本文選題：公鑰密碼 + 大整數(shù)��； 參考：《華中科技大學(xué)》2014年碩士論文

【摘要】：RSA公鑰密碼不僅可以用于加密，也是第一個(gè)可用于數(shù)字簽名和身份驗(yàn)證的密碼體制，其安全性和抗攻擊性在廣泛的應(yīng)用中不斷得到人們的肯定，是現(xiàn)代密碼學(xué)研究領(lǐng)域中一個(gè)重要的里程碑�；趯�(duì)密碼安全性的考慮，，RSA密碼對(duì)密鑰規(guī)模的要求已經(jīng)達(dá)到1024比特，具有更高要求的密碼體制要求密鑰長度為2048比特甚至以上。 RSA密碼技術(shù)討論集中于大素?cái)?shù)的生成、RSA密鑰對(duì)生成、RSA加密解密計(jì)算與對(duì)RSA作安全分析，其包括對(duì)模數(shù)的分解問題。這些都需要大數(shù)（1024比特以上）模冪等基本計(jì)算。而考慮到安全性RSA密碼還需要以Miller-Rabin檢測(cè)次數(shù)不限定的方法過濾出高概率的概率素?cái)?shù)。 為適應(yīng)RSA密碼實(shí)現(xiàn)與安全分析的需要，以RSA密碼相關(guān)計(jì)算技術(shù)為研究對(duì)象深入分析，設(shè)計(jì)并實(shí)現(xiàn)了RSA密碼基本運(yùn)算工具，其具有多種大整數(shù)的基本運(yùn)算、大素?cái)?shù)產(chǎn)生、RSA密鑰對(duì)生成、RSA加密解密以及模數(shù)n分解功能，運(yùn)算數(shù)據(jù)可達(dá)2048比特，滿足并超過了RSA密碼對(duì)現(xiàn)有應(yīng)用的基本要求，使生成的RSA密碼具有更高的安全性。除實(shí)現(xiàn)大數(shù)基本運(yùn)算外，工具還提供了模加、模減、模乘以及乘法逆元等大整數(shù)運(yùn)算功能，可用于大整數(shù)的基本計(jì)算。素?cái)?shù)生成工具采用隨機(jī)遞增搜索法對(duì)素?cái)?shù)進(jìn)行探測(cè)并可根據(jù)需要設(shè)定Miller-Rabin檢測(cè)次數(shù)，提高了素?cái)?shù)產(chǎn)生的質(zhì)量，對(duì)系統(tǒng)安全性有很大的影響。實(shí)現(xiàn)了基于中國剩余定理的解密算法，通過降低模指數(shù)提高RSA解密效率以及工具實(shí)用性。經(jīng)過測(cè)試，RSA密碼基本運(yùn)算工具基本實(shí)現(xiàn)了預(yù)期功能，對(duì)RSA的進(jìn)一步研究與工具的深度開發(fā)具有重要意義。
[Abstract]:RSA public key cryptography can be used not only for encryption, but also for digital signature and authentication. It is an important milestone in the field of modern cryptography. Based on the consideration of cryptographic security, the requirement of key size for RSA cryptography has reached 1024 bits. The cryptosystem with higher requirements requires the length of the key to be 2048 bits or more. The discussion of RSA cryptography technology focuses on the generation of large prime numbers and the encryption and decryption calculation of RSA encryption and decryption and the security analysis of RSA. It includes the decomposition of modulus. All of these require the basic calculation of the modular idempotent of large numbers (1024 bits or more). Considering the security of RSA cipher, we also need to filter the probabilistic prime number of high probability by Miller-Rabin detection method. In order to meet the needs of RSA cryptographic implementation and security analysis, a RSA cryptographic basic operation tool is designed and implemented with RSA cryptographic computing technology as the research object, which has a variety of basic operations of large integers. The large prime number produces RSA key pair to generate RSA encryption and decryption as well as the modulus n decomposition function. The operation data can reach 2048 bits, which satisfies and exceeds the basic requirements of the existing application of RSA cryptography, which makes the generated RSA cipher more secure. In addition to the basic operation of large numbers, the tool also provides large integer operations such as module addition, module subtraction, modular multiplication and multiplication inverse, which can be used for the basic calculation of large integers. The prime generating tool uses random incremental search method to detect prime number and can set Miller-Rabin detection times according to the need, which improves the quality of prime number generation and has a great influence on system security. The decryption algorithm based on the Chinese residue theorem is implemented. The efficiency of RSA decryption is improved by reducing the modulus index and the utility of the tool is improved. After testing, the basic cryptographic operation tool of RSA has basically realized the expected function, which is of great significance to the further study of RSA and the deep development of the tool.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN918.4

【相似文獻(xiàn)】

相關(guān)期刊論文 前10條

1 吳國兵;江效堯;;基于二進(jìn)制的概念格基本運(yùn)算研究[J];南京審計(jì)學(xué)院學(xué)報(bào);2007年04期

2 張正璽,焦占亞;關(guān)系代數(shù)中用基本運(yùn)算表示非基本運(yùn)算[J];陜西科技大學(xué)學(xué)報(bào);2003年01期

3 高博;;邏輯數(shù)學(xué)中的基本運(yùn)算——C、C++和Java串講之第二講[J];計(jì)算機(jī)教與學(xué).IT搜索;2002年12期

4 周文洪;陳興威;林雪華;;EXCEL在矩陣基本運(yùn)算中的應(yīng)用[J];民營科技;2007年11期

5 剛芹果,王佳星;FoxBASE在矩陣基本運(yùn)算中的應(yīng)用[J];現(xiàn)代計(jì)算機(jī);1997年01期

6 柴君;;大整數(shù)基本運(yùn)算的實(shí)現(xiàn)分析[J];科技傳播;2012年09期

7 ;新產(chǎn)品[J];中國計(jì)算機(jī)用戶;2008年21期

8 潘永柏;計(jì)算機(jī)中數(shù)的另一種表示法的嘗試[J];上海第二工業(yè)大學(xué)學(xué)報(bào);1985年02期

9 林菊英;;基于關(guān)系數(shù)據(jù)庫表的雙親結(jié)構(gòu)樹實(shí)現(xiàn)及基本運(yùn)算研究[J];福建電腦;2013年12期

10 華農(nóng);漫話電腦[J];農(nóng)村電工;1998年01期

相關(guān)重要報(bào)紙文章 前1條

1 ;據(jù)調(diào)查日本小學(xué)生基本運(yùn)算能力不足[N];新華每日電訊;2006年

相關(guān)碩士學(xué)位論文 前1條

1 黃亮;RSA密碼基本運(yùn)算工具的設(shè)計(jì)與實(shí)現(xiàn)[D];華中科技大學(xué);2014年

本文編號(hào)：2088364