RSA加密小结
2018-03-30 本文已影响44人
xxxxxxxxx_ios
在iOS中使用RSA加密解密，需要用到.der和.p12后缀格式的文件，其中.der格式的文件存放的是公钥（Public key）用于加密，.p12格式的文件存放的是私钥（Private key）用于解密. 首先需要先生成这些文件，然后再将文件导入工程使用！
一、使用openssl生成所需秘钥文件
生成环境是在mac系统下，使用openssl进行生成，首先打开终端，按下面这些步骤依次来做：
1. 生成模长为1024bit的私钥文件private_key.pem
openssl genrsa -out private_key.pem 1024
2. 生成证书请求文件rsaCertReq.csr
openssl req -new -key private_key.pem -out rsaCerReq.csr
注意：这一步会提示输入国家、省份、mail等信息，可以根据实际情况填写，或者全部不用填写，直接全部敲回车.
3. 生成证书rsaCert.crt，并设置有效时间为1年
openssl x509 -req -days 3650 -in rsaCerReq.csr -signkey private_key.pem -out rsaCert.crt
4. 生成供iOS使用的公钥文件public_key.der
openssl x509 -outform der -in rsaCert.crt -out public_key.der
5. 生成供iOS使用的私钥文件private_key.p12
openssl pkcs12 -export -out private_key.p12 -inkey private_key.pem -in rsaCert.crt
注意：这一步会提示给私钥文件设置密码，直接输入想要设置密码即可，然后敲回车，然后再验证刚才设置的密码，再次输入密码，然后敲回车，完毕！
在解密时，private_key.p12文件需要和这里设置的密码配合使用，因此需要牢记此密码.
6. 生成供Java使用的公钥rsa_public_key.pem
openssl rsa -in private_key.pem -out rsa_public_key.pem -pubout
7. 生成供Java使用的私钥pkcs8_private_key.pem
openssl pkcs8 -topk8 -in private_key.pem -out pkcs8_private_key.pem -nocrypt
全部执行成功后，会生成如下文件，其中public_key.der和private_key.p12就是iOS需要用到的文件，如下图：
图1
二、将文件导入工程使用
1.新建工程, 并导入Security.framework框架, 如下图:
图2
2.导入秘钥文件
导入.der和.p12格式的秘钥文件, 如下图:
图2
3.新建用于加密、解密的类RSAEncryptor, 并实现相关方法
新建RSAEncryptor类, 如下图:
图3
下面开始上代码,
RSAEncryptor.h代码如下:
#import <Foundation/Foundation.h>
@interface RSAEncryptor : NSObject
/**
* 加密方法
*
* @param str 需要加密的字符串
* @param path '.der'格式的公钥文件路径
*/
+ (NSString *)encryptString:(NSString *)str publicKeyWithContentsOfFile:(NSString *)path;
/**
* 解密方法
*
* @param str 需要解密的字符串
* @param path '.p12'格式的私钥文件路径
* @param password 私钥文件密码
*/
+ (NSString *)decryptString:(NSString *)str privateKeyWithContentsOfFile:(NSString *)path password:(NSString *)password;
/**
* 加密方法
*
* @param str 需要加密的字符串
* @param pubKey 公钥字符串
*/
+ (NSString *)encryptString:(NSString *)str publicKey:(NSString *)pubKey;
/**
* 解密方法
*
* @param str 需要解密的字符串
* @param privKey 私钥字符串
*/
+ (NSString *)decryptString:(NSString *)str privateKey:(NSString *)privKey;
@end
RSAEncryptor.m代码如下:
#import "RSAEncryptor.h"
#import <Security/Security.h>
@implementation RSAEncryptor
static NSString *base64_encode_data(NSData *data){
data = [data base64EncodedDataWithOptions:0];
NSString *ret = [[NSString alloc] initWithData:data encoding:NSUTF8StringEncoding];
return ret;
}
static NSData *base64_decode(NSString *str){
NSData *data = [[NSData alloc] initWithBase64EncodedString:str options:NSDataBase64DecodingIgnoreUnknownCharacters];
return data;
}
#pragma mark - 使用'.der'公钥文件加密
//加密
+ (NSString *)encryptString:(NSString *)str publicKeyWithContentsOfFile:(NSString *)path{
if (!str || !path) return nil;
return [self encryptString:str publicKeyRef:[self getPublicKeyRefWithContentsOfFile:path]];
}
//获取公钥
+ (SecKeyRef)getPublicKeyRefWithContentsOfFile:(NSString *)filePath{
NSData *certData = [NSData dataWithContentsOfFile:filePath];
