java里modulus的简单介绍
本篇文章给大家谈谈java里modulus，以及对应的知识点，希望对各位有所帮助，不要忘了收藏本站喔。
本文目录一览：
- 1、RSA PKCS#1在java中怎么实现？
- 2、java中如何得到公钥的key size
- 3、在java中使用KeyFactory将给定字符串转换为RSAPublicKey对象时报错公钥非法
- 4、java 中 mod 是什么意思
- 5、我想问一下 java 中没有有Complex 这个变量，是需要自己定义吗？可是我看有些代码是直接用的。代码如下
RSA PKCS#1在java中怎么实现？
楼主看看下面的代码是不是你所需要的，这是我原来用的时候收集的
import javax.crypto.Cipher;
import java.security.*;
import java.security.spec.RSAPublicKeySpec;
import java.security.spec.RSAPrivateKeySpec;
import java.security.spec.InvalidKeySpecException;
import java.security.interfaces.RSAPrivateKey;
import java.security.interfaces.RSAPublicKey;
import java.io.*;
import java.math.BigInteger;
/**
* RSA 工具类。提供加密，解密，生成密钥对等方法。
* 需要到下载bcprov-jdk14-123.jar。
* RSA加密原理概述
* RSA的安全性依赖于大数的分解，公钥和私钥都是两个大素数（大于100的十进制位）的函数。
* 据猜测，从一个密钥和密文推断出明文的难度等同于分解两个大素数的积
* ===================================================================
* （该算法的安全性未得到理论的证明）
* ===================================================================
* 密钥的产生：
* 1.选择两个大素数 p,q ,计算 n=p*q;
* 2.随机选择加密密钥 e ,要求 e 和 (p-1)*(q-1)互质
* 3.利用 Euclid 算法计算解密密钥 d , 使其满足 e*d = 1(mod(p-1)*(q-1)) (其中 n,d 也要互质)
* 4:至此得出公钥为 (n,e) 私钥为 (n,d)
* ===================================================================
* 加解密方法：
* 1.首先将要加密的信息 m(二进制表示) 分成等长的数据块 m1,m2,...,mi 块长 s(尽可能大) ,其中 2^sn
* 2:对应的密文是： ci = mi^e(mod n)
* 3:解密时作如下计算： mi = ci^d(mod n)
* ===================================================================
* RSA速度
* 由于进行的都是大数计算，使得RSA最快的情况也比DES慢上100倍，无论是软件还是硬件实现。
* 速度一直是RSA的缺陷。一般来说只用于少量数据加密。
* 文件名：RSAUtil.javabr
* @author 赵峰br
* 版本:1.0.1br
* 描述：本算法摘自网络，是对RSA算法的实现br
* 创建时间:2009-7-10 下午09:58:16br
* 文件描述：首先生成两个大素数，然后根据Euclid算法生成解密密钥br
*/
public class RSAUtil {
//密钥对
private KeyPair keyPair = null;
/**
* 初始化密钥对
*/
public RSAUtil(){
try {
this.keyPair = this.generateKeyPair();
} catch (Exception e) {
e.printStackTrace();
}
}
/**
* 生成密钥对
* @return KeyPair
* @throws Exception
*/
private KeyPair generateKeyPair() throws Exception {
try {
KeyPairGenerator keyPairGen = KeyPairGenerator.getInstance("RSA",new org.bouncycastle.jce.provider.BouncyCastleProvider());
//这个值关系到块加密的大小，可以更改，但是不要太大，否则效率会低
final int KEY_SIZE = 1024;
keyPairGen.initialize(KEY_SIZE, new SecureRandom());
KeyPair keyPair = keyPairGen.genKeyPair();
return keyPair;
} catch (Exception e) {
throw new Exception(e.getMessage());
}
}
/**
* 生成公钥
* @param modulus
* @param publicExponent
* @return RSAPublicKey
* @throws Exception
*/
private RSAPublicKey generateRSAPublicKey(byte[] modulus, byte[] publicExponent) throws Exception {
KeyFactory keyFac = null;
try {
keyFac = KeyFactory.getInstance("RSA", new org.bouncycastle.jce.provider.BouncyCastleProvider());
} catch (NoSuchAlgorithmException ex) {
throw new Exception(ex.getMessage());
}
RSAPublicKeySpec pubKeySpec = new RSAPublicKeySpec(new BigInteger(modulus), new BigInteger(publicExponent));
try {
return (RSAPublicKey) keyFac.generatePublic(pubKeySpec);
} catch (InvalidKeySpecException ex) {
throw new Exception(ex.getMessage());
}
}
/**
* 生成私钥
* @param modulus
* @param privateExponent
* @return RSAPrivateKey
