1
Introduction to Classical Cryptography

Vani Rajasekar1*, Premalatha J.2, Rajesh Kumar Dhanaraj3 and Oana Geman4

1Department of CSE, Kongu Engineering College, Tamil Nadu, India

2Department of IT, Kongu Engineering College, Tamil Nadu, India

3School of Computing Science and Engineering, Galgotias University, Greater Noida, India

4Department of Health and Human Development Computers, University of Suceava, Suceava, Romania

Abstract

In today's world, with societies of information that transmits a growing number of personal data via public channels, the protection of information is a global challenge. It is the technique used to authenticate users among two parties in the public environment, where there are unauthorized users and suspicious activities. Two types of process involved in classical cryptography are encryption and decryption, which are performed at the sender and receiver sides, respectively. Encryption is the method by which legible data or plain text is combined with key (additional information) and converted into an illegible data or cipher text. Decryption is the method by which cipher text is again transformed to plain text. Classical cryptography depends on mathematics and on the complexity of computing factorization in large numbers. The two major categories of classical cryptography are symmetric key cryptography and asymmetric key cryptography. In symmetric classical, both encryption and decryption are done using same key called private key [1]. In asymmetric classical, the sender uses public key to encrypt the message and the receiver uses private key to decrypt the message. The most widely used conventional cryptographic scheme is Data Encryption Standard (DES), Advanced Data Encryption Standard (AES), and Rivest-Shamir-Adleman (RSA). These algorithms have a primary advantage of flexibility and their protection, based on computational and validated security claims. The disadvantage relies on security of protocols against adversary.

Message authentication code (MAC) plays an important role in classical cryptography. MAC value ensures the authenticity and data privacy of message, and it will detect any changes in the transformed messages. Secure Hash Algorithm, also known as SHA, is a family of cryptographic approaches that is used to keep the information secured [2]. SHA and MAC functions generally include bitwise operations, compression functions, and modular operations. All cryptographic approaches should fulfill the security features such as confidentiality, integrity, privacy, reliability, authentication, and non-repudiation. Cryptography tools are far more effective in the instances of signatures confirmation, user authentication, and to conduct other cryptography practices. The most extensively used classical cryptographic tools are security token, Java Cryptographic Libraries (JCA), Docker, and authentication keys. The major applications of cryptography implies banking, digital currencies, military communications, secure network communications, disk encryption, health care, education, software, and marketing.

Keywords: Security, cryptography, authentication, privacy, key agreement

1.1 Introduction

The term "cryptography" is used to refer to the branch of science that sprang from historical secret writing. Secret writing is just one of many challenges for which cryptography has provided a solution. Cryptographic primitives relate to the answers to various cryptographic difficulties. The term "symmetric encryption" relates to a cipher in which the transmitter and receiver maintain a common secret key, allowing them to exchange a message in such a way that an adversary cannot decipher the message even if he witnesses it. In cybersecurity, a classical cipher is a form of encryption that has been employed in the past but has mostly fallen out of favors. Most classical ciphers, unlike modern cryptographic techniques, can be effectively calculated and decoded manually. However, with technological advances, they are usually fairly easy to break. The various classical ciphers are substitution cipher and transposition cipher.

1.2 Substitution Ciphers

A substitution cipher is a type of encryption in which plaintext elements are substituted with cipher text in a predetermined order using a key. The key units can be single letters, groups of letters, triplets of letters, combinations of the above, and so on. To retrieve the original message, the receiver uses the reverse substitution technique to decrypt the text. The plaintext elements are reorganized in a different, generally very complex order in a transposition cipher, but the elements themselves remain unaffected [3]. In a substitution cipher, on the other hand, the plaintext elements are kept in the same order in the cipher text, but the values themselves are changed.

1.2.1 Caesar Cipher

Caesar cipher, also referred as the shift cipher, Caesar's coding, or Caesar shifting, is among the most basic and extensively used encryption algorithms. It is a substitution cipher where each letter in the plaintext is chosen to replace that is a certain number of places down the alphabet. The conversion can be visualized by aligning the alphabets. The cipher letter is the plain letter rotated by a certain range of positions left or right. For example, here, a Caesar cipher uses a three-place left rotation, which is identical to a three-place right shift.

Encryption:

The encryption can alternatively be described using modular arithmetic by converting the letters into integers using the A = 0, B = 1, ., Z = 25 technique. The mathematical formula for encrypting a letter x with a shift n is

Similarly, the decryption is

In a cipher text-only environment, the Caesar cipher is easily broken. There are two scenarios to consider:

1. An attacker is aware that a simple substitution cipher has been employed.
2. An attacker recognizes the presence of a Caesar cipher but is unaware of the shifting value.

1.2.2 Polyalphabetic Cipher

Any cipher based on substitution that uses numerous substitution alphabets is known as a polyalphabetic cipher. Although it is a reduced particular case, the Vigenère cipher is possibly the best illustration of a polyalphabetic encryption [4].

1.2.2.1 Working of Polyalphabetic Cipher

• Select a keyword
• Construct the Vigenère table as shown in Figure 1.1.
• Write the key for plain text
• For each letter of plain text and a letter in key, look at the Vigenère table
• Trace down all the letters and finally write the cipher text

Figure 1.1 Vigenère table.

Example:

Key: KEYKEYE

Plain text: TRYTHIS

Then, based on the steps described above and from the Vigenère table, it is identified that the cipher text as follows:

Cipher: DVWDLGW

1.2.2.2 Cracking of Cipher Text

• Look for repeated sequences of letters in the ciphertext; the longer the sequences, the stronger. Make a note of where they are by underlining or marking them in the some fashion [5, 6].
• Determine how many letters are between the first letters in the string and add one for each appearance of a repetitive string.
• Factor the number obtained in above calculation.
• Create a table of common components by repeating this method with each repeated string that has found. The length of the phrase used to encrypt the cipher text is perhaps the most common factor.
• Count the number of times each letter appears in the cipher text. There should be n separate frequency counts in the end.
• To determine exactly how much each letter was displaced, compare these counts to regular frequency distribution.
• Shift should be undoing and the message can be read.

1.2.3 Hill Cipher

Hill cipher is a linear algebra-based polygraph substitution cipher. A value modulo 26 is assigned to each letter. The basic scheme A = 0, B = 1, ., Z = 25 is frequently employed, although it is not a requirement of the encryption [7]. Encryption is done by multiplying plain text matrix with the key matrix as nXn. The decryption is done by inverting the key matrix and it should be multiplied with cipher text to produce the plain text.

Example: Encryption

Plain text: ACT

Key: GYBNQKURP

Cipher Text: POH

Example: Decryption

Cipher Text: POH

Find the inverse of key as follows:

Plain Text: ACT

1.2.4 Playfair Cipher

The Playfair cipher was the very first digraph stream cipher to be used in practice. Unlike standard ciphers, Playfair cipher encrypts a pair of alphabets (digraphs) rather than a single alphabet. It starts by generating a 5*5 matrix key table. The matrix comprises alphabets that serve as the plaintext's encryption key. It is important to remember that no alphabet should be duplicated. Another thing to keep in mind is that there are 26 alphabets and only 25 blocks to fit a letter into. The message is encrypted digraph by digraph with the Playfair cipher. As a result, the Playfair cipher might be considered a digraph substitution cipher [8, 9].

1.2.4.1 Rules for Encrypting the Playfair Cipher

• To begin, divide the plaintext...