自古以來，大數的因數分解以及質數的特性就一直是令人感興趣的數學問題。研究因數分解不僅是一個有趣的數學問題，也具有極高的應用價值。所有的正整數都可以用唯一的質因數乘積來表示，而且可以很容易證明這樣的質因數分解存在。依據數學家的研究，因為有了機率式質數測試的技術，產生質數是相當容易的一件事情，甚至是數百位的大質數，也可在有效時間內產生。因此產生大質數相乘要比將一大數分解成數個大質數要來的簡單，以及有效率多了。
目前很多的密碼加密方法都是採用RSA演算法，其安全度是基於對大數作質因數分解的困難度。目前被認為對於129位數以下的大數，最有效率的大數分解方法是二次篩選分解法，而大於130位數以上的大數則以代數體篩選分解法的分解效率較好。經由多方考量，我們選用二次篩選分解法來分解大數。有鑑於近來網路技術發達，網路傳輸速度越來越迅速，所以本論文欲利用java applet來完成利用網路達成分散式的因數分解，並架構此applet在網頁中，藉由所有瀏覽此網頁的client端電腦，執行因數分解的動作，回傳篩選出有效之資料，以利因數分解之完成。由於廣域網路所連結的電腦不計其數，所以可以有大量的電腦輔助我們完成大數因數分解。

Studies the fractorization to not only is a mathematics of interesting problem, but also have the very high application value.
All positive integrals can indicate with only prime factor product, and can prove such prime factor to resolve the existence very easily.
According to the research of the mathematician, because there is probability type prime counting the technique of the test, produce a thing that quality number is very easy, even is a several hundred and big prime number, also can produce in validly time.
Therefore produce the big prime number multiplies each other and compares will a big number resolve several big prime numbers wants come of simple, and much more efficient.
A lot of passwords encryption method to adopt the algorithm of RSA at the present time, its security degree is owing to
count the difficulty that make prime factor's decomposition greatly.
Pass for at the present time for 129 several big numbers of the followingses, the most efficient factorization method is quadratic sieve factorization method, and be larger than 130 number can be better resolved factorization efficiency by using number field sieve.
Through consider in many ways, we choose to use quadratic sieve factorization to resolve the big number.
In light of the recently network technique flourishing, the network delivers the speed to come more more quickly, so this thesis wants to make use of the java applet to complete the exploitation network reaches the ractorization of the dispersion type, and configure this applet in web page, by all clients browse this web page carry out the action of the fractorization, return to spread the valid data be sieved, for the convenience of the fractorization it complete.
Although the numbers of the computers which link the world wide network is countless, so we can have a great deal of computer to help us to complete the big number fractorization.

[1.] A.K. Lenstra and M.S. Manasse. “Factoring with two large primes.” In Advances in Cryptology - Eurocrypt '90, pages 72-82, Springer-Verlag, Berlin, 1991.
[2.] C. Pomerance, J. W. Smith, and R. Tuler. “A pipeline architecture for factoring large integers with the quadratic sieve algorithm.” SIAM Journal on Computing, 17:387-403,1988
[3.] C. Pomerance, “The Quadratic Sieve Factoring Algorithm”, presented at Advances in Cryptology: Proceeding of EUROCRYPT 84,1985
[4.] DOUGLAS H. Wiedemann “Solving Sparse Linear Equations Over Finite Fields.” IEEE Transactions on Information Theory, vol. IT-32, no. 1, January 1986
[5.] D. Coppersmith, “Solving linear equations over GF(2): Block Lanczos algorithm”, Linear Algebra and its Applications 192(1993),pp. 33-60.
[6.] D. Coppersmith, “Solving homogeneous linear equation over GF(2) via block Wiedemann algorithm”, Math. Comp. 62(1994), pp333-350.
[7.] D. Wiedemann, “Solving sparse linear equations over finite fields”, IEEE Trans Inform. Yheory 32(1986), pp. 54-62
[8.] Eric Landquist “The Quadratic Sieve Factoring Algorithm”, MATH88: Cryptographic Algorithm,2001
[9.] E. R. Canfield, P. Erdös, C. Pomerance,”On a problem of Oppenheim concerning ‘factorisatio numerorum’,” J. Number Theory 17(1983), pp. 1-28.
[10.] H. Boender and H.J.J. te Riele “Factoring integers with large prime variations of the quadratic sieve” CWI, Department of Numerical Mathematics, NM-R9512, 1995
[11.] Hans Riesel. “Prime Numbers and Computer Methods for Factorization”. Birkäuser,1994
[12.] Hea Joung Kim, William H. Mangione-Smith, ”Factoring Large Numbers with Programmable Hardware”, ACM 2000
[13.] Henk Boender, Herman J. J. te Riele, “Factoring Integers with Large-Prime Variations of the Quadratic Sieve”, AMS Subject Classification 1996
[14.] Olof Åsbrink, Joel Brynielsson, ”Factoring Large Integers Using Parallel Quadratic Sieve” KTH, 2000
[15.] Peter L. Montgomery “Vectorization of the Elliptic Curve Method” ,CWI 1991
[16.] Peter L. Montgomery “An FFT Extension of the Elliptic Curve Method of Factorization”,CWI 1992
[17.] Paul Leyland, Arjen Lenstra, Bruce Dodson, Alec Muffett, and Sam Wagstaff “MPQS with Three Large Primes”, Springer-Verlag Berlin Heidelberg LNCS2369, P.446 ,2002
[18.] Richard P. Brent “Some Integer Factorization Algorithm using Elliptic Curves” Computer Sciences Laboratory Australian National University , 1985, Republished 7,Nov,1998
[19.] Richard P. Brent “Recent Progress and Prospects for Integer Factorisation Algorithm”, Springer-Verlag Berlin Heidelberg LNCS 1858, pp3-22,2000
[20.] R.D. Silverman. The multiple polynomial Quadratic Sieve. Math. Comp.,48:329-339,1987
[21.] Robert O. Silverman ”DISTRIBUTED COMPUTING AND FACTORING LARGE IHTEGERS” COMMUNICATIONS OFTHE ACM/November 1991/Vol.34, No.]]
[22.] S. Cavallar, B. Dodson, A.K. Lenstra, P. Leyland, W.M. Lioen, P.L. Montgomery, B. Murphy, H.J.J. te Riele, P. Zimmermann “Factorization of RSA-140 using the Number Field Sieve” CWI, MAS, MAS-R9925, 1999
[23.] Scott Patrick Contini “Factoring Integers with Self-Initializing Quadratic sieve”1997
[24.] S. Cavallar, B. Dodson, A.K. Lenstra, P. Leyland, W.M. Lioen, P.L. Montgomery, B. Murphy, H.J.J. te Riele, P. Zimmermann “Factorization of RSA-140 Using the Number Field Sieve” CWI, MAS, MAS- R9925 September 30, 1999
[25.] Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Walter Lioen, Peter L. Montgomery, Brian Murphy, Herman te Riele, Karen Aardal, Jeff Gilchrist, Gérard Guillerm, Paul Leyland, et al.”Factorization of a 512-bit RSA Modulus” Theory and Application of Cryptographic Techniques ,2000
[26.] 官大智，因數分解與RSA密碼系統，2002
[27.] 賴溪松、韓亮、張真誠，近代密碼學及其應用，松崗書局，2000。