@article{Baker:1987,
	key = "Baker 1987",
	author = "P. W. Baker",
	title = "Fast computation of {$A*B$} modulo {$N$}",
	journal = ELETT,
	volume = 23,
	year = 1987,
	pages = "794-795"}

@article{Itoh&Tsujii:1988a,
	key = "Itoh and Tsujii 1988a",
	author = "T. Itoh and S. Tsujii",
	title = "Effective recursive algorithm for computing multiplicative
		 inverses in {$GF(2^m)$}",
	journal = ELETT,
	volume = 24,
	year = "{\noopsort{1988a}}1988",
	pages = "334-335"}

@article{Shayan&Le-Ngoc:1988,
	key = "Shayan and Le-Ngoc 1988",
	author = "Y. R. Shayan and T. Le-Ngoc",
	title = "Direct hardware solution to quadratic equation
{$Z^2 \oplus Z \oplus \beta = 0$} in {Galois} fields based on normal
basis representation",
	journal = ELETT,
	volume = 24,
	year = 1988,
	pages = "847-848"}

@article{Piontas:1989,
	key = "Piontas 1989",
	author = "M. Piontas",
	title = "Algorithm for squaring in {$GF(2^m)$} in standard basis",
	journal = ELETT,
	volume = 25,
	year = 1989,
	pages = "1262-1263"}

@incollection{Beth&Cook&Gollmann:1986,
	key = "Beth, Cook, and Gollmann 1986",
	author = "T. Beth and B. M. Cook and D. Gollmann",
	title = "Architectures for exponentiation in {$GF(2^n)$}",
	booktitle = CRYPTO86,
	editor = "A. M. Odlyzko",
	series = LNICS,
	volume = 263,
	year = 1986,
	publisher = SV,
	pages = "302-310"}

@article{Weber:1990,
	key = "Weber 1990",
	author = "K. Weber",
	title = "An experiment in high-precision arithmetic on
shared memory multiprocessors",
	journal = ASB,
	month = "April",
	year = 1990,
	volume = 24,
	number = 2,
	pages = "22-40"}

@incollection{GordonJ:1989,
	key = "J. Gordon 1989",
	author = "J. A. Gordon", 
	title = "Fast multiplicative inverse in modular arithmetic",
	booktitle = "Cryptography and Coding",
	editor = "H. J. Beker and F. C. Piper",
	publisher = "Clarendon Press",
	address = "Oxford",
	year = 1989,
	pages = "269-279"}

@article{Scott&Simmons&Tavares&Peppard:1988,
	key = "Scott, Simmons, Tavares, and Peppard 1988",
	author = "P. A. Scott and S. J. Simmons and S. E. Tavares and
L. E. Peppard",
	title = "Architectures for exponentiation in {$GF(2^m)$}",
	journal = IEEE-JSAC,
	volume = 6,
	year = 1988,
	pages = "578-586"}

@article{Blakley:1983,
	key = "Blakley 1983",
	author = "G. R. Blakley",
	title = "A computer algorithm for calculating the product {$AB$}
modulo {$M$}",
	journal = IEEE-TC,
	volume = "C-32",
	year = 1983,
	pages = "497-500"}

@article{Gibson:1988,
	key = "Gibson 1988",
	author = "J. K. Gibson",
	title = "A generalisation of {Brickell's} algorithm for fast modular
multiplication",
	journal = BIT,
	volume = 28,
	year = 1988,
	pages = "755-763"}

@article{Head:1980,
	key = "Head 1980",
	author = "A. K. Head",
	title = "Multiplication modulo $n$",
	journal = BIT,
	volume = 20,
	year = 1960,
	pages = "115-116"}

@article{Walter&Eldridge:1990,
	key = "Walter and Eldridge 1990",
	author = "C. D. Walter and S. E. Eldridge",
	title = "A verification of {Brickell's} fast modular multiplication
algorithm",
	journal = IJCM,
	volume = 33,
	year = 1990,
	pages = "153-169"}