* @throws Exception
*/
private RSAPrivateKey generateRSAPrivateKey(byte[] modulus, byte[] privateExponent) throws Exception {
KeyFactory keyFac = null;
try {
keyFac = KeyFactory.getInstance("RSA", new org.bouncycastle.jce.provider.BouncyCastleProvider());
} catch (NoSuchAlgorithmException ex) {
throw new Exception(ex.getMessage());
}
RSAPrivateKeySpec priKeySpec = new RSAPrivateKeySpec(new BigInteger(modulus), new BigInteger(privateExponent));
try {
return (RSAPrivateKey) keyFac.generatePrivate(priKeySpec);
} catch (InvalidKeySpecException ex) {
throw new Exception(ex.getMessage());
}
}
/**
* 加密
* @param key 加密的密钥
* @param data 待加密的明文数据
* @return 加密后的数据
* @throws Exception
*/
public byte[] encrypt(Key key, byte[] data) throws Exception {
try {
Cipher cipher = Cipher.getInstance("RSA", new org.bouncycastle.jce.provider.BouncyCastleProvider());
cipher.init(Cipher.ENCRYPT_MODE, key);
// 获得加密块大小，如:加密前数据为128个byte，而key_size=1024 加密块大小为127 byte,加密后为128个byte;
// 因此共有2个加密块，第一个127 byte第二个为1个byte
int blockSize = cipher.getBlockSize();
// System.out.println("blockSize:"+blockSize);
int outputSize = cipher.getOutputSize(data.length);// 获得加密块加密后块大小
// System.out.println("加密块大小："+outputSize);
int leavedSize = data.length % blockSize;
// System.out.println("leavedSize:"+leavedSize);
int blocksSize = leavedSize != 0 ? data.length / blockSize + 1 : data.length / blockSize;
byte[] raw = new byte[outputSize * blocksSize];
int i = 0;
while (data.length - i * blockSize 0) {
if (data.length - i * blockSize blockSize)
cipher.doFinal(data, i * blockSize, blockSize, raw, i * outputSize);
else
cipher.doFinal(data, i * blockSize, data.length - i * blockSize, raw, i * outputSize);
// 这里面doUpdate方法不可用，查看源代码后发现每次doUpdate后并没有什么实际动作除了把byte[]放到ByteArrayOutputStream中
// 而最后doFinal的时候才将所有的byte[]进行加密，可是到了此时加密块大小很可能已经超出了OutputSize所以只好用dofinal方法。
i++;
}
return raw;
} catch (Exception e) {
throw new Exception(e.getMessage());
}
}
/**
* 解密
* @param key 解密的密钥
* @param raw 已经加密的数据
* @return 解密后的明文
* @throws Exception
*/
@SuppressWarnings("static-access")
public byte[] decrypt(Key key, byte[] raw) throws Exception {
try {
Cipher cipher = Cipher.getInstance("RSA", new org.bouncycastle.jce.provider.BouncyCastleProvider());
cipher.init(cipher.DECRYPT_MODE, key);
int blockSize = cipher.getBlockSize();
ByteArrayOutputStream bout = new ByteArrayOutputStream(64);
int j = 0;
while (raw.length - j * blockSize 0) {
bout.write(cipher.doFinal(raw, j * blockSize, blockSize));
j++;
}
return bout.toByteArray();
} catch (Exception e) {
throw new Exception(e.getMessage());
}
}
/**
* 返回公钥
* @return
* @throws Exception
*/
public RSAPublicKey getRSAPublicKey() throws Exception{
//获取公钥
RSAPublicKey pubKey = (RSAPublicKey) keyPair.getPublic();
//获取公钥系数(字节数组形式)
byte[] pubModBytes = pubKey.getModulus().toByteArray();
//返回公钥公用指数(字节数组形式)
byte[] pubPubExpBytes = pubKey.getPublicExponent().toByteArray();
//生成公钥
RSAPublicKey recoveryPubKey = this.generateRSAPublicKey(pubModBytes,pubPubExpBytes);
return recoveryPubKey;
}
/**
* 获取私钥
* @return
