01---密码学 HASH RSA

RSA数学原理

上世纪70年代产生的一种加密算法。其加密方式比较特殊，需要两个密钥：公开密钥简称公钥（publickey）和私有密钥简称私钥（privatekey）。公钥加密，私钥解密；私钥加密，公钥解密。这个加密算法就是伟大的RSA.

互质关系:
如果两个正整数，除了1以外，没有其他公因数，我们就称这两个数是互质关系（coprime）

欧拉函数

• 思考

计算这个值的方式叫做欧拉函数，使用：Φ(n)表示如: 计算8的欧拉函数，和8互质的 1、2、3、4、5、6、7、8 φ(8) = 4 计算7的欧拉函数，和7互质的 1、2、3、4、5、6、7 φ(7) = 6 计算56的欧拉函数 φ(56) = φ(8) * φ(7) = 4 * 6 = 24

一、当n是质数的时候，φ(n)=n-1。
二、如果n可以分解成两个互质的整数之积，如n=A*B则： φ(A*B)=φ(A)* φ(B)根据以上两点得到： 如果N是两个质数P1和 P2的乘积则 φ(N)=φ(P1)* φ(P2)=(P1-1)*(P2-1)

欧拉定理  费马小定理

image.png

欧拉定理:一:如果两个正整数m和n互质，那么m的φ(n)次方减去1，可以被n整除。举例子: 7 15   φ(15) = φ(3) *φ(5) = 2*4 =87**8%15 = 1

image.png 费马小定理举例子:7 5互质 7 **4%5 = 1! image.png

公式转换

image.png

第一个都知道第二个k 不影响第三个: 两边同时m 
模反元素举例子: m=4 n=15 φ(15) = 8 
假设: e = 3   得到 3*d % x = 1 (ed-1)才会被整除 所以求与=1同理: 3*d = k*x +1  红色框替换  m**(e*d) = m得到; 3*d = k*8+1 当k=4 d=11
所以:4 **(3*11)%15 = 4;!

迪菲赫尔曼密钥交换

image.png

如果 客户端和服务器规定好 m:3 n:17  
客户端有个数13 服务器15
第一步:服务器向客服端发送6 客户端想后台发送12然后得到最后要发送的 10.

`

这里有人问?为啥不是3  因为不满足一些关系

15*13 != k *16 +1;

image.png

终端加密

由于Mac系统内置OpenSSL(开源加密库),所以我们可以直接在终端上使用命令来玩RSA. OpenSSL中RSA算法常用指令主要有三个：

image.png

终端加密小数据 pem证书不能直接使用 在苹果中 

1.生成私钥
openssl genrsa -out private.pem 1024

2.生成公钥
openssl rsa -in private.pem -pubout -out public.pem
writing RSA key

cat XXX  查看 

vim message.txt  生成文本 

转成text文本
openssl rsa -in private.pem -text -out private.text
writing RSA key 
公钥加密:
openssl rsautl -encrypt -in message.txt -inkey public.pem -pubin -out enc.txt
私钥解密
openssl rsautl -decrypt -in enc.txt -inkey private.pem -out dec.txt

证书生成  csr cer 

csr请求文件 
openssl req -new -key private.pem -out rsacert.csr 

签名 https协议 用这个签名 放在服务器   —>公钥 
openssl x509 -req -days 3650 -in rsacert.csr -signkey private.pem -out rsacert.crt

生成p12文件   —>私钥
openssl pkcs12 -export -out p.p12 -inkey private.pem -in rsacert.crt

crt后面要变成der文件 苹果才支持使用

openssl x509 -outform der -in rsacert.crt -out rsacert.cer

base64

//  base64 可以将任意的二进制数据进行编码。 编码成为65个字符组成的文本文件。
//  0 ~ 9 a ~ z， A ~ Z + / =
// $base64 源文件 -o 目标文件    编码
// $base64 源文件 -o 目标文件 -D 解码
//  101001 010101 010100 010101
//  A 字节   =  =
//  010000 010000 000000 000000

@implementation ViewController
- (void)viewDidLoad {
    [super viewDidLoad];
    
    NSLog(@"%@",[self base64Encode:@"A"]);
    NSLog(@"解码：%@",[self base64Decode:@"QQ=="]);
    