@article{Agnew&Beth&Mullin&Vanstone:1993,
	key = "Agnew, Beth, Mullin, and Vanstone 1993",
	author = "G. B. Agnew and T. Beth and R. C. Mullin and S. A. Vanstone",
	title = "Arithmetic operations in ${GF(2^m)}$",
	journal = JC,
	volume = 6,
	year = 1993,
	pages = "3-13"}

@article{Stinson:1990,
	key = "Stinson 1990",
	author = "D. R. Stinson",
	title = "Some observations on parallel algorithms for fast
exponentiation in ${GF(2^n)}$",
	journal = SIAMJC,
	volume = 19,
	year = 1990,
	pages = "711-717"}

@article{Mnuk:1991,
	key = "{M\u nuk} 1991",
	author = "{\noopsort{M. Mnuk}}M. {M\u nuk}",
	title = "A div$(n)$ depth {Boolean} circuit for smooth modular inverse",
	journal = IPL,
	volume = 38,
	year = 1991,
	pages = "153-156"}

@article{Pincin:1989,
	key = "Pincin 1989",
	author = "A. Pincin",
	title = "A new algorithm for multiplication in finite fields",
	journal = IEEE-TC,
	volume = 38,
	year = 1989,
	pages = "1045-1049"}

@article{Brent&Kung:1981,
	key = "Brent and Kung 1981",
	author = "R. P. Brent and H. T. Kung",
	title = "The area-time complexity of binary multiplication",
	journal = JACM,
	volume = 28,
	year = 1981,
	pages = "521-534"}

@article{Shankar&Ramachandran:1988,
	key = "Shankar and Ramachandran 1988",
	author = "N. Shankar and V. Ramachandran",
	title = "Efficient parallel circuits and algorithms for division",
	journal = IPL,
	volume = 29,
	year = 1988,
	pages = "307-313"}

@incollection{Takagi:1991,
	key = "N. Takagi 1991",
	author = "N. Takagi",
	title = "A Radix-4 Modular Multiplication hardware algorithm efficient
for iterative modular multiplication",
	booktitle = "Proc. 10th IEEE Symp. Comp. Arith.",
	publisher = "IEEE Computer Society Press",
	year = 1991,
	pages = "35-42",
	editor = "P. Kornerup and D. W. Matula"}

@article{Eldridge:1991,
	key = "Eldridge 1991",
	author = "S. E. Eldridge",
	title = "A faster modular multiplication algorithm",
	journal = IJCM,
	volume = 40,
	year = 1991,
	pages = "63-68"}

@article{Walter:1991,
	key = "Walter 1991",
	author = "C. D. Walter",
	title = "Fast modular multiplication using $2$--power radix",
	journal = IJCM,
	volume = 39,
	year = 1991,
	pages = "21-28"}

@incollection{Geiselmann&Gollmann:1990,
	key = "Geiselmann and Gollmann 1990",
	author = "W. Geiselmann and D. Gollmann",
	title = "{VLSI} design for exponentiation in {$GF(2^n)$}",
	booktitle = AUSCRYPT90,
	editor = "J. Seberry and J. Pieprzyk",
	publisher = SV,
	series = LNICS,
	volume = 453,
	year = 1990,
	pages = "398-405"}

@incollection{Morita:1990a,
	key = "Morita 1990a",
	author = "H. Morita",
	title = "A fast modular-multiplication module for smart cards",
	booktitle = AUSCRYPT90,
	editor = "J. Seberry and J. Pieprzyk",
	publisher = SV,
	series = LNICS,
	volume = 453,
	year = "{\noopsort{1990a}}1990",
	pages = "406-409"}

@incollection{Morii&Takamatsu:1991,
	key = "Morii and Takamatsu 1991",
	author = "M. Morii and Y. Takamatsu",
	title = "Exponentiation in finite fields using dual basis multiplier",
	booktitle = AAECC8,
	editor = "S. Sakata",
	publisher = SV,
	series = LNICS,
	volume = 508,
	year = 1991,
	pages = "354-366"}

@incollection{Diab:1991,
	key = "Diab 1991",
	author = "M. Diab",
	title = "Systolic architectures for multiplication over finite
field {$GF(2^m)$}",
	booktitle = AAECC8,
	editor = "S. Sakata",
	publisher = SV,
	series = LNICS,
	volume = 508,
	year = 1991,
	pages = "329-340"}