* @throws Exception
*/
public RSAPrivateKey getRSAPrivateKey() throws Exception{
// 获取私钥
RSAPrivateKey priKey = (RSAPrivateKey) keyPair.getPrivate();
// 返回私钥系数(字节数组形式)
byte[] priModBytes = priKey.getModulus().toByteArray();
// 返回私钥专用指数(字节数组形式)
byte[] priPriExpBytes = priKey.getPrivateExponent().toByteArray();
// 生成私钥
RSAPrivateKey recoveryPriKey = this.generateRSAPrivateKey(priModBytes,priPriExpBytes);
return recoveryPriKey;
}
/**
* 测试
* @param args
* @throws Exception
*/
public static void main(String[] args) throws Exception {
RSAUtil rsa = new RSAUtil();
String str = "天龙八部、神雕侠侣、射雕英雄传白马啸西风";
RSAPublicKey pubKey = rsa.getRSAPublicKey();
RSAPrivateKey priKey = rsa.getRSAPrivateKey();
// System.out.println("加密后==" + new String(rsa.encrypt(pubKey,str.getBytes())));
String mw = new String(rsa.encrypt(pubKey, str.getBytes()));
System.out.println("加密后："+mw);
// System.out.println("解密后：");
System.out.println("解密后==" + new String(rsa.decrypt(priKey,rsa.encrypt(pubKey,str.getBytes()))));
}
}
java中如何得到公钥的key size
接你代码后面
String algorithm = publickey.getAlgorithm(); // 获取算法
KeyFactory keyFact = KeyFactory.getInstance(algorithm);
BigInteger prime = null;
if ("RSA".equals(algorithm)) { // 如果是RSA加密
RSAPublicKeySpec keySpec = (RSAPublicKeySpec)keyFact.getKeySpec(publickey, RSAPublicKeySpec.class);
prime = keySpec.getModulus();
} else if ("DSA".equals(algorithm)) { // 如果是DSA加密
DSAPublicKeySpec keySpec = (DSAPublicKeySpec)keyFact.getKeySpec(publickey, DSAPublicKeySpec.class);
prime = keySpec.getP();
}
int len = prime.toString(2).length(); // 转换为二进制，获取公钥长度
在java中使用KeyFactory将给定字符串转换为RSAPublicKey对象时报错公钥非法
//将byte数组变成RSAPublicKey
public RSAPublicKey bytes2PK(byte[] buf) {
buf=Base64.decode(buf);
byte size=buf[0];
byte size2=buf[1];
byte[] b1 = new byte[size];
System.arraycopy(buf,2,b1,0,b1.length);
byte[] b2 = new byte[size2];
System.arraycopy(buf,b1.length+2,b2,0,b2.length);
BigInteger B1 = new BigInteger(b1);
BigInteger B2 = new BigInteger(b2);
RSAPublicKeySpec spec = new RSAPublicKeySpec(B1, B2);//存储的就是这两个大整形数
KeyFactory keyFactory;
PublicKey pk = null;
try {
keyFactory = KeyFactory.getInstance("RSA");
pk = keyFactory.generatePublic(spec);
} catch (Exception e) {
e.printStackTrace();
}
return (RSAPublicKey)pk;
}
公钥所包含的数据，实际上就是modulus、publicExponent这两个。都可以用byte数组的方式表示。我这边为了网络传输方便，将两个byte数组拼接在了一起。实际上分开存储更容易理解。
java 中 mod 是什么意思
java中mod放入意思是取模，或者说是取余，就是得到除法算式的余数。
例如：
int i , a = 10 , b = 3; //定义变量
i = a mod b; //相当于 i = a % b ;计算结果是 i 的值为1
我想问一下 java 中没有有Complex 这个变量，是需要自己定义吗？可是我看有些代码是直接用的。代码如下
从你的问题描述看你是问是否有一个复数类型complex,我查了一下没有，都是自己定义的。下面的代码你可以参考：
/******************************************************************************
* Compilation: javac Complex.java
* Execution: java Complex
*
* Data type for complex numbers.
*
* The data type is "immutable" so once you create and initialize
* a Complex object, you cannot change it. The "final" keyword
* when declaring re and im enforces this rule, making it a
* compile-time error to change the .re or .im instance variables after
* they've been initialized.
