RSA加密小结

作者: xxxxxxxxx_ios | 来源:发表于2018-03-30 14:23 被阅读44次

    在iOS中使用RSA加密解密,需要用到.der.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.derprivate_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.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.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!

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