if (!certData) {
return nil;
}
SecCertificateRef cert = SecCertificateCreateWithData(NULL, (CFDataRef)certData);
SecKeyRef key = NULL;
SecTrustRef trust = NULL;
SecPolicyRef policy = NULL;
if (cert != NULL) {
policy = SecPolicyCreateBasicX509();
if (policy) {
if (SecTrustCreateWithCertificates((CFTypeRef)cert, policy, &trust) == noErr) {
SecTrustResultType result;
if (SecTrustEvaluate(trust, &result) == noErr) {
key = SecTrustCopyPublicKey(trust);
}
}
}
}
if (policy) CFRelease(policy);
if (trust) CFRelease(trust);
if (cert) CFRelease(cert);
return key;
}
+ (NSString *)encryptString:(NSString *)str publicKeyRef:(SecKeyRef)publicKeyRef{
if(![str dataUsingEncoding:NSUTF8StringEncoding]){
return nil;
}
if(!publicKeyRef){
return nil;
}
NSData *data = [self encryptData:[str dataUsingEncoding:NSUTF8StringEncoding] withKeyRef:publicKeyRef];
NSString *ret = base64_encode_data(data);
return ret;
}
#pragma mark - 使用'.12'私钥文件解密
//解密
+ (NSString *)decryptString:(NSString *)str privateKeyWithContentsOfFile:(NSString *)path password:(NSString *)password{
if (!str || !path) return nil;
if (!password) password = @"";
return [self decryptString:str privateKeyRef:[self getPrivateKeyRefWithContentsOfFile:path password:password]];
}
//获取私钥
+ (SecKeyRef)getPrivateKeyRefWithContentsOfFile:(NSString *)filePath password:(NSString*)password{
NSData *p12Data = [NSData dataWithContentsOfFile:filePath];
if (!p12Data) {
return nil;
}
SecKeyRef privateKeyRef = NULL;
NSMutableDictionary * options = [[NSMutableDictionary alloc] init];
[options setObject: password forKey:(__bridge id)kSecImportExportPassphrase];
CFArrayRef items = CFArrayCreate(NULL, 0, 0, NULL);
OSStatus securityError = SecPKCS12Import((__bridge CFDataRef) p12Data, (__bridge CFDictionaryRef)options, &items);
if (securityError == noErr && CFArrayGetCount(items) > 0) {
CFDictionaryRef identityDict = CFArrayGetValueAtIndex(items, 0);
SecIdentityRef identityApp = (SecIdentityRef)CFDictionaryGetValue(identityDict, kSecImportItemIdentity);
securityError = SecIdentityCopyPrivateKey(identityApp, &privateKeyRef);
if (securityError != noErr) {
privateKeyRef = NULL;
}
}
CFRelease(items);
return privateKeyRef;
}
+ (NSString *)decryptString:(NSString *)str privateKeyRef:(SecKeyRef)privKeyRef{
NSData *data = [[NSData alloc] initWithBase64EncodedString:str options:NSDataBase64DecodingIgnoreUnknownCharacters];
if (!privKeyRef) {
return nil;
}
data = [self decryptData:data withKeyRef:privKeyRef];
NSString *ret = [[NSString alloc] initWithData:data encoding:NSUTF8StringEncoding];
return ret;
}
#pragma mark - 使用公钥字符串加密
/* START: Encryption with RSA public key */
//使用公钥字符串加密
+ (NSString *)encryptString:(NSString *)str publicKey:(NSString *)pubKey{
NSData *data = [self encryptData:[str dataUsingEncoding:NSUTF8StringEncoding] publicKey:pubKey];
NSString *ret = base64_encode_data(data);
return ret;
}