}
-(NSString *)base64Encode:(NSString *)string{
    //
    NSData * data = [string dataUsingEncoding:NSUTF8StringEncoding];
    return [data base64EncodedStringWithOptions:0];
}
-(NSString *)base64Decode:(NSString *)str{
    NSData * data = [[NSData alloc] initWithBase64EncodedString:str options:0];
    return [[NSString alloc] initWithData:data encoding:NSUTF8StringEncoding];
}
@end

RSA代码演示

#import <Foundation/Foundation.h>
@interface RSACryptor : NSObject
    
+ (instancetype)sharedRSACryptor;
    
    /**
     *  生成密钥对
     *
     *  @param keySize 密钥尺寸，可选数值(512/1024/2048)
     */
- (void)generateKeyPair:(NSUInteger)keySize;
    
    /**
     *  加载公钥
     *
     *  @param publicKeyPath 公钥路径
     *
     @code
     # 生成证书
     $ openssl genrsa -out ca.key 1024
     # 创建证书请求
     $ openssl req -new -key ca.key -out rsacert.csr
     # 生成证书并签名
     $ openssl x509 -req -days 3650 -in rsacert.csr -signkey ca.key -out rsacert.crt
     # 转换格式
     $ openssl x509 -outform der -in rsacert.crt -out rsacert.der
     @endcode
     */
- (void)loadPublicKey:(NSString *)publicKeyPath;
    
    /**
     *  加载私钥
     *
     *  @param privateKeyPath p12文件路径
     *  @param password      p12文件密码
     *
     @code
     openssl pkcs12 -export -out p.p12 -inkey ca.key -in rsacert.crt
     @endcode
     */
- (void)loadPrivateKey:(NSString *)privateKeyPath password:(NSString *)password;
    
    /**
     *  加密数据
     *
     *  @param plainData 明文数据
     *
     *  @return 密文数据
     */
- (NSData *)encryptData:(NSData *)plainData;
    
    /**
     *  解密数据
     *
     *  @param cipherData 密文数据
     *
     *  @return 明文数据
     */
- (NSData *)decryptData:(NSData *)cipherData;
    
@end

#import "RSACryptor.h"
// 填充模式  kSecPaddingNone 每次解密结果是固定的
//          kSecPaddingPKCS1 是随机变化的。
#define kTypeOfWrapPadding        kSecPaddingNone
// 公钥/私钥标签
#define kPublicKeyTag            "com.logic.EncryptDemo.publickey"
#define kPrivateKeyTag            "com.logic.EncryptDemo.privatekey"
static const uint8_t publicKeyIdentifier[]        = kPublicKeyTag;
static const uint8_t privateKeyIdentifier[]        = kPrivateKeyTag;
@interface RSACryptor() {
    SecKeyRef publicKeyRef;                             // 公钥引用
    SecKeyRef privateKeyRef;                            // 私钥引用
}
    
    @property (nonatomic, retain) NSData *publicTag;        // 公钥标签
    @property (nonatomic, retain) NSData *privateTag;       // 私钥标签
    
    @end
@implementation RSACryptor
    
+ (instancetype)sharedRSACryptor {
    static id instance;
    
    static dispatch_once_t onceToken;
    dispatch_once(&onceToken, ^{
        instance = [[self alloc] init];
    });
    return instance;
}
    
- (instancetype)init {
    self = [super init];
    if (self) {
        // 查询密钥的标签
        _privateTag = [[NSData alloc] initWithBytes:privateKeyIdentifier length:sizeof(privateKeyIdentifier)];
        _publicTag = [[NSData alloc] initWithBytes:publicKeyIdentifier length:sizeof(publicKeyIdentifier)];
    }
    return self;
}
    
#pragma mark - 加密 & 解密数据
- (NSData *)encryptData:(NSData *)plainData {
    OSStatus sanityCheck = noErr;
    size_t cipherBufferSize = 0;
    size_t keyBufferSize = 0;
    
    NSAssert(plainData != nil, @"明文数据为空");
    NSAssert(publicKeyRef != nil, @"公钥为空");
    
    NSData *cipher = nil;
    uint8_t *cipherBuffer = NULL;
    
    // 计算缓冲区大小
    cipherBufferSize = SecKeyGetBlockSize(publicKeyRef);
    keyBufferSize = [plainData length];
    
    if (kTypeOfWrapPadding == kSecPaddingNone) {
        NSAssert(keyBufferSize <= cipherBufferSize, @"加密内容太大");
    } else {
        NSAssert(keyBufferSize <= (cipherBufferSize - 11), @"加密内容太大");
    }
    
