization in quadratic number
fields",
	journal = "Colloq. Math.",
	volume = 17,
	year = 1967,
	pages = "167-190"}

@article{Redei:1949,
	key = "{R\'edei} 1949",
	author = "L. {R\'edei}",
	title = "{\"Uber} die {Klassengruppen} und {Klassenk\"orper}
algebraischer {Zahlk\"orper}",
	journal = JFRAM,
	volume = 186,
	year = 1949,
	pages = "80-90"}

@techreport{Rivest&Pinter:1979,
	key = "Rivest and Pinter 1979",
	author = "R. L. Rivest and R. Y. Pinter",
	title = "Using hyperbolic tangents in integer factoring",
	institution = "MIT Laboratory for Computer Science",
	month = "November",
	year = 1979}

@article{Seysen:1987,
	key = "Seysen 1987",
	author = "M. Seysen",
	title = "A probabilistic factorization algorithm with quadratic
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	journal = MC,
	volume = 48,
	year = 1987,
	pages = "757-780"}

@article{Strassen:1976,
	key = "Strassen 1976",
	author = "V. Strassen",
	title = "Einige {Resultate} {\"uber} {Berechnungskomplexit\"at}",
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	volume = 78,
	year = 1976,
	pages = "1-8"}

@techreport{Sorenson:1990a,
	key = "Sorenson 1990a",
	author = "J. Sorenson",
	title = "Counting the integers cyclotomic methods can factor",
	institution = "Univ. of Wisconsin, Madison; Department of
Computer Science",
	number = "919",
	month = "March",
	year = "{\noopsort{1990a}}1990"}

@article{Hazlewood:1973,
	key = "Hazlewood 1973",
	author = "D. G. Hazlewood",
	title = "On integers all of whose prime factors are small",
	journal = BLMS,
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	year = 1973,
	pages = "159-163"}

@article{Montgomery&Silverman:1990,
	key = "Montgomery and Silverman 1990",
	author = "P. L. Montgomery and R. D. Silverman",
	title = "An {FFT} extension to the $p-1$ factoring
algorithm",
	journal = MC,
	volume = 54,
	year = 1990,
	pages = "839-854"}

@techreport{Condie&Lo&Pieprzyk:1988,
	key = "Condie, Lo, and Pieprzyk 1988",
	author = "L. E. Condie and J. Lo and J. Pieprzyk",
	title = "Factorization using quadratic sieves",
	institution = "University College, University of New South Wales,
Department of Computer Science",
	month = "January",
	year = 1988}

@inproceedings{Lenstra&Lenstra&Manasse&Pollard:1990,
	key = "A. K. Lenstra, Lenstra, Manasse, and Pollard 1990",
	author = "A. K. Lenstra and Lenstra, Jr., H. W. and M. S. Manasse
and J. M. Pollard",
	title = "The number field sieve",
	booktitle = STOC90,
	year = 1990,
	pages = "564-572"}

@article{Bach:1991a,
	key = "Bach 1991a",
	author = "E. Bach",
	title = "Toward a theory of {Pollard}'s rho method",
	journal = IC,
	volume = 90,
	year = "{\noopsort{1991a}}1991",
	pages = "139-155"}

@incollection{Brent:1990,
	key = "Brent 1990",
	author = "R. P. Brent",
	title = "Parallel algorithms for integer factorisation",
	booktitle = "Number Theory and Cryptography",
	editor = "J. H. Loxton",
	publisher = "Cambridge University Press",
	series = "London Mathematical Society Lecture Note Series",
	year = 1990,
	volume = 154,
	pages = "26-37"}

@article{Lebesgue:1864,
	key = "Lebesgue 1864",
	author = "V.-A. Lebesgue",
	title = "Tables diverses pour la {d\'ecomposition} des nombres en
leurs facteurs premiers",
	journal = "M\'emoires Soc. Sc. Phys. Nat. Bordeaux",
	volume = 3,
	year = 1864,
	pages = "1-37"}

@inproceedings{Adleman:1991,
	key = "Adleman 1991",
	author = "L. M. Adleman",
	title = "Factoring numbers using singular integers",
	booktitle = STOC91,
	year = 1991,
	pages = "64-71"}