+ (NSData *)encryptData:(NSData *)data publicKey:(NSString *)pubKey{
if(!data || !pubKey){
return nil;
}
SecKeyRef keyRef = [self addPublicKey:pubKey];
if(!keyRef){
return nil;
}
return [self encryptData:data withKeyRef:keyRef];
}
+ (SecKeyRef)addPublicKey:(NSString *)key{
NSRange spos = [key rangeOfString:@"-----BEGIN PUBLIC KEY-----"];
NSRange epos = [key rangeOfString:@"-----END PUBLIC KEY-----"];
if(spos.location != NSNotFound && epos.location != NSNotFound){
NSUInteger s = spos.location + spos.length;
NSUInteger e = epos.location;
NSRange range = NSMakeRange(s, e-s);
key = [key substringWithRange:range];
}
key = [key stringByReplacingOccurrencesOfString:@"\r" withString:@""];
key = [key stringByReplacingOccurrencesOfString:@"\n" withString:@""];
key = [key stringByReplacingOccurrencesOfString:@"\t" withString:@""];
key = [key stringByReplacingOccurrencesOfString:@" " withString:@""];
// This will be base64 encoded, decode it.
NSData *data = base64_decode(key);
data = [self stripPublicKeyHeader:data];
if(!data){
return nil;
}
//a tag to read/write keychain storage
NSString *tag = @"RSAUtil_PubKey";
NSData *d_tag = [NSData dataWithBytes:[tag UTF8String] length:[tag length]];
// Delete any old lingering key with the same tag
NSMutableDictionary *publicKey = [[NSMutableDictionary alloc] init];
[publicKey setObject:(__bridge id) kSecClassKey forKey:(__bridge id)kSecClass];
[publicKey setObject:(__bridge id) kSecAttrKeyTypeRSA forKey:(__bridge id)kSecAttrKeyType];
[publicKey setObject:d_tag forKey:(__bridge id)kSecAttrApplicationTag];
SecItemDelete((__bridge CFDictionaryRef)publicKey);
// Add persistent version of the key to system keychain
[publicKey setObject:data forKey:(__bridge id)kSecValueData];
[publicKey setObject:(__bridge id) kSecAttrKeyClassPublic forKey:(__bridge id)
kSecAttrKeyClass];
[publicKey setObject:[NSNumber numberWithBool:YES] forKey:(__bridge id)
kSecReturnPersistentRef];
CFTypeRef persistKey = nil;
OSStatus status = SecItemAdd((__bridge CFDictionaryRef)publicKey, &persistKey);
if (persistKey != nil){
CFRelease(persistKey);
}
if ((status != noErr) && (status != errSecDuplicateItem)) {
return nil;
}
[publicKey removeObjectForKey:(__bridge id)kSecValueData];
[publicKey removeObjectForKey:(__bridge id)kSecReturnPersistentRef];
[publicKey setObject:[NSNumber numberWithBool:YES] forKey:(__bridge id)kSecReturnRef];
[publicKey setObject:(__bridge id) kSecAttrKeyTypeRSA forKey:(__bridge id)kSecAttrKeyType];
// Now fetch the SecKeyRef version of the key
SecKeyRef keyRef = nil;
status = SecItemCopyMatching((__bridge CFDictionaryRef)publicKey, (CFTypeRef *)&keyRef);
if(status != noErr){
return nil;
}
return keyRef;
}
+ (NSData *)stripPublicKeyHeader:(NSData *)d_key{
// Skip ASN.1 public key header
if (d_key == nil) return(nil);
unsigned long len = [d_key length];
if (!len) return(nil);
unsigned char *c_key = (unsigned char *)[d_key bytes];
unsigned int idx = 0;