@article{Schonhage:1986,
	key = "{Sch\"onhage} 1986",
	author = "A. {Sch\"onhage}",
	title = "Tapes versus Pointers, a study in implementing fast algorithms",
	journal = BEATCS,
	number = 30,
	month = "October",
	year = "1986",
	pages = "23-32"}

@inproceedings{Shand&Bertin&Vuillemin:1990,
	key = "Shand, Bertin, and Vuillemin 1990",
	author = "M. Shand and P. Bertin and J. Vuillemin",
	title = "Hardware speedups in long integer multiplication",
	booktitle = SPAA90,
	year = 1990,
	pages = "138-145",
	publisher = ACM}

@unpublished{Fagin:1992,
	key = "Fagin 1992",
	author = "B. Fagin",
	title = "Large integer multiplication on hypercubes",
	note = "To appear, {\it J. Parallel Distrib. Comput.}",
	year = 1992}

@incollection{Findlay&Johnson:1990,
	key = "Findlay and Johnson 1990",
	author = "P. A. Findlay and B. A. Johnson",
	title = "Modular exponentiation using recursive sums of residues",
	booktitle = CRYPTO89,
	editor = "G. Brassard",
	publisher = SV,
	year = 1990,
	series = LNICS,
	volume = 435,
	pages = "371-386"}

@incollection{Even:1991,
	key = "Even 1991",
	author = "S. Even",
	title = "Systolic modular multiplication",
	booktitle = CRYPTO90,
	editor = "A. J. Menezes and S. A. Vanstone",
	publisher = SV,
	year = 1991,
	series = LNICS,
	volume = 537,
	pages = "619-624"}

@incollection{Walter:1992,
	key = "Walter 1992",
	author = "C. D. Walter",
	title = "Faster modular multiplication by operand scaling",
	booktitle = CRYPTO91,
	editor = "J. Feigenbaum",
	publisher = SV,
	year = 1992,
	series = LNICS,
	volume = 576,
	pages = "313-323"}

@incollection{Morita:1990b,
	key = "Morita 1990b",
	author = "H. Morita",
	title = "A fast modular-multiplication algorithm based on
a higher radix",
	booktitle = CRYPTO89,
	editor = "G. Brassard",
	publisher = SV,
	year = "{\noopsort{1990b}}1990",
	series = LNICS,
	volume = 435,
	pages = "387-399"}

@article{Booth:1951,
	key = "Booth 1951",
	author = "A. D. Booth",
	title = "A signed binary multiplication technique",
	journal = QJMAM,
	volume = 4,
	year = 1951,
	pages = "236-240"}

@article{Feng:1989,
	key = "Feng 1989",
	author = "G.-L. Feng",
	title = "A {VLSI} architecture for fast inversion in {$GF(2^m)$}",
	journal = IEEE-TC,
	volume = 38,
	year = 1989,
	pages = "1383-1386"}

@article{Kukihara:1985,
	key = "Kukihara 1985",
	author = "K. Kukihara",
	title = "An algorithm of {Euclidean} type for multiplication modulo {$P$}",
	journal = JIP,
	volume = 9,
	year = 1985,
	pages = "14-16"}

@article{Kukihara:1989,
	key = "Kukihara 1989",
	author = "K. Kukihara",
	title = "Euclidean type algorithm for multiplication modulo {$P$} {II}",
	journal = JIP,
	volume = 12,
	year = 1989,
	pages = "147-153"}

@inproceedings{Willoner&Chen:1981,
	key = "Willoner and Chen 1981",
	author = "R. Willoner and I-N. Chen",
	title = "An algorithm for modular exponentiation",
	booktitle = "Proc. 5th IEEE Symp. Comput. Arith.",
	publisher = IEEEPR,
	year = 1981,
	pages = "135-138"}

@article{Alia&Martinelli:1991,
	key = "Alia and Martinelli 1991",
	author = "G. Alia and E. Martinelli",
	title = "A {VLSI} modulo {$m$} multiplier",
	journal = IEEE-TC,
	volume = 40,
	year = 1991,
	pages = "873-878"}