@incollection{DHLehmer:1990,
	key = "D. H. Lehmer 1990",
	author = "D. H. Lehmer",
	title = "Factorization then and now",
	booktitle = "Computers in Mathematics", 
	editor = "D. V. Chudnovsky and R. D. Jenks",
	series = "Lecture Notes in Pure and Applied Mathematics",
	volume = 125,
	publisher = "Marcel Dekker, Inc.",
	address = NY,
	year = 1990,
	pages = "311-320"}

@incollection{McCurdy:1987,
	key = "McCurdy 1987",
	author = "K. J. McCurdy",
	title = "Factoring large numbers on the {MPP}",
	booktitle = "Sixth Annual International Phoenix Conference on Computers and Communications",
	year = 1987,
	editor = "O. Friesen and F. Golshani",
	publisher = "IEEE Computer Society Press",
	pages = "79-81"}

@incollection{McCurdy&Wunderlich:1987,
	key = "McCurdy and Wunderlich 1987",
	author = "K. J. McCurdy and M. C. Wunderlich",
	title = "The factorization of large composite numbers on the {MPP}",
	booktitle = "Frontiers of Massively Parallel Scientific Computation 
		     (Proceedings of the First
		     Symposium held at NASA Goddard Space Flight Center,
		     Greenbelt, MD)",
	series = "NASA Conference Publication 2478",
	year = 1987,
	publisher = "National Aeronautics and Space Administration
		     Scientific and Technical Information Office",
	pages = "265-269"}

@techreport{Coppersmith:1991a,
	key = "Coppersmith 1991a",
	author = "D. Coppersmith",
	title = "Modifications to the number field sieve",
	institution = "IBM T. J. Watson Research Center",
	number = "RC 16264",
	month = "March",
	year = "{\noopsort{1991a}}1991"}

@article{Coppersmith:1993,
	key = "Coppersmith 1993",
	author = "D. Coppersmith",
	title = "Modifications to the number field sieve",
	journal = JC,
	volume = 6,
	year = 1993,
	pages = "169-180"}

@unpublished{Schnorr:1990,
	key = "Schnorr 1990",
	author = "C. P. Schnorr",
	title = "Factoring integers and computing discrete logarithms
via {Diophantine} approximation",
	year = 1990,
	note = "Manuscript"}

@incollection{Pomerance:1990,
	key = "Pomerance 1990",
	author = "C. Pomerance",
	title = "Factoring",
	booktitle = "Cryptology and Computational Number Theory",
	series = PSAM,
	volume = 42,
	publisher = AMS,
	year = 1990,
	pages = "27-47"}

@article{Hafner&McCurley:1989b,
	key = "Hafner and McCurley 1989b",
	author = "J. L. Hafner and K. S. McCurley",
	title = "On the distribution of running times of certain
		 integer factoring algorithms",
	journal = JA,
	volume = 10,
	year = "{\noopsort{1989b}}1989",
	pages = "531-556"}

@incollection{LenstraAK&Manasse:1990,
	key = "A. K. Lenstra and Manasse 1990",
	author = "A. K. Lenstra and M. S. Manasse",
	title = "Factoring by electronic mail",
	booktitle = EUROCRYPT89,
	editor = "J.-J. Quisquater and J. Vandewalle",
	publisher = SV,
	year = 1990,
	pages = "355-371"}

@article{Silverman:1991b,
	key = "Silverman 1991b",
	author = "R. D. Silverman",
	title = "Massively distributed computing and factoring large integers",
	journal = CACM,
	volume = 34,
	number = 11,
	year = "{\noopsort{1991b}}1991",
	pages = "94-103",
	note = "Corrigendum, {\bf 35} (2) (1992), 26"}

@article{teRiele&Lioen&Winter:1991,
	key = "te Riele, Lioen, and Winter 1991",
	author = "Riele, H. te and W. Lioen and D. Winter",
	title = "Factorization beyond the googol with {MPQS} on a single computer",
	journal = CWIQ,
	volume = 4,
	number = 1,
	year = 1991,
	pages = "69-72"}

@article{Western:1928,
	key = "Western 1928",
	author = "A. E. Western",
	title = "Allan {Joseph} {Cunningham}",
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	volume = 3,
	year = 1928,
	pages = "317-318"}

@article{Williams:1993,
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	author = "H. C. Williams",
	title = "How was {$F_6$} factored?",
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	volume = 61,
	year = 1993,
	pages = "463-474"}