    // 分配缓冲区
    cipherBuffer = malloc(cipherBufferSize * sizeof(uint8_t));
    memset((void *)cipherBuffer, 0x0, cipherBufferSize);
    
    // 使用公钥加密
    sanityCheck = SecKeyEncrypt(publicKeyRef,
                                kTypeOfWrapPadding,
                                (const uint8_t *)[plainData bytes],
                                keyBufferSize,
                                cipherBuffer,
                                &cipherBufferSize
                                );
    
    NSAssert(sanityCheck == noErr, @"加密错误，OSStatus == %d", sanityCheck);
    
    // 生成密文数据
    cipher = [NSData dataWithBytes:(const void *)cipherBuffer length:(NSUInteger)cipherBufferSize];
    
    if (cipherBuffer) free(cipherBuffer);
    
    return cipher;
}
    
- (NSData *)decryptData:(NSData *)cipherData {
    OSStatus sanityCheck = noErr;
    size_t cipherBufferSize = 0;
    size_t keyBufferSize = 0;
    
    NSData *key = nil;
    uint8_t *keyBuffer = NULL;
    
    SecKeyRef privateKey = NULL;
    
    privateKey = [self getPrivateKeyRef];
    NSAssert(privateKey != NULL, @"私钥不存在");
    
    // 计算缓冲区大小
    cipherBufferSize = SecKeyGetBlockSize(privateKey);
    keyBufferSize = [cipherData length];
    
    NSAssert(keyBufferSize <= cipherBufferSize, @"解密内容太大");
    
    // 分配缓冲区
    keyBuffer = malloc(keyBufferSize * sizeof(uint8_t));
    memset((void *)keyBuffer, 0x0, keyBufferSize);
    
    // 使用私钥解密
    sanityCheck = SecKeyDecrypt(privateKey,
                                kTypeOfWrapPadding,
                                (const uint8_t *)[cipherData bytes],
                                cipherBufferSize,
                                keyBuffer,
                                &keyBufferSize
                                );
    
    NSAssert1(sanityCheck == noErr, @"解密错误，OSStatus == %d", sanityCheck);
    
    // 生成明文数据
    key = [NSData dataWithBytes:(const void *)keyBuffer length:(NSUInteger)keyBufferSize];
    
    if (keyBuffer) free(keyBuffer);
    
    return key;
}
    
#pragma mark - 密钥处理
    /**
     *  生成密钥对
     */
- (void)generateKeyPair:(NSUInteger)keySize {
    OSStatus sanityCheck = noErr;
    publicKeyRef = NULL;
    privateKeyRef = NULL;
    
    NSAssert1((keySize == 512 || keySize == 1024 || keySize == 2048), @"密钥尺寸无效 %tu", keySize);
    
    // 删除当前密钥对
    [self deleteAsymmetricKeys];
    
    // 容器字典
    NSMutableDictionary *privateKeyAttr = [[NSMutableDictionary alloc] init];
    NSMutableDictionary *publicKeyAttr = [[NSMutableDictionary alloc] init];
    NSMutableDictionary *keyPairAttr = [[NSMutableDictionary alloc] init];
    
    // 设置密钥对的顶级字典
    [keyPairAttr setObject:(__bridge id)kSecAttrKeyTypeRSA forKey:(__bridge id)kSecAttrKeyType];
    [keyPairAttr setObject:[NSNumber numberWithUnsignedInteger:keySize] forKey:(__bridge id)kSecAttrKeySizeInBits];
    
    // 设置私钥字典
    [privateKeyAttr setObject:[NSNumber numberWithBool:YES] forKey:(__bridge id)kSecAttrIsPermanent];
    [privateKeyAttr setObject:_privateTag forKey:(__bridge id)kSecAttrApplicationTag];
    
    // 设置公钥字典
    [publicKeyAttr setObject:[NSNumber numberWithBool:YES] forKey:(__bridge id)kSecAttrIsPermanent];
    [publicKeyAttr setObject:_publicTag forKey:(__bridge id)kSecAttrApplicationTag];
    
    // 设置顶级字典属性
    [keyPairAttr setObject:privateKeyAttr forKey:(__bridge id)kSecPrivateKeyAttrs];
    [keyPairAttr setObject:publicKeyAttr forKey:(__bridge id)kSecPublicKeyAttrs];
    
