Question

Consider the block cipher in Figure 8.5. For a given “key” Alice and Bob would need to keep eight tables, each 8 bits by 8 bits. For Alice (or Bob) to store all eight tables, how many bits of storage are necessary? How does this number compare with the number of bits required for a full-table 64- bit block cipher?

Short answer

The eight tables require 512 bits, while a full 64-bit block cipher requires an impractical \(2^{64} \times 64\) bits, making the tables significantly more efficient in terms of storage.

Step-by-step solution

Understand Table Requirements

Each table is 8 bits by 8 bits. Since each entry in these tables is also 8 bits, each table contains \(8 \times 8 = 64\) bits.

Calculate Total Bits for All Tables

There are eight such tables. Therefore, the total storage required for all tables is \(8 \times 64 = 512\) bits.

Calculate Storage for Full-Table 64-bit Block Cipher

A full-table 64-bit block cipher requires a table with \(2^{64}\) entries, where each entry is 64 bits. Hence, the storage required is \(2^{64} \times 64\) bits.

Compare the Storage Requirements

The storage required for the eight tables is 512 bits, while for a full-table 64-bit block cipher, it's astronomically larger, specifically \(2^{64} \times 64\) bits, which is not practical to store.

Key concepts

Encryption

Encryption is the backbone of ensuring that only authorized parties can read the information. It involves transforming readable data, known as plaintext, into an unreadable format called ciphertext. This is achieved using an algorithm and an encryption key. The key is crucial, as it dictates how the data is transformed and can vary the output, even with the same algorithm. In a block cipher, which is the type of encryption being discussed, data is divided into fixed-size blocks and encrypted one block at a time. This method ensures data security, as it masks actual information by substituting values through complex processes and key manipulation.

Block ciphers are widely utilized because they maintain data integrity and confidentiality during transmission. Some well-known block cipher algorithms include AES (Advanced Encryption Standard) and DES (Data Encryption Standard). They work through a series of rounds, performing substitution and permutation on blocks of data, thereby ensuring a high level of security for digital communications and data storage.

Storage Requirements

When dealing with block ciphers and table-based encryption methods, understanding storage requirements is essential. Each component of the cipher—typically organized into tables or arrays—must be stored in memory. For instance, in this exercise, each table needs 64 bits of storage, as it is composed of an 8 by 8 grid with every entry holding 8 bits of data.

Consequently, if you require holding multiple tables, the total storage is the multiplication of the number of tables by the bits per table. In our example, eight similarly sized tables need 512 bits of storage. This calculation is pivotal in understanding and designing practical cryptographic systems, especially when resources might be scarce or constrained. Compared to other configurations, like a full-table block cipher which can demand an extreme storage capacity, selecting the right structure for table storage is key to balancing security and resource availability.

Table Size Calculation

Calculating the size of tables in block ciphers is essential in defining the cryptographic system's efficiency and feasibility. For each 8x8 table in this exercise, obtaining the table size involves multiplying the width by the height and the size of each entry. Each 8x8 table contains 64 entries, and with each entry consuming 8 bits, the table size amounts to 64 bits.

Understanding the mathematics behind the size calculations ensures efficient system design and implementation. Such calculations also aid in making comparisons between different encryption schemes, enabling you to select the most efficient approach for your specific needs without compromising on security. When the amount of data to manage in tables is clearly quantified, it is easier to plan for and allocate the necessary computing resources.

Cryptography

Cryptography is the field of study focused on securing information through encoding and decoding data. It is an essential domain in computer science and telecommunications, addressing issues of security, privacy, and data integrity. Block ciphers, like the one discussed, are one of many cryptographic methods used to protect data.

One of the primary objectives of cryptography is to encrypt information in such a way that it can only be read or understood by someone possessing the appropriate decryption key. Beyond block ciphers, there are other cryptographic approaches such as stream ciphers, symmetric and asymmetric encryption, and hashing. These methodologies ensure that critical information remains safe from unauthorized access and tampering.

As we advance in digital technologies, cryptography continues to evolve, addressing new security and privacy threats. It becomes an ever more vital part of safeguarding sensitive data in every sector, from government communications to personal digital transactions.