@article{Takagi&Yajima:1992,
	key = "N. Takagi and Yajima 1992",
	author = "N. Takagi and S. Yajima",
	title = "Modular multiplication hardware algorithms with a redundant
representation and their application to {RSA} cryptosystems",
	journal = IEEE-TC,
	volume = 41,
	year = 1992,
	pages = "887-891"}

@article{Takagi:1992,
	key = "N. Takagi 1992",
	author = "N. Takagi",
	title = "A radix-$4$ modular multiplication hardware algorithm for
modular exponentiation",
	journal = IEEE-TC,
	volume = 41,
	year = 1992,
	pages = "949-956"}

@article{Skavantzos&Rao:1992,
	key = "Skavantzos and Rao 1992",
	author = "A. Skavantzos and P. B. Rao",
	title = "New multipliers modulo {$2^N - 1$}",
	journal = IEEE-TC,
	volume = 41,
	year = 1992,
	pages = "957-961"}

@article{Hasan&Wang&Bhargava:1992,
	key = "Hasan, Wang, and Bhargava 1992",
	author = "M. A. Hasan and M. Wang and V. K. Bhargava",
	title = "Modular construction of low complexity parallel
multipliers for a class of finite fields ${GF(2^m)}$",
	journal = IEEE-TC,
	volume = 41,
	year = "1992",
	pages = "962-971"}

@article{Hasan&Bhargava:1992a,
	key = "Hasan and Bhargava 1992a",
	author = "M. A. Hasan and V. K. Bhargava",
	title = "Bit-serial systolic divider and multiplier for
finite fields {$GF(2^m)$}",
	journal = IEEE-TC,
	volume = 41,
	year = "{\noopsort{1992a}}1992",
	pages = "972-980"}

@article{Orton&Peppard&Tavares:1992,
	key = "Orton, Peppard, and Tavares 1992",
	author = "G. A. Orton and L. E. Peppard and S. E. Tavares",
	title = "New fault tolerant techniques for residue number
systems",
	journal = IEEE-TC,
	volume = 41,
	year = 1992,
	pages = "1453-1464"}

@article{Yen&Laih:1993a,
	key = "Yen and Laih 1993a",
	author = "S.-M. Yen and C.-S. Laih",
	title = "Common-multiplicand multiplication and its applications
to public key cryptography",
	journal = ELETT,
	volume = 29,
	year = "{\noopsort{1993a}}1993",
	pages = "1583-1584"}

@article{Hasan&Bhargava:1992b,
	key = "Hasan and Bhargava 1992b",
	author = "M. A. Hasan and V. K. Bhargava",
	title = "Low complexity architecture for exponentiation in {$GF(2^m)$}",
	journal = ELETT,
	volume = 28,
	year = "{\noopsort{1992b}}1992",
	pages = "1984-1986"}

@article{Rao&Skavantzos:1992,
	key = "Rao and Skavantzos 1992",
	author = "P. B. Rao and A. Skavantzos",
	title = "Efficient computation of the squaring operation in modular rings", 
	journal = ELETT,
	volume = 28,
	year = 1992,
	pages = "1628-1630"}

@article{Zhang&Shirazi&Yun:1993,
	key = "Zhang, Shirazi, and Yun 1993",
	author = "C. N. Zhang and B. Shirazi and D. Y. Y. Yun",
	title = "An efficient algorithm and parallel implementations
for binary and residue number systems",
	journal = JSC,
	volume = 15,
	year = 1993,
	pages = "451-462"}

@incollection{Zuras:1993,
	key = "Zuras 1993",
	author = "D. Zuras",
	title = "On squaring and multiplying large integers",
	booktitle = "Proc. 11th IEEE Symp. Comp. Arith.",
	publisher = IEEEPR,
	editor = "Swartzlander, Jr., E. and M. J. Irwin and G. Jullien",
	year = 1993,
	pages = "260-271"}

@incollection{Takagi:1993,
	key = "N. Takagi 1993",
	author = "N. Takagi",
	title = "A modular multiplication algorithm with triangle additions",
	booktitle = "Proc. 11th IEEE Symp. Comp. Arith.",
	publisher = IEEEPR,
	editor = "Swartzlander, Jr., E. and M. J. Irwin and G. Jullien",
	year = 1993,
	pages = "272-276"}