@article{Pepin:1890,
	key = "Pepin 1890",
	author = "T. Pepin",
	title = "Sur la {d\'ecomposition} des grands nombres
en facteurs premiers",
	journal = AAPNL,
	volume = 43,
	year = "1889-90",
	pages = "163-191"}

@article{Pepin:1900,
	key = "Pepin 1900",
	author = "T. Pepin",
	title = "Sur la {d\'ecomposition} des grands nombres en
facteurs premiers",
	journal = MAPNL,
	volume = 17,
	year = 1900,
	pages = "321-344"}

@article{Pepin:1893,
	key = "Pepin 1893",
	author = "T. Pepin",
	title = "Extension de la {m\'ethode} {d'Euler} pour la
{d\'ecomposition} des grands nombres en facteurs premiers",
	journal = MAPNL,
	volume = 9,
	year = 1893,
	pages = "47-76"}

@article{Pepin:1889,
	key = "Pepin 1889",
	author = "T. Pepin",
	title = "Sur une table auxiliaire de {Gauss} (i)",
	journal = AAPNL,
	volume = 42,
	year = 1889,
	pages = "135-156"}

@article{DNLehmer:1930,
	key = "D. N. Lehmer 1930",
	author = "D. N. Lehmer",
	title = "On the factorization of large numbers",
	journal = "Univ. of California Chronicle",
	volume = 32,
	year = 1930,
	pages = "326-341"}

@incollection{Lenstra&Manasse:1991,
	key = "A. K. Lenstra and Manasse 1991",
	author = "A. K. Lenstra and M. S. Manasse",
	title = "Factoring with two large primes",
	booktitle = EUROCRYPT90,
	editor = "I. B. {Damg\aa rd}",
	publisher = SV,
	year = 1991,
	series = LNICS,
	volume = 473,
	pages = "72-82"}

@article{Vallee:1991a,
	key = "{Vall\'ee} 1991a",
	author = "B. {Vall\'ee}",
	title = "Generation of elements with small modular squares and provably
fast integer factoring algorithms",
	journal = MC,
	volume = 56,
	year = "{\noopsort{1991a}}1991",
	pages = "823-849"}

@article{Vallee:1989,
	key = "{Vall\'ee} 1989",
	author = "B. {Vall\'ee}",
	title = "Factorisation {enti\`ere} par {g\'en\'eration} quasi-uniforme de
petits {r\'esidus} quadratiques",
	journal = CRASP,
	volume = 308,
	year = 1989,
	pages = "59-62"}

@incollection{Granville:1989b,
	key = "Granville 1989b",
	author = "A. Granville",
	title = "On positive integers $\leq x$ with prime factors $\leq t \log x$",
	booktitle = "Number Theory and Applications",
	editor = "R. A. Mollin",
        series = "NATO ASI Series C:  Mathematical and Physical Sciences",
        volume = 265,
        publisher = "Kluwer",
        year = "{\noopsort{1989b}}1989",
        pages = "403-422"}

@techreport{Naur:1982,
	key = "Naur 1982",
	author = "T. Naur",
	title = "Integer Factorization",
	month = "May",
	year = 1982,
	number = "DAIMI PB-144",
	institution = "Computer Science Department, Aarhus University, Denmark"}

@unpublished{Peralta:1992b,
	key = "Peralta 1992b",
	author = "R. Peralta",
	title = "A quadratic sieve on the $n$-dimensional cube",
	note = "To appear, CRYPTO 92",
	year = 1992}

@incollection{Schnorr:1991,
	key = "Schnorr 1991",
	author = "C. P. Schnorr",
	title = "Factoring integers and computing discrete logarithms
via diophantine approximation",
	booktitle = EUROCRYPT91,
	editor = "D. W. Davies",
	publisher = SV,
	series = LNICS,
	year = 1991,
	volume = 547,
	pages = "281-293"}

@article{LenstraHW&Pomerance:1992,
	key = "H. W. Lenstra and Pomerance 1992",
	author = "Lenstra, Jr., H. W. and C. Pomerance",
	title = "A rigorous time bound for factoring integers",
	journal = JAMS,
	volume = 5,
	year = 1992,
	pages = "483-516"}