if (c_key[idx++] != 0x30) return(nil);
if (c_key[idx] > 0x80) idx += c_key[idx] - 0x80 + 1;
else idx++;
// PKCS #1 rsaEncryption szOID_RSA_RSA
static unsigned char seqiod[] =
{ 0x30, 0x0d, 0x06, 0x09, 0x2a, 0x86, 0x48, 0x86, 0xf7, 0x0d, 0x01, 0x01,
0x01, 0x05, 0x00 };
if (memcmp(&c_key[idx], seqiod, 15)) return(nil);
idx += 15;
if (c_key[idx++] != 0x03) return(nil);
if (c_key[idx] > 0x80) idx += c_key[idx] - 0x80 + 1;
else idx++;
if (c_key[idx++] != '\0') return(nil);
// Now make a new NSData from this buffer
return ([NSData dataWithBytes:&c_key[idx] length:len - idx]);
}
+ (NSData *)encryptData:(NSData *)data withKeyRef:(SecKeyRef) keyRef{
const uint8_t *srcbuf = (const uint8_t *)[data bytes];
size_t srclen = (size_t)data.length;
size_t block_size = SecKeyGetBlockSize(keyRef) * sizeof(uint8_t);
void *outbuf = malloc(block_size);
size_t src_block_size = block_size - 11;
NSMutableData *ret = [[NSMutableData alloc] init];
for(int idx=0; idx<srclen; idx+=src_block_size){
//NSLog(@"%d/%d block_size: %d", idx, (int)srclen, (int)block_size);
size_t data_len = srclen - idx;
if(data_len > src_block_size){
data_len = src_block_size;
}
size_t outlen = block_size;
OSStatus status = noErr;
status = SecKeyEncrypt(keyRef,
kSecPaddingPKCS1,
srcbuf + idx,
data_len,
outbuf,
&outlen
);
if (status != 0) {
NSLog(@"SecKeyEncrypt fail. Error Code: %d", status);
ret = nil;
break;
}else{
[ret appendBytes:outbuf length:outlen];
}
}
free(outbuf);
CFRelease(keyRef);
return ret;
}
/* END: Encryption with RSA public key */
#pragma mark - 使用私钥字符串解密
/* START: Decryption with RSA private key */
//使用私钥字符串解密
+ (NSString *)decryptString:(NSString *)str privateKey:(NSString *)privKey{
if (!str) return nil;
NSData *data = [[NSData alloc] initWithBase64EncodedString:str options:NSDataBase64DecodingIgnoreUnknownCharacters];
data = [self decryptData:data privateKey:privKey];
NSString *ret = [[NSString alloc] initWithData:data encoding:NSUTF8StringEncoding];
return ret;
}
+ (NSData *)decryptData:(NSData *)data privateKey:(NSString *)privKey{
if(!data || !privKey){
return nil;
}
SecKeyRef keyRef = [self addPrivateKey:privKey];
if(!keyRef){
return nil;
}
return [self decryptData:data withKeyRef:keyRef];
}
+ (SecKeyRef)addPrivateKey:(NSString *)key{
NSRange spos = [key rangeOfString:@"-----BEGIN RSA PRIVATE KEY-----"];
NSRange epos = [key rangeOfString:@"-----END RSA PRIVATE KEY-----"];
if(spos.location != NSNotFound && epos.location != NSNotFound){
NSUInteger s = spos.location + spos.length;
NSUInteger e = epos.location;
NSRange range = NSMakeRange(s, e-s);
key = [key substringWithRange:range];
}
key = [key stringByReplacingOccurrencesOfString:@"\r" withString:@""];
key = [key stringByReplacingOccurrencesOfString:@"\n" withString:@""];
key = [key stringByReplacingOccurrencesOfString:@"\t" withString:@""];
key = [key stringByReplacingOccurrencesOfString:@" " withString:@""];
// This will be base64 encoded, decode it.
