本篇文章以密碼學為出發點，探討其中的加密方法與攻擊模式，接著介紹雜湊函數之原理與應用。加密方法可分為對稱式加密和非對稱式加密，攻擊模式可分為唯密文攻擊，選擇明文攻擊與已知明文攻擊。我們將由雜湊函數訊息摘要演算法（Message-Digest Algorithm, MD）與安全雜湊演算法（Secure Hash Algorithm, SHA）系列的歷史發展，帶出MD5訊息摘要演算法（MD5 Message-Digest Algorithm）與SHA-256（Secure Hash Algorithm 256）並探討MD5與其前身MD4演算法之差異，比較MD5相較於MD4的優勢，然後介紹如何修改MD5使其更加複雜。最後介紹雜湊函數於近來非常受矚目的虛擬貨幣之應用，主要包含比特幣以及非同質化代幣（NFT, Non-Fungible Token）。

In this paper, we start from discussion of encryption and attack methods in Cryptography and then introduce the theory and application of hash functions. The encryption methods can be classified into two main approaches, one is symmetric encryption and another is asymmetric encryption. The attacking method can be classified into Ciphertext-only attack, Chosen-plaintext attack, and Known-plaintext attack. We will begin with the history of hash function with Message-Digest Algorithm (MD) and Secure Hash Algorithm (SHA), and then introduce MD5 Message-Digest Algorithm and Secure Hash Algorithm 256). The differences between MD5 and its predecessor MD4 are discussed and we show the advantage of MD5 compared with MD4. Then, we introduce the reform of MD5 to make it more complicated. At last, we show the applications of hash function on the Blockchain, which includes the Bit coin and the Non-Fungible Token (NFT).