@article{Riesel:1991,
	key = "Riesel 1991",
	author = "H. Riesel",
	title = "Wie schnell kann man {Zahlen} in {Faktoren} zerlegen?",
	journal = MMGH,
	volume = 12,
	year = 1991,
	pages = "253-260"}

@incollection{Namba:1991,
	key = "Namba 1991",
	author = "K. Namba",
	title = "Legendre polynomial over finite fields and factorization
of integers",
	booktitle = "International Symposium in Memory of Hua Loo Keng",
	volume = "I (Number Theory)",
	editor = "S. Gong and Q.-K. Lu and Y. Wang and L. Yang",
	publisher = "Science Press and Springer-Verlag",
	year = 1991,
	pages = "209-223"}

@article{vonThielmann:1906,
	key = "von Thielmann 1906",
	author = "Thielmann, M. von",
	title = "Die {Zerlegung} von {Zahlen} mit {Hilfe} periodischer
{Kettenbr\"uche}",
	journal = MA,
	volume = 62,
	year = 1906,
	pages = "401-408"}

@article{Hahn&Oh:1993,
	key = "Hahn and Oh 1993",
	author = "S. Hahn and Y. Oh",
	title = "Factorizations of {$17^n - 1$} for $n \leq 78$",
	journal = MJAP,
	volume = 38,
	year = 1993,
	pages = "225-233"}

@incollection{Maurer:1993,
	key = "Maurer 1993",
	author = "U. M. Maurer",
	title = "Factoring with an oracle",
	booktitle = EUROCRYPT92,
	editor = "R. A. Rueppel",
	series = LNICS,
	volume = 658,
	year = 1993,
	publisher = SV,
	pages = "429-436"}

@incollection{DixonB&Lenstra:1993,
	key = "B. Dixon and Lenstra 1993",
	author = "B. Dixon and A. K. Lenstra",
	title = "Massively parallel elliptic curve factoring",
	booktitle = EUROCRYPT92,
	editor = "R. A. Rueppel",
	series = LNICS,
	volume = 658,
	year = 1993,
	publisher = SV,
	pages = "183-193"}

@article{Lebon:1907,
	key = "Lebon 1907",
	author = "E. Lebon",
	title = "Pour la recherche rapide des facteurs premiers
des grands nombres",
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	volume = 36,
	year = 1907,
	pages = "49-55"}

@article{Peterson:1994,
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	number = 5,
	year = 1994,
	pages = "71"}

@unpublished{Fergusson:1993,
	key = "Fergusson 1993",
	author = "K. J. Fergusson",
	title = "Integer factorisation using cyclotomic polynomials",
	note = "Unpublished manuscript, dated November",
	year = 1993}

@inproceedings{Shor:1994a,
	key = "Shor 1994a",
	author = "P. W. Shor",
	title = "Algorithms for quantum computation:  discrete logarithms
and factoring",
	booktitle = FOCS94,
	year = "{\noopsort{1994a}}1994",
	pages = "124-134"}

@incollection{Shor:1994b,
	key = "Shor 1994b",
	author = "P. W. Shor",
	title = "Polynomial time algorithms for discrete logarithms
and factoring on a quantum computer",
	booktitle = ANTS1,
	editor = "L. M. Adleman and M.-D. Huang",
	series = LNICS,
	volume = 877,
	publisher = SV,
	year = 1994,
	pages = "289"}

@techreport{Hafner:1990,
	key = "Hafner 1990",
	author = "J. L. Hafner",
	title = "On smooth numbers in short intervals under the {R}iemann
		 hypothesis",
	month = "October",
	year = 1990,
	number = "RJ 7728 (71593)",
	institution = "IBM Almaden Research Center"}

@article{Chamayou:1973,
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	author = "J.-M.-F. Chamayou",
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	journal = MC,
	volume = 27,
	year = 1973,
	pages = "197-203"}
	
@unpublished{Buchmann&Hollinger:1993,
	key = "Buchmann and Hollinger 1993",
	author = "J. A. Buchmann and C. S. Hollinger",
	title = "On smooth ideals in number fields",
	note = "Unpublished manuscript, dated 8 September 1993",
	year = 1993}

@unpublished{Zhang:1994,
	key = "Zhang 1994",
	author = "M. Zhang",
	title = "Factoring integers with conics",
	note = "Unpublished manuscript, dated 27 May",
	year = 1994}

