Reprinted: Original address https://blog.csdn.net/zhangmengleiblog/article/details/51362761
To use RSA encryption and decryption in iOS, you need to use files in .der
and .p12
suffix format, where the .der
format file stores the public key (Public key) for encryption, and .p12
the format file stores the private key (Private key) for decryption. First of all, you need to generate these files first, and then import the files into the project for use. Not much to say, let's do it!
1. Use openssl to generate the required key file
The generation environment is under the mac system, using openssl to generate, first open the terminal, and follow these steps in turn:
1. Generate a private key file with a modulo length of 1024bitprivate_key.pem
openssl genrsa -out private_key.pem 1024
2. Generate the certificate request filersaCertReq.csr
openssl req -new -key private_key.pem -out rsaCerReq.csr
Note: In this step, you will be prompted to enter information such as country, province, mail, etc., which can be filled in according to the actual situation, or don't need to fill in all, just hit Enter.
3. Generate a certificate rsaCert.crt
and set the validity period to 10 years
openssl x509 -req -days 3650 -in rsaCerReq.csr -signkey private_key.pem -out rsaCert.crt
4. Generate a public key file for iOSpublic_key.der
openssl x509 -outform der -in rsaCert.crt -out public_key.der
5. Generate a private key file for iOS useprivate_key.p12
openssl pkcs12 -export -out private_key.p12 -inkey private_key.pem -in rsaCert.crt
Note: In this step, you will be prompted to set a password for the private key file, just enter the password you want to set, then press Enter, then verify the password you just set, enter the password again, and press Enter, done!
When decrypting, the private_key.p12
file needs to be used with the password set here, so you need to keep this password in mind.
6. Generate a public key for use by Javarsa_public_key.pem
openssl rsa -in private_key.pem -out rsa_public_key.pem -pubout
7. Generate a private key for use in Javapkcs8_private_key.pem
openssl pkcs8 -topk8 -in private_key.pem -out pkcs8_private_key.pem -nocrypt
After all the execution is successful, the following files will be generated, and the public_key.der
sum private_key.p12
is the file that iOS needs to use, as shown below:
generated file
2. Import the file into the project for use
1. Create a new project and import Security.framework
the framework, as shown below:
Create a new project and add a framework
2. Import the key file
Import .der
and .p12
format the key file, as shown below:
import key file
3. Create new classes for encryption and decryption RSAEncryptor
, and implement related methods
Create a new RSAEncryptor
class, as shown below:
Create a new class for encryption and decryption
Start the code below, you can copy it directly: the
RSAEncryptor.h
code is as follows:
#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
code show as below:
#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. Test encryption and decryption
First test the encryption and decryption using and the key file, .der
and test in , the code is as follows:.p12
ViewController.m
#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
After running, the output information is as follows:
output result
It can be seen that the encryption and decryption can be successfully completed.
Next, we will test the use of the key string for encryption and decryption, so where does the key string come from? You can come here: http://web.chacuo.net/netrsakeypair , this is a website that generates RSA keys online, generate After the public key and the secret key, copy them out for testing. Then ViewController.m
use RSAEntryptor.h
the corresponding encryption method in the header file to encrypt, ViewController.m
the code is as follows:
#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
After running, the output information is as follows:
output result
As you can see, it is also successfully encrypted and decrypted.
At this point, the RSA encryption demonstration is complete!