NSData *data = base64_decode(key);
data = [self stripPrivateKeyHeader:data];
if(!data){
return nil;
}
//a tag to read/write keychain storage
NSString *tag = @"RSAUtil_PrivKey";
NSData *d_tag = [NSData dataWithBytes:[tag UTF8String] length:[tag length]];
// Delete any old lingering key with the same tag
NSMutableDictionary *privateKey = [[NSMutableDictionary alloc] init];
[privateKey setObject:(__bridge id) kSecClassKey forKey:(__bridge id)kSecClass];
[privateKey setObject:(__bridge id) kSecAttrKeyTypeRSA forKey:(__bridge id)kSecAttrKeyType];
[privateKey setObject:d_tag forKey:(__bridge id)kSecAttrApplicationTag];
SecItemDelete((__bridge CFDictionaryRef)privateKey);
// Add persistent version of the key to system keychain
[privateKey setObject:data forKey:(__bridge id)kSecValueData];
[privateKey setObject:(__bridge id) kSecAttrKeyClassPrivate forKey:(__bridge id)
kSecAttrKeyClass];
[privateKey setObject:[NSNumber numberWithBool:YES] forKey:(__bridge id)
kSecReturnPersistentRef];
CFTypeRef persistKey = nil;
OSStatus status = SecItemAdd((__bridge CFDictionaryRef)privateKey, &persistKey);
if (persistKey != nil){
CFRelease(persistKey);
}
if ((status != noErr) && (status != errSecDuplicateItem)) {
return nil;
}
[privateKey removeObjectForKey:(__bridge id)kSecValueData];
[privateKey removeObjectForKey:(__bridge id)kSecReturnPersistentRef];
[privateKey setObject:[NSNumber numberWithBool:YES] forKey:(__bridge id)kSecReturnRef];
[privateKey setObject:(__bridge id) kSecAttrKeyTypeRSA forKey:(__bridge id)kSecAttrKeyType];
// Now fetch the SecKeyRef version of the key
SecKeyRef keyRef = nil;
status = SecItemCopyMatching((__bridge CFDictionaryRef)privateKey, (CFTypeRef *)&keyRef);
if(status != noErr){
return nil;
}
return keyRef;
}
+ (NSData *)stripPrivateKeyHeader:(NSData *)d_key{
// Skip ASN.1 private key header
if (d_key == nil) return(nil);
unsigned long len = [d_key length];
if (!len) return(nil);
unsigned char *c_key = (unsigned char *)[d_key bytes];
unsigned int idx = 22; //magic byte at offset 22
if (0x04 != c_key[idx++]) return nil;
//calculate length of the key
unsigned int c_len = c_key[idx++];
int det = c_len & 0x80;
if (!det) {
c_len = c_len & 0x7f;
} else {
int byteCount = c_len & 0x7f;
if (byteCount + idx > len) {
//rsa length field longer than buffer
return nil;
}
unsigned int accum = 0;
unsigned char *ptr = &c_key[idx];
idx += byteCount;
while (byteCount) {
accum = (accum << 8) + *ptr;
ptr++;
byteCount--;
}
c_len = accum;
}
// Now make a new NSData from this buffer
return [d_key subdataWithRange:NSMakeRange(idx, c_len)];
}
+ (NSData *)decryptData:(NSData *)data withKeyRef:(SecKeyRef) keyRef{
const uint8_t *srcbuf = (const uint8_t *)[data bytes];
size_t srclen = (size_t)data.length;
size_t block_size = SecKeyGetBlockSize(keyRef) * sizeof(uint8_t);
UInt8 *outbuf = malloc(block_size);
size_t src_block_size = block_size;
NSMutableData *ret = [[NSMutableData alloc] init];
for(int idx=0; idx<srclen; idx+=src_block_size){
//NSLog(@"%d/%d block_size: %d", idx, (int)srclen, (int)block_size);
size_t data_len = srclen - idx;
if(data_len > src_block_size){
data_len = src_block_size;
}
size_t outlen = block_size;
OSStatus status = noErr;
status = SecKeyDecrypt(keyRef,
kSecPaddingNone,
srcbuf + idx,
data_len,
outbuf,
&outlen
);
if (status != 0) {
NSLog(@"SecKeyEncrypt fail. Error Code: %d", status);
ret = nil;
break;
}else{
//the actual decrypted data is in the middle, locate it!
