【正文】 getting more and more important. Meanwhile, Products that ensure work information show a great prospect due to the importance .Of transmitting data by work safely, and as an important means of information Security, cryptography must be is the core of the information security. Modern cryptograph is, Divided into the public key system and the private key system. The private key system, Is also called the single key system, in which the encryption process is the same as the. Decryption process. The public key system is also called the double key system, Where the encryption process is different with the decryption process. Since the Public key system can publish its public key and keep its private key secret, it has, Many new applications such as the digital signature and authentication, which is. ideally used in every field of the the various public key cryptosystem, RSA algorithm is the best choice in, Both theory and application, and it is open used in digital signature and identificationSystem. Modular exponentiation and modular multiplication are the basic algorithms. For implementing the public key algorithms such as RSA, etc. However the, Timeconsuming modulo exponentiation putation, which has always been the, Bottleneck of RSA restricts its wider application. The first chapter introduces the domestic and foreign progress of cryptograph。本論文的第一章介紹了國內(nèi)外密碼學(xué)和 RSA 的有關(guān)動(dòng)態(tài)以及本論文的意義，第二章介紹密碼學(xué)的有關(guān)知識(shí)，第三章對(duì) RSA 算法進(jìn)行分析、介紹，第四章是RSA 加密與解密的實(shí)現(xiàn)的代碼和測試，第五章對(duì)本課題的結(jié)論。RSA 是目前公認(rèn)的在理論和實(shí)際應(yīng)用中最為成熟和完善的一種公鑰密碼體制，不僅可以進(jìn)行加密，還可以用來進(jìn)行數(shù)字簽名和身份驗(yàn)證，是公鑰密碼體制的代表。密碼學(xué)是信息安全技術(shù)的核心，現(xiàn)代密碼體制分為公鑰體制和私鑰體制兩大類:私鑰體制又稱單鑰體制，其加密密鑰和解密密鑰相同。河 南 科 技 大 學(xué)畢 業(yè) 設(shè) 計(jì)（論 文） 題目:＿＿RSA 加密算法的分析與實(shí)現(xiàn)＿＿姓 名：＿ 姚 維＿ ＿考 號(hào)：＿ 120220100269 ＿院 系：＿ 信系工程系 ＿專 業(yè)： 計(jì)算機(jī)及應(yīng)用 指導(dǎo)教師：＿ ＿金 淵 智＿＿ 2022 年 04 月 24 日河南科技大學(xué)畢業(yè)論文設(shè)計(jì)摘 要隨著信息產(chǎn)業(yè)的迅速發(fā)展，人們對(duì)信息和信息技術(shù)的需要不斷增加，信息安全也顯得越來越重要?；趯?duì)網(wǎng)絡(luò)傳輸數(shù)據(jù)安全性的考慮，保障網(wǎng)絡(luò)信息安全的加密產(chǎn)品具有廣泛的應(yīng)用前景，密碼技術(shù)則是保障信息安全的一個(gè)重要手段。公鑰體制又稱為雙鑰體制，其加、解密密鑰不同，可以公開加密密鑰，而僅需保密解密密鑰，從而具有數(shù)字簽名、鑒別等新功能，被廣泛應(yīng)用于金融、商業(yè)等社會(huì)生活各領(lǐng)域。大數(shù)模冪乘運(yùn)算是實(shí)現(xiàn) RSA 等公鑰密碼的基本運(yùn)算，該算法存在的問題是在實(shí)現(xiàn)時(shí)耗時(shí)太多，這也是制約其廣泛應(yīng)用的瓶頸。最后是致謝和參考文獻(xiàn)。 The RSA related tendency as well as the meaning of the research. The second chapter Explains cryptograph. The third chapter describes and analyzes the RSA algorithm. The 河南科技大學(xué)畢業(yè)論文設(shè)計(jì)fourth chapter discusses the improvement of the RSA algorithm including the big, Number restore and operation, and the improvement algorithm of the” Square multiply algorithm. The fifth chapter reprints an improved algorithm and Comparisons.KEY WORDS: cryptography, RSA, public key cryptosystem, information security河南科技大學(xué)畢業(yè)論文設(shè)計(jì)目 錄摘 要 ...............................................................1ABSTRACT .............................................................2第一章 引 言 ........................................................6 研究背景 .......................................................6 信息加密技術(shù) ...................................................6 密碼技術(shù)研究現(xiàn)狀 ...............................................8 研究本課題的意義 ...............................................9第二章 密碼學(xué)概論 ...................................................11 密碼學(xué)的基本概念 ..............................................11 古典密碼體制 ..................................................14 對(duì)稱密碼體制 ..................................................14 DES (Data Encryption Standard) ............................16 AES(Advanced Encryption Standard) ........................18 公鑰密碼體制 ..................................................19 密碼分析技術(shù) ...................................................21第三章 RSA 公鑰密碼體制 ..............................................24 的數(shù)學(xué)基礎(chǔ)知識(shí) ..............................................24 因子的概念 ................................................24 素?cái)?shù)與合數(shù) ................................................25 公約數(shù)與最大公約數(shù) ........................................26．4 互質(zhì)數(shù) ...................................................27 RSA 算法 .......................................................28 RSA 體制描述 ...............................................28 RSA 工作原理 ..............................................29第四章 RAS 的加密與解密技術(shù)的實(shí)現(xiàn) ....................................32 RSA 加密與解密代碼 .............................................32 測試的環(huán)境與工具 ..............................................34河南科技大學(xué)畢業(yè)論文設(shè)計(jì) 測試的結(jié)果 ....................................................35第五章 結(jié)論 .........................................................36 結(jié)論 ..........................................................36致謝 ................................................................37參考文獻(xiàn) ............................................................38河南科技大學(xué)畢業(yè)論文設(shè)計(jì)第一章 引 言 研究背景自 20 世紀(jì) 90 年代以來，計(jì)算機(jī)網(wǎng)絡(luò)技術(shù)得到了空前飛速的發(fā)展和廣泛的應(yīng)用，但網(wǎng)絡(luò)在帶給我們方便快捷的同時(shí)，也存在著種種安全危機(jī)，隨著計(jì)算機(jī)應(yīng)用的日益廣泛和深入，信息交流和資源共享的范圍不斷擴(kuò)大，計(jì)算機(jī)應(yīng)用環(huán)境日趨復(fù)雜，計(jì)算機(jī)的數(shù)據(jù)安全問題也越來越重要。其內(nèi)容主要包括: (1)實(shí)體安全。 (2)數(shù)據(jù)傳輸網(wǎng)絡(luò)安全。 (3)軟件安全。 (4)信息安全。所以，如何實(shí)現(xiàn)計(jì)算機(jī)網(wǎng)絡(luò)中數(shù)據(jù)安全傳輸近年來一直是人們研究的課題之一。數(shù)據(jù)加密技術(shù)可以提高信息系統(tǒng)及數(shù)據(jù)的安全性和保密性，防止秘密數(shù)據(jù)被外部破譯所采用的主要技術(shù)手段之一。前者研究將發(fā)送的信息(明文)變換成沒有密鑰不能解或很難解的密文的方法。其發(fā)展經(jīng)歷了相當(dāng)長的時(shí)期。直到 1918 年由 論述了重合指數(shù)及其在