RSA是一個是非對稱加密系統將內文加密後傳送經由解密後得知內文，當要破譯RSA可以使用其中一種演算法Quadratic sieve來將兩個質數拆解出來，當金鑰很大時使用Quadratic sieve需要解大矩陣。Standard Lanczos演算法可以解稀疏對稱大矩陣的空向量，但這個演算法使用於實數上， 而要解的大矩陣在 mod(2)的環境下運算所以經由推倒與假設，將Standard Lanczos經由推導與假設改變演算法結構並運算於GF(2)也就是Block Lanczos。

RSA is an asymmetric cryptographic system, the system is easy to encrypt and decrypt but difficult to find the key. Quadratic sieve algorithm is a way to factor two multiply prime integers(RSA). When the primes are too large, we have to solve null vectors of an enormous sparse matrix. The Standard Lanczos algorithm can solve sparse symmetric matrix over R, Using framework of Standard Lanczos extend Block Lanczos. Block Lanczos can solve sparse symmetric matrix over GF(2).

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