int idxFirstZero = -1;
int idxNextZero = (int)outlen;
for ( int i = 0; i < outlen; i++ ) {
if ( outbuf[i] == 0 ) {
if ( idxFirstZero < 0 ) {
idxFirstZero = i;
} else {
idxNextZero = i;
break;
}
}
}
[ret appendBytes:&outbuf[idxFirstZero+1] length:idxNextZero-idxFirstZero-1];
}
}
free(outbuf);
CFRelease(keyRef);
return ret;
}
/* END: Decryption with RSA private key */
@end
4. 测试加密、解密
首先先测试使用.der和.p12秘钥文件进行加密、解密, 在ViewController.m中进行测试, 代码如下:
#import "ViewController.h"
#import "RSAEncryptor.h"
@interface ViewController ()
@end
@implementation ViewController
- (void)viewDidLoad {
[super viewDidLoad];
//原始数据
NSString *originalString = @"这是一段将要使用'.der'文件加密的字符串!";
//使用.der和.p12中的公钥私钥加密解密
NSString *public_key_path = [[NSBundle mainBundle] pathForResource:@"public_key.der" ofType:nil];
NSString *private_key_path = [[NSBundle mainBundle] pathForResource:@"private_key.p12" ofType:nil];
NSString *encryptStr = [RSAEncryptor encryptString:originalString publicKeyWithContentsOfFile:public_key_path];
NSLog(@"加密前:%@", originalString);
NSLog(@"加密后:%@", encryptStr);
NSLog(@"解密后:%@", [RSAEncryptor decryptString:encryptStr privateKeyWithContentsOfFile:private_key_path password:@"123456"]);
}
- (void)didReceiveMemoryWarning {
[super didReceiveMemoryWarning];
// Dispose of any resources that can be recreated.
}
@end
运行后, 输出信息如下:
图4
可以看到已经可以成功加密、解密了.
下面接着测试使用秘钥字符串进行加密、解密, 那么秘钥字符串从哪里来? 可以来这里:http://web.chacuo.net/netrsakeypair, 这是一个在线生成RSA秘钥的网站, 生成公钥和秘钥后, 复制出来用于测试. 然后在
ViewController.m中使用
RSAEntryptor.h头文件中对应的加密方法进行加密,
ViewController.m中代码如下:
#import "ViewController.h"
#import "RSAEncryptor.h"
@interface ViewController ()
@end
@implementation ViewController
- (void)viewDidLoad {
[super viewDidLoad];
//原始数据
NSString *originalString = @"这是一段将要使用'秘钥字符串'进行加密的字符串!";
//使用字符串格式的公钥私钥加密解密
NSString *encryptStr = [RSAEncryptor encryptString:originalString publicKey:@"MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQDTbZ6cNH9PgdF60aQKveLz3FTalyzHQwbp601y77SzmGHX3F5NoVUZbdK7UMdoCLK4FBziTewYD9DWvAErXZo9BFuI96bAop8wfl1VkZyyHTcznxNJFGSQd/B70/ExMgMBpEwkAAdyUqIjIdVGh1FQK/4acwS39YXwbS+IlHsPSQIDAQAB"];
NSLog(@"加密前:%@", originalString);
NSLog(@"加密后:%@", encryptStr);
NSLog(@"解密后:%@", [RSAEncryptor decryptString:encryptStr privateKey:@"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"]);
}
- (void)didReceiveMemoryWarning {
[super didReceiveMemoryWarning];
// Dispose of any resources that can be recreated.
}
@end
运行后, 输出信息如下:
图5
至此, RSA加密演示完毕!
