SageMath: Deeper Insights into Cybersecurity

In the previous article in this SageMath series (published in the January 2025 issue of OSFY), we concluded our discussion of classical encryption techniques and moved on to the exploration of modern cryptography by looking at symmetric-key cryptography. In this ninth article in the series, we will continue the focus on symmetric-key cryptography.

- Dr Deepu Benson

In the last article, we wrote a SageMath program to implement a simple symmetric-key cryptographic algorithm called DES using a Python package called ‘PyCryptodome’. As promised, we will discuss the implementation of DES briefly in this article.

Most cryptography textbooks covering DES introduce a simplified version called the Simplified Data Encryption Standard (S-DES) to explain its working. S-DES follows the same fundamental principles as DES but operates on a smaller scale. It is a block cipher that encrypts 8-bit plaintext blocks using a 10-bit key, which is processed to generate two 8-bit subkeys for encryption and decryption. For a detailed analysis of S-DES, I recommend the classic textbook ‘Cryptography and Network Security: Principles and Practice’ by William Stallings. Let’s first explore the concept of block ciphers before examining how DES functions as one.

Block ciphers

A block cipher is an encryption method that processes data in fixed-size blocks, transforming plaintext into ciphertext using a secret key. A block cipher encrypts a block of N bits at a time (for example, DES uses 64-bit blocks). Each block is encrypted independently but may be linked to other blocks depending on the mode in which the block cipher operates.

In addition to DES, other examples of block ciphers include AES (Advanced Encryption Standard), which operates on a 128-bit block of data with key sizes of 128, 192, or 256 bits; Blowfish, which operates on a 64-bit block of data with a variable-length key ranging from 32 to 448 bits; and Twofish, which operates on a 128-bit block of data with key sizes up to 256 bits.