@article{Kemeny:1993,
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	author = "J. Kemeny",
	title = "Largest prime factor",
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	year = 1993,
	pages = "181-186"}

@book{LenstraAK&LenstraHW:1993,
	key = "A. K. Lenstra and H. W. Lenstra 1993",
	editor = "A. K. Lenstra and Lenstra, Jr., H. W.",
	title = "The development of the number field sieve",
	publisher = SV,
	series = LNIM,
	volume = 1554,
	year = 1993}

@article{Lenstra&Manasse:1994,
	key = "A. K. Lenstra and Manasse 1994",
	author = "A. K. Lenstra and M. S. Manasse",
	title = "Factoring with two large primes",
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	volume = 63,
	year = 1994,
	pages = "785-798"}

@article{Brent:1993,
	key = "Brent 1993",
	author = "R. P. Brent",
	title = "On computing factors of cyclotomic polynomials",
	journal = MC,
	volume = 61,
	year = 1993,
	pages = "131-149"}

@incollection{DixonB&Lenstra:1994",
	key = "B. Dixon and Lenstra 1994",
	author = "B. Dixon and A. K. Lenstra",
	title = "Factoring integers using {SIMD} sieves",
	booktitle = EUROCRYPT93,
	series = LNICS,
	editor = "T. Helleseth",
	volume = 765,
	year = 1994,
	publisher = SV,
	pages = "28-39"}

@article{Biermann:1964,
	key = "K. Biermann 1964",
	author = "K.-R. Biermann",
	title = "Thomas {Clausen}, {Mathematiker} und {Astronom}",
	journal = JFRAM,
	volume = 216,
	year = 1964,
	pages = "159-198"}

@article{Billingsley:1973,
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	year = 1973,
	pages = "1099-1115"}

@article{Golliver&Lenstra&McCurley:1994,
	key = "Golliver, Lenstra, and McCurley 1994",
	author = "R. A. Golliver and A. K. Lenstra and K. S. McCurley",
	title = "Lattice sieving and trial division",
	booktitle = ANTS1,
	editor = "L. M. Adleman and M.-D. Huang",
	series = LNICS,
	volume = 877,
	publisher = SV,
	year = 1994,
	pages = "18-27"}

@incollection{Lipton:1994,
	key = "Lipton 1994",
	author = "R. J. Lipton",
	title = "Straight-line complexity and integer factorization",
	booktitle = ANTS1,
	editor = "L. M. Adleman and M.-D. Huang",
	series = LNICS,
	volume = 877,
	publisher = SV,
	year = 1994,
	pages = "71-79"}

@incollection{Adleman:1994,
	key = "Adleman 1994",
	author = "L. M. Adleman",
	title = "The function field sieve",
	booktitle = ANTS1,
	editor = "L. M. Adleman and M.-D. Huang",
	series = LNICS,
	volume = 877,
	publisher = SV,
	year = 1994,
	pages = "108-121"}

@techreport{Coppersmith:1995a,
	key = "Coppersmith 1995a",
	author = "D. Coppersmith",
	title = "Factoring with a hint",
	institution = "IBM T. J. Watson Research Center",
	number = "RC 19905",
	month = "January",
	year = "{\noopsort{1995a}}1995"}

@techreport{Coppersmith:1995b,
	key = "Coppersmith 1995b",
	author = "D. Coppersmith",
	title = "Factoring with a hint",
	institution = "IBM T. J. Watson Research Center",
	number = "RC 20089",
	month = "June",
	year = "{\noopsort{1995b}}1995"}

@article{Riesel:1969b,
	key = "Riesel 1969b",
	author = "H. Riesel",
	title = "Some factors of the numbers
{$G_n = 6^{2^n} + 1$} and {$H_n = 10^{2^n} + 1$}",
	journal = MC,
	volume = 23,
	year = 1969,
	pages = "413-415"}

@article{Beeger:1946,
	key = "Beeger 1946",
	author = "N. G. W. H. Beeger",
	title = "Note sur la factorisation de quelques grands nombres",
	journal = "Archives Sect. d. Sc. nat. phys. math. Institut Grand-Ducal
de Luxembourg",
	volume = 16,
	year = 1946,
	pages = "93-95"}

