DevOps is a crucial aspect of modern software development and has a significant impact on the security and performance of the systems being developed. Cryptocurrency is a popular and rapidly growing field that relies heavily on mathematics and cryptography to ensure the security and reliability of transactions. Cryptocurrency has become so popular that even children know about it. It is a new type of digital currency that uses encryption technology to check the generation of currencies and verify the transfer of funds. Cryptocurrency ensures the security and verification of transactions, as well as control over the creation of new units. Cryptocurrencies work independently of central banks and governments. Their value is determined by market supply and demand. Thanks to mathematics, cryptocurrency has cryptographic strength- the ability to withstand theoretical and practical hacking. That’s why it is becoming increasingly popular.

In this blog, we will explore the role of mathematics in the development of modern cryptography, with a specific focus on how DevOps practices can enhance the security and performance of cryptocurrency systems.

## Historical Background of Cryptography

Cryptocurrency is a modern form of currency that was first launched in 2009. The history of cryptography is the same age as human language. Initially, writing itself was a cryptographic system. The sacred books of ancient Egypt and India are written using cryptography. David Chaum developed the cryptographic system in 1983. It was called eCash. The development of blockchain and cryptography gave impetus to the development of cryptocurrencies.

A similar system DigiCash was launched about twelve years later. DigiCash used cryptography to transact money anonymously. However, the term “cryptocurrency” first appeared in 1998. It will take about 10 more years before the cryptocurrency becomes available to users.

## Bitcoin

In 2009, Satoshi Nakamoto launched the world’s first public cryptocurrency bitcoin. Bitcoin used SHA-256 cryptography in a so-called proof-of-work system. In the next years, Bitcoin was further developed. And other cryptocurrencies appeared on the market soon.

## Mathematical Principles of Cryptography

Cryptocurrency completely changes the usual concept of ownership. In the traditional world, owning something means having it physically. Knowledge of mathematics opens up new opportunities. Check plainmath.net and find the best math solver for everything related to math. Blockchain works differently, but it is not possible to own technology without mathematical knowledge. Get the biggest collection of all math questions and answers in one place. Digital coins are records in a distributed ledger that have no physical equivalent. Owning bitcoins allows you to use them at your discretion, and record transactions on the blockchain.

This capability is provided by the Elliptic Curve digital signature algorithm mechanism. It is a cryptographic signature system built on elliptic curves and finite fields. It cannot be faked. The reliability is easy to check for any member of the network. ECDSA includes 2 separate procedures for signature creation and verification. Each is a mechanism that combines several mathematical operations. The first uses the private key to activate the transaction. The second checks it using an open character set.

Asymmetric encryption works on the following principles:

- Generation of key pairs – public and private. Knowing the first, it is impossible to pick up the second in a reasonable time. However, by owning the second, you can create an unlimited number of open keys.
- Using open source and well-known encryption methods, information is encrypted in such a way that it can only be decrypted using a private one.
- The public key distributes through unprotected information transmission channels.

## Modern usage Asymmetric Encryption and Bitcoin Blockchain

Bitcoin uses public and private key pairs in its work, but asymmetric encryption does not use in it. Digital signatures are the most popular usage of asymmetric cryptography. Any message within the blockchain might not be encrypted but must be digitally signed as an identifier. Blockchain uses a more secure ECDSA algorithm. It does not provide an additional coding system, unlike the simpler but functional RSA algorithm.

The most well-known uses of encryption methods are as follows:

**RSA**– an algorithm suitable for generating digital signatures and encrypting information. It underlies asymmetric cryptography in general.**DSA**– basic algorithm for generating a digital signature without extra coding. It is the main one for FIPS-186-4, the official digital signature standard in the United States.**ECDSA**– the most common algorithm for creating a digital signature.

In addition, similar encryption methods are used to create hybrid systems. There are two existing methods of encoding information – Security Sockets Layer (SSL) and Transport Layer Security (TLS). Which formed the basis for creating secure

communication channels on the Internet. In particular – HTTPs.

**Asymmetric encryption has quite significant drawbacks:**

- It is extremely difficult to make changes to this algorithm.
- The encryption and decryption process is slow and requires large computing resources.
- The keys used are much longer than in symmetric encryption The long length is due to the fact that between the public and private keys, there is a direct pattern that can be trivially picked up. To maintain security, you need a symmetric key with a length of 128 bits (the minimum that is actually used) and an asymmetric key of 2304 bits. Working with such dimensions is inconvenient, so the process is slow.

In addition, despite its high stability, this method of encoding information can still be cracked. Most often use two methods.

The *first* is the real calculation of the private key by the known public. If the algorithm is known and the cracker has several encrypted texts at his disposal, then hacking is technically possible. Especially with the use of modern technological possibilities.

The *second * is wedging a third party into the process of transferring encrypted data.

Replacing the transmitted public keys with their own and decrypting messages at the expense of their own private ones. However, this method does not work in a situation

with the use of protected certificates.

## Research in cryptography and mathematics

**Quantum cryptography:** Research in quantum cryptography focuses on the development of protocols and systems. It helps to ensure the security of information transmission using the principles of quantum mechanics. This includes the development of quantum key contracts, quantum networks, and quantum devices.

Mathematics helps in the creation of new cryptographic algorithms and protocols. It provides a theoretical framework for creating secure encryption and authentication methods. Mathematical concepts such as number theory, group theory, elliptic curves, and probability theory. All this knowledge is used to analyze and create new cryptographic protocols.

**Mass distribution cryptographic protocols:** Researchers are working to develop protocols. That allows cryptographic keys to be securely distributed and shared between many parties. This is important to protect privacy and data integrity in large-scale systems such as cloud computing and the Internet of Things (IoT). Quantum cryptography is the relationship between quantum physics and mathematics. Quantum mechanics, information theory, and matrix algebra are used for this.

**Protection against quantum computing attacks:** One of the most pressing research topics is the development of cryptographic algorithms that are resistant to quantum computing attacks. It is important to develop new algorithms. Quantum-resistant cryptography provides resistance even against quantum attacks. Hackers use mathematical techniques such as cryptanalysis, algebraic analysis, and information theory to identify potential weaknesses in ciphers and protocols and design attacks against them.

**The future of cryptocurrencies depends on the following factors:**

- Legislative framework- might both positively and negatively affect cryptocurrency.
- New technologies can improve the quality of cryptocurrency usage.
- Popularity among the users – depends on how many people are ready to receive payments in cryptocurrency.
- Request for privacy is one of the advantages of usage, which can significantly increase the popularity of electronic currencies.

The reason for the popularity of cryptocurrency is a combination of factors: security, anonymity, lack of borders, and others. But the main thing is the mathematics of Bitcoin, on which the cryptocurrency is built. Thanks to the synergy of elliptic curves and finite fields, the system works properly.

Cryptography is the most important part of all information systems today. From e-mail to cellular, from access to the Internet to electronic cash. Cryptography and mathematics are two interrelated fields that are constantly evolving.

Cryptography ensures accountability, transparency, accuracy, and confidentiality. It prevents fraud attempts in e-commerce and provides legal force for financial transactions.

Cryptography helps establish your identity but also provides you with anonymity. It prevents bullies from messing up the server and prevents competitors from getting into your confidential documents.