# Asymmetric cryptography and blockchain

Elliptic-curve cryptography ECC is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography based on plain Galois fields to provide equivalent security. Elliptic curves are applicable for key agreement , digital signatures , pseudo-random generators and other tasks. Indirectly, they can be used for encryption by combining the key agreement with a symmetric encryption scheme. Elliptic curves are also used in several integer factorization algorithms based on elliptic curves that have applications in cryptography, such as Lenstra elliptic-curve factorization.

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Content:

- What is Public Key Cryptography?
- Blockchain - Public Key Cryptography
- What Is Cryptography?
- What is Public-key Cryptography?
- Elliptic Curve Cryptography In Online Voting
- Public-Key Cryptography
- Asymmetric Cryptography
- Digital signature scheme for information non-repudiation in blockchain: a state of the art review
- Quantum Threat to Blockchains: Shor’s and Grover’s Algorithms
- German Wear, Mokassins driving moc Freizeitschuhe lederschuhe Nubukleder Senffarben

**WATCH RELATED VIDEO: Asymmetric Encryption - Simply explained**

## What is Public Key Cryptography?

For thousands of years the art of encryption consisted in hiding one secret from the enemy. By gaining access to this secret the opponent could decode the message and, perhaps, future messages encoded using the same key.

The Nazis created a fabulous machine called Enigma, which would use a complex mechanical system of rotors to produce very strong encryption in the age before computers. In fact modern electronic computers were researched and developed greatly by Alan Turing and a team of allied codebreakers at Bletchley Park during the wartime efforts to break Enigma!

Cryptography is at the heart of Computer Science and has been a major driving force for computer development throughout the years. Today games and entertainment are likely the greatest drivers of innovation, but cryptography will never lose its place at the birth of the computer.

Breaking cryptography, then, for hundreds of years boiled down to guessing a key. But modern computers can break any historical cryptographic key in minutes. All a computer has to do is try billions of combinations.

Since this was impossible up until WWII, such crypto systems were considered secure. It was clear that against modern computers more would be needed than the clever combinatorial mechanisms of the past. Computers are applied math, and advanced math would be needed to keep computers from breaking codes.

This was the reality of cryptanalysis post World War II - math was the new weapon against programmable computers. Intelligence agencies quickly shifted more and more resources towards math geeks fresh out of top universities.

Newly graduated mathematicians, computer scientists and logicians would find excellent jobs researching number theory, cryptography, abstract algebra and correlated subjects. It was the dream job for any geek, to play with the world's greatest computers and do what they loved the most, cryptographic research. After years of hard work, they finally published what is now considered a classic paper in cryptographic research entitled "New Directions in Cryptography". The need for a new kind of cryptographic system was highlighted right on the first paragraph of their text:.

This paper suggests ways to solve these currently open problems. The Diffie-Hellman paper is easily found via web search. The impact of this publication can be felt to this day. The name Diffie-Hellman has become as natural in cryptographic research as Coca Cola is to soft drinks. It's fundamental knowledge for any cryptography student, even if they've never read the paper, its two great contributions are everywhere around us to this day: public key cryptography and its corresponding routine for key exchange.

In fact, this last concept has been named the Diffie-Hellman key exchange, and it's exactly what your web browser does when accessing a https page, it's what happens when 2 people want to trade cryptocurrencies, it's what email signature verification programs do - in short, Diffie-Hellman is everywhere in the modern world.

What the world didn't know yet is that there was secret work being done in public key cryptography for at least 6 years before Diffie-Hellman. James Ellis of the United Kingdom's intelligence services had developed a system for public key encryption long before Diffie-Hellman, but this was classified information up until when it was announced that the UK had invented "non secret encryption" a long time ago, which was proved by a internal and secret publication from that was then made public.

Ellis and the British team are now academically accepted as pioneers in public key encryption. But since this was all secret work, we couldn't have known any better, so Diffie-Hellman, which didn't work for the spooks as far as we know, got all the fame for their incredible development. But something was missing. This great new idea needed a commercially viable implementation.

Someone had to take this a step further and develop it into something everyone could use. Enter three names which form another acronym that is widely recognized in the cryptographic world: Rivest, Shamir and Adler. RSA is a system for encryption, it's not a single particular technique, but in practice it refers to public key cryptography that uses the factoring problem at its mathematical core. Several different types of functions are usable for the public key math, but prime number factorization is the one used by RSA and it's basically everywhere.

RSA is everywhere, in your browser, the system used by credit card processors, it's in popular email security and privacy programs, it's in free and open source encryption programs. Yeah, RSA is everywhere - except in Bitcoin! Bitcoin uses a different mathematical system than RSA. The public key encryption system used in Bitcoin is called Elliptic Curve Cryptography and it exploits the fact that if you know certain parameters that are used to draw an elliptic curve, then you can easily follow this curve, but if you're only given a certain piece of the information used to draw these curves, then you are in for a hard time figuring out the path taken along the elliptic curve.