*
* % java Complex
* a = 5.0 + 6.0i
* b = -3.0 + 4.0i
* Re(a) = 5.0
* Im(a) = 6.0
* b + a = 2.0 + 10.0i
* a - b = 8.0 + 2.0i
* a * b = -39.0 + 2.0i
* b * a = -39.0 + 2.0i
* a / b = 0.36 - 1.52i
* (a / b) * b = 5.0 + 6.0i
* conj(a) = 5.0 - 6.0i
* |a| = 7.810249675906654
* tan(a) = -6.685231390246571E-6 + 1.0000103108981198i
*
******************************************************************************/
import java.util.Objects;
public class Complex {
private final double re; // the real part
private final double im; // the imaginary part
// create a new object with the given real and imaginary parts
public Complex(double real, double imag) {
re = real;
im = imag;
}
// return a string representation of the invoking Complex object
public String toString() {
if (im == 0) return re + "";
if (re == 0) return im + "i";
if (im 0) return re + " - " + (-im) + "i";
return re + " + " + im + "i";
}
// return abs/modulus/magnitude
public double abs() {
return Math.hypot(re, im);
}
// return angle/phase/argument, normalized to be between -pi and pi
public double phase() {
return Math.atan2(im, re);
}
// return a new Complex object whose value is (this + b)
public Complex plus(Complex b) {
Complex a = this; // invoking object
double real = a.re + b.re;
double imag = a.im + b.im;
return new Complex(real, imag);
}
// return a new Complex object whose value is (this - b)
public Complex minus(Complex b) {
Complex a = this;
double real = a.re - b.re;
double imag = a.im - b.im;
return new Complex(real, imag);
}
// return a new Complex object whose value is (this * b)
public Complex times(Complex b) {
Complex a = this;
double real = a.re * b.re - a.im * b.im;
double imag = a.re * b.im + a.im * b.re;
return new Complex(real, imag);
}
// return a new object whose value is (this * alpha)
public Complex scale(double alpha) {
return new Complex(alpha * re, alpha * im);
}
// return a new Complex object whose value is the conjugate of this
public Complex conjugate() {
return new Complex(re, -im);
}
// return a new Complex object whose value is the reciprocal of this
public Complex reciprocal() {
double scale = re*re + im*im;
return new Complex(re / scale, -im / scale);
}
// return the real or imaginary part
public double re() { return re; }
public double im() { return im; }
// return a / b
public Complex divides(Complex b) {
Complex a = this;
return a.times(b.reciprocal());
}
// return a new Complex object whose value is the complex exponential of this
public Complex exp() {
return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im));
}
// return a new Complex object whose value is the complex sine of this
public Complex sin() {
return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im));
}
// return a new Complex object whose value is the complex cosine of this
public Complex cos() {
return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));
}
// return a new Complex object whose value is the complex tangent of this
public Complex tan() {
return sin().divides(cos());
}
// a static version of plus
public static Complex plus(Complex a, Complex b) {
double real = a.re + b.re;
double imag = a.im + b.im;
Complex sum = new Complex(real, imag);
return sum;
}
// See Section 3.3.
public boolean equals(Object x) {
if (x == null) return false;
if (this.getClass() != x.getClass()) return false;
Complex that = (Complex) x;
return (this.re == that.re) (this.im == that.im);
}
// See Section 3.3.
public int hashCode() {
return Objects.hash(re, im);
}
// sample client for testing
public static void main(String[] args) {
Complex a = new Complex(5.0, 6.0);
Complex b = new Complex(-3.0, 4.0);
StdOut.println("a = " + a);
StdOut.println("b = " + b);
StdOut.println("Re(a) = " + a.re());
StdOut.println("Im(a) = " + a.im());
StdOut.println("b + a = " + b.plus(a));
StdOut.println("a - b = " + a.minus(b));
StdOut.println("a * b = " + a.times(b));
StdOut.println("b * a = " + b.times(a));
StdOut.println("a / b = " + a.divides(b));
StdOut.println("(a / b) * b = " + a.divides(b).times(b));
StdOut.println("conj(a) = " + a.conjugate());
StdOut.println("|a| = " + a.abs());
StdOut.println("tan(a) = " + a.tan());
}
}
关于java里modulus和的介绍到此就结束了，不知道你从中找到你需要的信息了吗 ？如果你还想了解更多这方面的信息，记得收藏关注本站。
发布于：2022-11-28，除非注明，否则均为原创文章，转载请注明出处。