    // SecKeyGeneratePair 返回密钥对引用
    sanityCheck = SecKeyGeneratePair((__bridge CFDictionaryRef)keyPairAttr, &publicKeyRef, &privateKeyRef);
    NSAssert((sanityCheck == noErr && publicKeyRef != NULL && privateKeyRef != NULL), @"生成密钥对失败");
}
    
    /**
     *  加载公钥
     */
- (void)loadPublicKey:(NSString *)publicKeyPath {
    
    NSAssert(publicKeyPath.length != 0, @"公钥路径为空");
    // 删除当前公钥
    if (publicKeyRef) CFRelease(publicKeyRef);
    
    // 从一个 DER 表示的证书创建一个证书对象
    NSData *certificateData = [NSData dataWithContentsOfFile:publicKeyPath];
    SecCertificateRef certificateRef = SecCertificateCreateWithData(kCFAllocatorDefault, (__bridge CFDataRef)certificateData);
    NSAssert(certificateRef != NULL, @"公钥文件错误");
    
    // 返回一个默认 X509 策略的公钥对象，使用之后需要调用 CFRelease 释放
    SecPolicyRef policyRef = SecPolicyCreateBasicX509();
    // 包含信任管理信息的结构体
    SecTrustRef trustRef;
    
    // 基于证书和策略创建一个信任管理对象
    OSStatus status = SecTrustCreateWithCertificates(certificateRef, policyRef, &trustRef);
    NSAssert(status == errSecSuccess, @"创建信任管理对象失败");
    
    // 信任结果
    SecTrustResultType trustResult;
    // 评估指定证书和策略的信任管理是否有效
    status = SecTrustEvaluate(trustRef, &trustResult);
    NSAssert(status == errSecSuccess, @"信任评估失败");
    
    // 评估之后返回公钥子证书
    publicKeyRef = SecTrustCopyPublicKey(trustRef);
    NSAssert(publicKeyRef != NULL, @"公钥创建失败");
    
    if (certificateRef) CFRelease(certificateRef);
    if (policyRef) CFRelease(policyRef);
    if (trustRef) CFRelease(trustRef);
}
    
    /**
     *  加载私钥
     */
- (void)loadPrivateKey:(NSString *)privateKeyPath password:(NSString *)password {
    
    NSAssert(privateKeyPath.length != 0, @"私钥路径为空");
    
    // 删除当前私钥
    if (privateKeyRef) CFRelease(privateKeyRef);
    
    NSData *PKCS12Data = [NSData dataWithContentsOfFile:privateKeyPath];
    CFDataRef inPKCS12Data = (__bridge CFDataRef)PKCS12Data;
    CFStringRef passwordRef = (__bridge CFStringRef)password;
    
    // 从 PKCS #12 证书中提取标示和证书
    SecIdentityRef myIdentity;
    SecTrustRef myTrust;
    const void *keys[] =   {kSecImportExportPassphrase};
    const void *values[] = {passwordRef};
    CFDictionaryRef optionsDictionary = CFDictionaryCreate(NULL, keys, values, 1, NULL, NULL);
    CFArrayRef items = CFArrayCreate(NULL, 0, 0, NULL);
    
    // 返回 PKCS #12 格式数据中的标示和证书
    OSStatus status = SecPKCS12Import(inPKCS12Data, optionsDictionary, &items);
    
    if (status == noErr) {
        CFDictionaryRef myIdentityAndTrust = CFArrayGetValueAtIndex(items, 0);
        myIdentity = (SecIdentityRef)CFDictionaryGetValue(myIdentityAndTrust, kSecImportItemIdentity);
        myTrust = (SecTrustRef)CFDictionaryGetValue(myIdentityAndTrust, kSecImportItemTrust);
    }
    
    if (optionsDictionary) CFRelease(optionsDictionary);
    
    NSAssert(status == noErr, @"提取身份和信任失败");
    
    SecTrustResultType trustResult;
    // 评估指定证书和策略的信任管理是否有效
    status = SecTrustEvaluate(myTrust, &trustResult);
    NSAssert(status == errSecSuccess, @"信任评估失败");
    
    // 提取私钥
    status = SecIdentityCopyPrivateKey(myIdentity, &privateKeyRef);
    NSAssert(status == errSecSuccess, @"私钥创建失败");
}
    