@incollection{Kornerup:1993,
	key = "Kornerup 1993",
	author = "P. Kornerup",
	title = "High-radix modular multiplication for cryptosystems",
	booktitle = "Proc. 11th IEEE Symp. Comp. Arith.",
	publisher = IEEEPR,
	editor = "Swartzlander, Jr., E. and M. J. Irwin and G. Jullien",
	year = 1993,
	pages = "277-283"}

@incollection{Shand&Vuillemin:1993,
	key = "Shand and Vuillemin 1993",
	author = "M. Shand and J. Vuillemin",
	title = "Fast implementation of {RSA} cryptography",
	booktitle = "Proc. 11th IEEE Symp. Comp. Arith.",
	publisher = IEEEPR,
	editor = "Swartzlander, Jr., E. and M. J. Irwin and G. Jullien",
	year = 1993,
	pages = "252-259"}

@incollection{Sauerbrey:1993,
        key = "Sauerbrey 1993",
        author = "J. Sauerbrey",
        title = "A modular exponentiation unit based on systolic arrays",
        booktitle = AUSCRYPT92,
        editor = "J. Seberry and Y. Zheng",
        series = LNICS,
        volume = 718,
        year = 1993,
        publisher = SV,
        pages = "505-516"}

@book{Schonhage&Grotefeld&Vetter:1994,
	key = "{Sch\"onhage}, Grotefeld, and Vetter 1994",
	author = "A. {Sch\"onhage} and A. F. W. Grotefeld and E. Vetter",
	title = "Fast Algorithms:  A Multitape Turing Machine Implementation",
	publisher = "BI-Wissenschaftsverlag",
	address = "Mannheim",
	year = 1994}

@article{Avizienis:1961,
	key = "Avizienis 1961",
	author = "A. Avizienis",
	title = "Signed-digit number representations for fast parallel
		 arithmetic",
	journal = IRE-TEC,
	volume = 10,
	year = 1961,
	pages = "389-400"}

@article{Laws&Rushworth:1971,
	key = "Laws and Rushworth 1971",
	author = "Laws, Jr., B. A. and C. K. Rushworth",
	title = "A cellular-array multiplier for {$GF(2^m)$}",
	journal = IEEE-TC,
	volume = "C-20",
	year = 1971,
	pages = "1573-1578"}

@article{Hehner&Horspool:1979,
	key = "Hehner and Horspool 1979",
	author = "E. C. R. Hehner and R. N. S. Horspool",
	title = "A new representation of the rational numbers for
		 fast easy arithmetic",
	journal = SIAMJC,
	volume = 8,
	year = 1979,
	pages = "124-134"}

@article{Barsi:1991,
	key = "Barsi 1991",
	author = "F. Barsi",
	title = "Mod $m$ arithmetic in binary systems",
	journal = IPL,
	volume = 40,
	year = 1991,
	pages = "303-309"}

@misc{Volpi:1995,
	key = "Volpi 1995",
	author = "A. Volpi",
	title = "$p$-th roots of integers modulo $p^n$ and for $p$-adic
integers",
	note = "{\it ACM SIGSAM Bull.}, Special Issue (June, 1995), 9--15"}

@article{Walter:1995,
	key = "Walter 1995",
	author = "C. D. Walter",
	title = "Still faster modular multiplication",
	journal = ELETT,
	volume = 31,
	year = 1995,
	pages = "263-264"}

@incollection{Monagan:1993,
	key = "Monagan 1993",
	author = "M. Monagan",
	title = "In-place arithmetic for polynomials over {$\Zee_n$}",
	booktitle = DISCO92,
	editor = "J. Fitch",
	series = LNICS,
	volume = 721,
	publisher = SV,
	year = 1993,
	pages = "22-34"}

@article{Smith:1996,
	key = "D. Smith 1996",
	author = "D. M. Smith",
	title = "A multiple-precision division algorithm",
	journal = MC,
	volume = 65,
	year = 1996,
	pages = "157-163"}