**Description of the topic (The **History and** Development of Cryptography). Give a brief overview of the topic, its applications and value in mathematics.**

Cryptography is described as codes and ciphers which can help in safeguarding and protecting the secret which was generated several years ago. Currently, it is also been referred to as classic cryptography — which includes the methods of encryption such as the use of the pen and paper, which can simply help in the mechanical aids. In modern times, such an invention is often described as a complex mechanical along with the working of the electromechanical machines, which are often referred to as an Enigma rotor machine. This helps in providing the efficient means of encryption which can help in the working of the introduction of electronics along with the working of the computing that can help in the elaborate schemes which ensure in minimizing the complexities, that works unlikely similar to the unsuited pen and paper.

Towards the progress in the development of the cryptography, often it is described and associated as a similar attribution to the development of cryptanalysis which is often called as a "breaking" of codes along with the working of the ciphers. It needs to also be discovered in association with the frequency analysis in terms of reading with references to the encrypted communications which has altered in terms of the course of history. for example, it has been stated that the Zimmermann Telegram highlights the main reasons of the United States' entry into World War I and another example, the Allied reading which is the part of Nazi Germany's ciphers has also cut short the World War II which was done in the research & evaluations two years ago. During the 1970s, the adaptability of the securing the cryptography is also referred to be part of the large preserve part of the governments. It has been noted that the two events which have also brought together the squarely part of the public domain is often described as a public encryption standard (DES) along with the description of the invention of public-key cryptography.

Cryptography is also called as a hidden, secret"; and it is often referred to as a practice along with bringing in the study of techniques in terms of the secure communication which works for the presence of third parties often called as adversaries. It is also associated as cryptography which is often termed as a constructing along with the beginning of the analyzing protocols that help in minimizing or eliminating the third parties along with bringing in the public that can help in the private messages. It also includes the various aspects along with bringing in information security such as the integration of the data confidentiality and highlighting the data integrity. it also includes the authentication and non-repudiation which are often the part and references of the modern cryptography. While referring to the Modern cryptography it is often described as an intersection and the part of the disciplines of mathematics along with bringing in the computer science in terms of the electrical engineering, communication science or the working of the physics. In terms of discussing the Applications of cryptography, it often includes the references made to the electronic commerce along with bringing in the element of the chip-based payment cards, digital currencies and the inclusion of the computer passwords, along with bringing in the element of the military communications.

Cryptography which is used in the modern age is often associated with the encryption, which results from the conversion of information done from the readable state towards the apparent nonsense. For the application of the mathematical part it engages the modern cryptography which is dependent on the mathematical theory along with bringing in the element of the computer science practice; cryptographic algorithms which are based around the computational hardness assumptions, that makes the algorithms not to be decoded easily (DuPont, 2016). It also helps in protecting the digital era in terms of the legal and used as a tool of espionage for the government.

**Describe the full range of its development over time. You should include examples from at least 5 different cultures. You should be detailed within each culture as to how they viewed and developed the topic.**

The full range of development of the Cryptography

It started with the year of 1900 BC and it has a similar coding and attributes to the computer’s information which helps in safeguarding it in the big deal, but it involved different cultures and aspects which have contributed to its evolution significantly (Taylor, 2015).

Classical Cryptography - It was the introductory phase of presenting the basic manifestation and presenting the message concealment that came in the mere form of the use of the pen on paper. It was evident that the individuals were not able to concisely read or use it with the blend of legible transcriptions which was the reference to the jumbles of graphemes. It was the Egyptians who began with the ciphertext and craved on the stones that had concealed information.

- 1500 BC: This was the information that has been crafted on the clay slabs in Mesopotamia which helped in safeguarding the valuable information to be used with the main aim of valuable or sensitive.
- 400 BC: The art of the Karma Sutra also engages the cryptography making the lovers record and understand the intercepted messages secret.

Medieval Cryptography - Advancement and inclusion of innovation transcript

- 800 AD: Progressed and used by the Arab Al-Kindi mathematician who wrote with the frequency of individual characters along with bringing in the monoalphabetic ciphers.
- 1467 AD: In this year, the Leon Battista Alberti decoded the polyalphabetic ciphers or codes, along with being referred to as a “Father of Western Cryptology.”
- The 1400s – 1600s: The transition in the European culture and during the era of European Renaissance, that used the Italian states in working towards the cryptographic practices. the purpose to communicate political and legal languages.
- 1586: Used by the Babington plot, that resulted in the assassination of Queen Elizabeth I, and advanced use of the cryptanalysis.

1800 to WWI

- The 1800s and into World War 1, this era used more cryptography
- The 1840s: Popular and key poets such as Edgar Allan Poe used vast methods to solve ciphers aid in the British WWI towards the Germans.
- 1853 – 1856: The era popularly used by the Charles Babbage who helped the British Crimean War efforts towards the various enemies by decoding the polyalphabetic ciphers, such as the Vigenère’s autokey cipher along with the weaker Vigenère cipher.

WWII – 1950s

- WW2 Used both the methods of mechanical and electromechanical cipher machines.
- The 1920s – 1930s: Used by the Enigma rotor machine for a popular cipher machine as a result of the German Army, who created the Arthur Scherbius. Used increasingly by the Poland Cipher Bureau’s mathematician along with the Marian Rejewski, that resulted in the solving the codes in 1932.
- 1942: In this, the Japanese Navy cryptography system can be used diligently by the JN-25, that helped in the broken by the US Navy.
- The 1950s: The VIC cipher, as evidently used by the Russian spy Reino Häyhänen.

Recent times-:

More use of the computer, algorithms along with the advancement in ciphers became more complex.

- 1975: The US Federal Register uses more progressively the Data Encryption Standard (DES), which is also known for the data encryption algorithm, in order to decode and safeguard the electronic communication in banks.
- 1991: PGP also called a Pretty Good Privacy known to be a top-notch cryptography system, as used heavily by Phil Zimmerman (Connolly, 2015).
- 2001: The DES along with the FIPS now also been reinvented into the Advanced Encryption Standard (AES).

**Include at least one specific mathematical example.**

ASCII is also referred in the encoding scheme such as the use of the A = 45, B = 46, C = 47 which can be used in an *encoding scheme*, that has a text message used evidently for the unique corresponding number, along with the inclusion of the mathematical functions that can rightfully be applied. In the early era, the decoding and the writing were different due to the corresponding languages been used (Ahadullah, 2015). While describing the originator in terms of the encrypted message it is often referred to the decoding technique that is required to recover in terms of the original information which works for the intended recipients, along with ensuring the unwanted persons which can be done from the same. Describing the cryptography literature it is often referred to as a use of the name such as the Alice ("A") or describing the sender, Bob ("B") along with bringing in the intended recipient described as an Eve ("eavesdropper") in terms of describing it for the adversary. The whole point of discussion is the development of rotor cipher machines described in the World War I which also has an advent of computers in terms of the World War II, that can often include the methods while describing the cryptology along with bringing in the complex nature and working of the application.

__References__

Ahadullah, M., Said, M. R. M., & Banerjee, S. (2015). History, development, and trend of fractal-based biometric cryptography. In *Chaos, Complexity, and Leadership 2013* (pp. 27-33). Springer, Cham.

Connolly, R. (2015). *Fundamentals of web development*. Pearson Education.

DuPont, Q., & Fidler, B. (2016). Edge cryptography and the development of computer networks and cybersecurity. *IEEE Annals of the History of Computing*, *38*(4), 55-73.

Taylor, R. W., Fritsch, E. J., & Liederbach, J. (2015). *Digital crime and digital terrorism*. Prentice Hall Press.