    /**
     *  删除非对称密钥
     */
- (void)deleteAsymmetricKeys {
    OSStatus sanityCheck = noErr;
    NSMutableDictionary *queryPublicKey = [[NSMutableDictionary alloc] init];
    NSMutableDictionary *queryPrivateKey = [[NSMutableDictionary alloc] init];
    
    // 设置公钥查询字典
    [queryPublicKey setObject:(__bridge id)kSecClassKey forKey:(__bridge id)kSecClass];
    [queryPublicKey setObject:_publicTag forKey:(__bridge id)kSecAttrApplicationTag];
    [queryPublicKey setObject:(__bridge id)kSecAttrKeyTypeRSA forKey:(__bridge id)kSecAttrKeyType];
    
    // 设置私钥查询字典
    [queryPrivateKey setObject:(__bridge id)kSecClassKey forKey:(__bridge id)kSecClass];
    [queryPrivateKey setObject:_privateTag forKey:(__bridge id)kSecAttrApplicationTag];
    [queryPrivateKey setObject:(__bridge id)kSecAttrKeyTypeRSA forKey:(__bridge id)kSecAttrKeyType];
    
    // 删除私钥
    sanityCheck = SecItemDelete((__bridge CFDictionaryRef)queryPrivateKey);
    NSAssert1((sanityCheck == noErr || sanityCheck == errSecItemNotFound), @"删除私钥错误，OSStatus == %d", sanityCheck);
    
    // 删除公钥
    sanityCheck = SecItemDelete((__bridge CFDictionaryRef)queryPublicKey);
    NSAssert1((sanityCheck == noErr || sanityCheck == errSecItemNotFound), @"删除公钥错误，OSStatus == %d", sanityCheck);
    
    if (publicKeyRef) CFRelease(publicKeyRef);
    if (privateKeyRef) CFRelease(privateKeyRef);
}
    
    /**
     *  获得私钥引用
     */
- (SecKeyRef)getPrivateKeyRef {
    OSStatus sanityCheck = noErr;
    SecKeyRef privateKeyReference = NULL;
    
    if (privateKeyRef == NULL) {
        NSMutableDictionary * queryPrivateKey = [[NSMutableDictionary alloc] init];
        
        // 设置私钥查询字典
        [queryPrivateKey setObject:(__bridge id)kSecClassKey forKey:(__bridge id)kSecClass];
        [queryPrivateKey setObject:_privateTag forKey:(__bridge id)kSecAttrApplicationTag];
        [queryPrivateKey setObject:(__bridge id)kSecAttrKeyTypeRSA forKey:(__bridge id)kSecAttrKeyType];
        [queryPrivateKey setObject:[NSNumber numberWithBool:YES] forKey:(__bridge id)kSecReturnRef];
        
        // 获得密钥
        sanityCheck = SecItemCopyMatching((__bridge CFDictionaryRef)queryPrivateKey, (CFTypeRef *)&privateKeyReference);
        
        if (sanityCheck != noErr) {
            privateKeyReference = NULL;
        }
    } else {
        privateKeyReference = privateKeyRef;
    }
    
    return privateKeyReference;
}
    
@end

RSA使用

#import "ViewController.h"
#import "RSACryptor.h"
@interface ViewController ()
@end
@implementation ViewController
- (void)viewDidLoad {
    [super viewDidLoad];
    
    //1.加载公钥
    [[RSACryptor sharedRSACryptor] loadPublicKey: [[NSBundle mainBundle] pathForResource:@"rsacert.der" ofType:nil]];
    //2.加载私钥
    [[RSACryptor sharedRSACryptor] loadPrivateKey:[[NSBundle mainBundle] pathForResource:@"p.p12" ofType:nil] password:@"123456"];
    
}
- (void)touchesBegan:(NSSet<UITouch *> *)touches withEvent:(UIEvent *)event
{
    //1.加密
    NSData * result = [[RSACryptor sharedRSACryptor] encryptData:[@"hello" dataUsingEncoding:NSUTF8StringEncoding]];
    NSLog(@"加密的结果是:%@",[result base64EncodedStringWithOptions:0]);
    
    //2.解密
    NSData * jiemi = [[RSACryptor sharedRSACryptor] decryptData:result];
    NSLog(@"解密的结果：%@",[[NSString alloc] initWithData:jiemi encoding:NSUTF8StringEncoding]);
}
@end