一、下载openssl库源码，下载地址：https://ftp.openssl.org/source/

我下载的版本：

 二、编译源码

1、解压源码：

tar zxvf openssl-1.1.1u.tar.gz

 2、进入到解压后的文件夹中：

cd openssl-1.1.1u/

3、执行配置，生成makefile文件：

./config shared --prefix=/usr/local/openssl

4、编译：

make

5、安装

sudo make install

至此，编译完成！

三、测试rsa加密解密：

1、找到编译后的头文件和库文件，起目录为：/usr/local/openssl

将头文件和库文件拷贝到程序目录中：

2、将头文件和库文件添加项目中：

 3、测试：

#ifndef MAINWINDOW_H
#define MAINWINDOW_H

#include <QMainWindow>
#include <openssl/rsa.h>
#include <openssl/pem.h>
#include <openssl/bn.h>
#include <openssl/bio.h>
#include <openssl/evp.h>
#include <openssl/ssl.h>
#include <openssl/err.h>

QT_BEGIN_NAMESPACE
namespace Ui { class MainWindow; }
QT_END_NAMESPACE

class MainWindow : public QMainWindow
{
    Q_OBJECT

public:
    MainWindow(QWidget *parent = nullptr);
    ~MainWindow();
    //加密函数
    QString rsa_pri_encrypt_base64(const QString &strClearData);
    //解密函数
    QString rsa_pub_decrypt_base64(const QString &strDecryptData);
private:
    Ui::MainWindow *ui;
};
#endif // MAINWINDOW_H

#include "mainwindow.h"
#include "ui_mainwindow.h"
#include <QDebug>

MainWindow::MainWindow(QWidget *parent)
    : QMainWindow(parent)
    , ui(new Ui::MainWindow)
{
    ui->setupUi(this);

    QString encrypt_str =  rsa_pri_encrypt_base64("123abc");

    QString decrypt_str = rsa_pub_decrypt_base64(encrypt_str);
    qDebug() << "解析后：" << decrypt_str << endl;
}

MainWindow::~MainWindow()
{
    delete ui;
}

//私钥加密
QString MainWindow::rsa_pri_encrypt_base64 (const QString& strClearData)
{
    //私钥  长度为512  （使用自己生成的公秘钥）
    char private_key[] = "-----BEGIN PRIVATE KEY-----\n"
            "MIIBVAIBADANBgkqhkiG9w0BAQEFAASCAT4wggE6AgEAAkEAypZS0ybGDs7WWDIs\n"
            "bN9qNnojaHpQn6wiQf23U3Tm0pe1vCR803+gY3We7hBYfT7+uXK3pykQ8bIKnWdb\n"
            "XmoddQIDAQABAkAFCE7uZ9wrqf+xGS35VmNxDv+qLL+r976yHPdc316MhKTi9zfS\n"
            "9qAnilqB7LE6YedPpMMrKCK7AobBlTrzqF/RAiEA/KdNO+w7WDwYjC98ocOZqHLb\n"
            "49AP85nQL1Hu0eUf1HsCIQDNRUG+W9/IIK3kJ76eVwfSkq+LhM85yEY3vVIVmXmK\n"
            "zwIgT6KoLHgUaIZgsmcRYKeXmknB13ewX3ce8JthrFUNCFsCIHySNx+q6det3VnE\n"
            "tO2qq1ijJF1rL8dFPze8cQAir5wJAiEAmMP+WBohdEzXQMFYFkaVCIyfB8Zs6Muv\n"
            "cUsvIxOqW2o=\n"
            "-----END PRIVATE KEY-----";

    //将字符串键加载到bio对象
    BIO* pKeyBio = BIO_new_mem_buf(private_key, strlen(private_key));
    if (pKeyBio == NULL){
        return "";
    }
    RSA* pRsa = RSA_new();
    pRsa = PEM_read_bio_RSAPrivateKey(pKeyBio, &pRsa, NULL, NULL);
    if ( pRsa == NULL ){
        BIO_free_all(pKeyBio);
        return "";
    }
    int nLen = RSA_size(pRsa);
    char* pEncryptBuf = new char[nLen];
    memset(pEncryptBuf, 0, nLen);
    QByteArray clearDataArry = strClearData.toUtf8();
    int nClearDataLen = clearDataArry.length();
    uchar* pClearData = (uchar*)clearDataArry.data();
    int nSize = RSA_private_encrypt(nClearDataLen,
                                    pClearData,
                                    (uchar*)pEncryptBuf,
                                    pRsa,
                                    RSA_PKCS1_PADDING);

    QString strEncryptData = "";
    if ( nSize >= 0 ){
        QByteArray arry(pEncryptBuf, nSize);
        strEncryptData = arry.toBase64();
    }
    // 释放内存
    delete []pEncryptBuf;
    BIO_free_all(pKeyBio);
    RSA_free(pRsa);
    return strEncryptData;
}

//公钥解密
QString MainWindow::rsa_pub_decrypt_base64(const QString& strDecryptData)
{
    //公钥解密
    char public_key[] = "-----BEGIN PUBLIC KEY-----\n"\
            "MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBAMqWUtMmxg7O1lgyLGzfajZ6I2h6UJ+s\n"\
            "IkH9t1N05tKXtbwkfNN/oGN1nu4QWH0+/rlyt6cpEPGyCp1nW15qHXUCAwEAAQ==\n"\
            "-----END PUBLIC KEY-----";


    //将字符串键加载到bio对象
    BIO* pKeyBio = BIO_new_mem_buf(public_key, strlen(public_key));
    if (pKeyBio == NULL){
        return "";
    }

    RSA* pRsa = RSA_new();

    pRsa = PEM_read_bio_RSA_PUBKEY(pKeyBio, &pRsa, NULL, NULL);


    if ( pRsa == NULL ){
        BIO_free_all(pKeyBio);
        return "";
    }
    int nLen = RSA_size(pRsa);
    char* pClearBuf = new char[nLen];
    memset(pClearBuf, 0, nLen);
    //解密
    QByteArray decryptDataArry = strDecryptData.toUtf8();
    decryptDataArry = QByteArray::fromBase64(decryptDataArry);
    int nDecryptDataLen = decryptDataArry.length();
    uchar* pDecryptData = (uchar*)decryptDataArry.data();
    int nSize = RSA_public_decrypt(nDecryptDataLen,
                                   pDecryptData,
                                   (uchar*)pClearBuf,
                                   pRsa,
                                   RSA_PKCS1_PADDING);
    QString strClearData = "";
    if ( nSize >= 0 ){
        strClearData = QByteArray(pClearBuf, nSize);
    }

    // 释放内存
    delete []pClearBuf;
    BIO_free_all(pKeyBio);
    RSA_free(pRsa);
    return strClearData;
}