Authentication of restricted memory devices presents significant problems since memory consumption is high in mutual authentication using cryptographic protocols in IoT environments. According to previous studies, the development of a multi-factor mutual authentication method that can be used in fog and cloud computing remains a challenge. The present work aims to improve a method of mutual authentication with multi-factor using an adjustable variable response time, challenge-response function, and nonce. With these factors, the same method can be regulated for both the Fog and Cloud Computing contexts. We compared the present method with the evaluations carried out in related works, achieving a satisfactory result regarding the cost of computing and communication. The code developed in Java showed a better average processing time, low energy consumption than other studies, and a linear complexity metric. Finally, using the Proverif tool and an informal analysis to provide the security assessment, it was demonstrated that it is impossible to derive the discovery of keys, keeping the proposed method safe.

由于在IoT环境中使用密码协议进行双向身份验证时，内存消耗很高，因此对受限内存设备的身份验证存在重大问题。根据以前的研究，可用于雾和云计算的多因素相互认证方法的开发仍然是一个挑战。本工作旨在改进一种使用可调变量响应时间，质询响应功能和随机数的多因素相互认证方法。有了这些因素，就可以针对Fog和Cloud Computing上下文调整相同的方法。我们将本方法与相关工作中进行的评估进行了比较，在计算和通信成本方面取得了令人满意的结果。用Java开发的代码显示出更好的平均处理时间，与其他研究相比能耗低，并且具有线性复杂度指标。最后，使用Proverif工具和非正式分析来提供安全性评估，结果表明，在确保所提出的方法安全的情况下，不可能导出密钥的发现。