@incollection{Coppersmith:1987b,
	key = "Coppersmith 1987b",
	author = "D. Coppersmith",
	title = "Knapsack used in factoring",
	booktitle = "Open Problems in Communication and Complexity",
	editor = "T. M. Cover and B. Gopinath",
	publisher = SV,
	year = "{\noopsort{1987b}}1987",
	pages = "117-119"}

@article{Blair&Lacampagne&Selfridge:1986,
	key = "Blair, Lacampagne, and Selfridge 1986",
	author = "W. D. Blair and C. B. Lacampagne and J. L. Selfridge",
	title = "Factoring large numbers on a pocket calculator",
	journal = AMM,
	volume = 93,
	year = 1986,
	pages = "802-808"}

@techreport{Sorenson:1989,
	key = "Sorenson 1989",
	author = "J. Sorenson",
	title = "Polylog depth circuits for integer factoring and discrete logarithms",
	institution = "University of Wisconsin, Computer Sciences Department",
	number = 872,
	month = "August",
	year = 1989}

@inproceedings{Woods:1976,
	key = "Woods 1976",
	author = "D. Woods",
	title = "Hunting big game -- with a bow and arrow",
	booktitle = "AEDS International Convention Proceedings",
	year = 1976,
	publisher = IBM,
	pages = "290-292"}

@article{Alway:1952,
	key = "Alway 1952",
	author = "G. G. Alway",
	title = "A method of factorisation using a high-speed computer",
	journal = MTAC,
	volume = 6,
	year = 1952,
	pages = "59-60"}

@article{LehmerDN:1907,
	key = "D. N. Lehmer 1907",
	author = "D. N. Lehmer",
	title = "A theorem in the theory of numbers",
	journal = BAMS,
	volume = "???",
	year = 1907,
	pages = "501-502"}

@article{LehmerDN:1927,
	key = "D. N. Lehmer 1927",
	author = "D. N. Lehmer",
	title = "A theorem on factorization",
	journal = BAMS,
	volume = "???",
	year = 1927,
	pages = "35-36"}

@article{Tennant:1900,
	key = "Tennant 1900",
	author = "J. Tennant",
	title = "On the factorisation of high numbers",
	journal = QJM,
	volume = 32,
	year = 1900,
	pages = "322-341"}

@article{Bickmore:1897,
	key = "Bickmore 1897",
	author = "C. E. Bickmore",
	title = "On the numerical factors of {$a^n - 1$} (second notice)",
	journal = MESSM,
	volume = 26,
	year = 1897,
	pages = "1-38"}

@article{Bickmore:1895,
	key = "Bickmore 1895",
	author = "C. E. Bickmore",
	title = "On the numerical factors of {$a^n - 1$}",
	journal = MESSM,
	volume = 25,
	year = 1895,
	pages = "1-44"}

@article{Isemonger:1965,
	key = "Isemonger 1965",
	author = "K. R. Isemonger",
	title = "Some additional factorizations of $2^n \pm 1$",
	journal = MC,
	volume = 19,
	year = 1965,
	pages = "145-146"}

@phdthesis{Broder:1985,
	key = "Broder 1985",
	author = "A. Z. Broder",
	title = "Weighted random mappings; properties and applications",
	school = "Department of Computer Science, Stanford University",
	month = "May",
	year = 1985,
	note = "Technical Report STAN-CS-85-1054"}

@article{Gold&Sattler:1983,
	key = "Gold and Sattler 1983",
	author = "R. Gold and J. Sattler",
	title = "Modifikationen des {Pollard-Algorithmus}",
	journal = COMP,
	volume = 30,
	year = 1983,
	pages = "77-89"}

@inproceedings{Fich:1981,
	key = "Fich 1981",
	author = "F. E. Fich",
	title = "Lower bounds for the cycle detection problem",
	booktitle = STOC81,
	year = 1981,
	pages = "96-105"}

@unpublished{Bach&Peralta:1996,
	key = "Bach and Peralta 1996",
	author = "E. Bach and R. Peralta",
	title = "Asymptotic semismoothness probabilities",
	journal = MC,
	year = 1996,
	note = "To appear"}

@article{Buhrman:1996,
	key = "Buhrman 1996",
	author = "H. Buhrman",
	title = "A short note on {Shor's} factoring algorithm",
	journal = SIGACT,
	volume = 27,
	number = 1,
	month = "March",
	year = "1996",
	pages = "89-90"}