First, you may be wondering what an elliptic curve looks like. Here's one, courtesy of Wikipedia:. It doesn't look too fancy and in fact it's mathematically very simple. But its use in Bitcoin encryption has made it one of the most researched and popular cryptographic subjects by academics from around the world. The curve is symmetric around the X axis, every positive value has a corresponding negative value with the same magnitude.

This is exploited by elliptic curve encryption which switches between the positive and negative sides of the curve in order to make it even more difficult to reverse the process. Here's an animation, authored by Cloudflare , which shows how a path is followed on the curve. Bitcoin exploits this system for its public key cryptography. There are infinite elliptic curves EC so when you want to use EC's for encryption you must first publish its formula.

This deceivingly simple looking formula is the powerhouse behind Bitcoin. Those two variables and the number 7 guard the Bitcoin blockchain from being tampered with.

Every single Bitcoin address is derived from parameters of Secpk1, every single Bitcoin private key is a different parameter of the encryption system that uses that formula. Let's do a simple example using pencil and paper a calculator will come in handy for the exponentials , so you can grasp how public key encryption works. Since the Bitcoin elliptic curve is used for signing and not for encrypting, we'll use RSA to encrypt the message "Hi".

The idea is very similar to any other kind of public key system: one piece of the system is kept secret, the other is made public and only by having the two piece of data can you reverse the process easily, otherwise you need to try an immense number of guesses. This big number of guesses establishes how hard it is to reverse the process. So, let's get back to our experiment. First, choose two prime numbers which we'll call p and q these letters are just convention, they're traditionally used in RSA and other crypto examples.

In reality these two numbers would be very, very large. It's easy to break RSA when these numbers are tiny, but again this is just an example to show you how RSA can be done with pencil and paper. The explanation for the following step involves a bit of number theory which we won't get into. In short, it uses a piece of magic called Euler's Totient. We now need exponents for the numbers we just chose and to get those we use Euler's Totient to calculate a new parameter we'll call z.

Now we need another prime number which does not divide z. So let's choose the next prime after 5, which is 7. Now comes the fun part. Our public key is n and k! You send n and k to the public and anyone who wishes to send us a message can use these two parameters to encode secret messages that only we can decode. So to receive secret messages, we send all our friends our RSA public key:. What about the private key?

Since our k equals 7 and our z equals 8, we get. We hand this to Wolfram Alpha which tells us that the solution is:. So any whole number greater than zero that we plug in there will give us a valid j. Plugging in 2 for n, we get:. And there it is. Note that we have deliberately chosen this number, in fact it could have been 31 or 39 just keep on adding 8. Any of these numbers solve the equation for j. A real encryption program would ask you to randomly move your mouse around the screen or type random stuff on your keyboard in order to generate an unpredictable value of j at this point.

Start short digression. In Bitcoin an eventual real number "j", after encoding , would be about this big :. That's a typical value of "j" in a Bitcoin public key system. Let's get back to our example. End short digression. Now comes the Diffie-Hellman exchange. Anyone who wishes to send you secret messages must have our calculated values for n and k. Our peer, who we don't trust and we assume that they don't trust us either, then replies by saying "ok, received, and here's our n and k".

We've just done a simple version of a Diffie Hellman exchange. There's more to it in real life, but this is enough for our pencil and paper experiment. We can now send secret messages to our peer and they can send us secret messages. But we're only interested in what they'll send us for the sake of this example.

So let's get in the shoes of our peer for a moment and let's encrypt the message "Hi" that we'll send back to ourselves. The RSA formula for encryption is If T is "Hi" then how do we turn this into a number?! Great question indeed.

What we have here is a case where we need to turn text into a whole number. How do we do that? Well, we do exactly as if we were dealing with decimal numbers, except we're working with a weird base here instead of What does the number mean in practice? It's just 6 in the thousands, 7 in the hundreds, 4 in the tens and 3 in the units.

We can do the same thing for "Hi". H is in the 10th power, e is in the 9th and so on until d is in the units.

## Blockchain - Public Key Cryptography

Metrics details. Blockchain, as one of the most promising technology, has attracted tremendous attention. The interesting characteristics of blockchain are decentralized ledger and strong security, while non-repudiation is the important property of information security in blockchain. A digital signature scheme is an effective approach to achieve non-repudiation. In this paper, the characteristics of blockchain and the digital signature to guarantee information non-repudiation are firstly discussed. Secondly, the typical digital signature schemes in blockchain are classified and analyzed, and then the state-of-the-art digital signatures are investigated and compared in terms of application fields, methods, security, and performance.

## What Is Cryptography?

Cryptography grows ever more prominent in our lives. Every time you log into an app or send an email, you are relying on an ingenious cryptographic infrastructure that is descended largely from breakthroughs in the s. Beyond just specialist software developers, beyond just coders, even the non-programming general public can benefit from understanding how cryptography works, especially in an age of crypto currency and crypto investment. Cryptography is the practice of securing communications. This is achieved using a variety of techniques that boil down to implementing protocols that prevent unwelcome parties from viewing or altering data. Cryptography before the advent of computers relied on the use of ciphers. A cipher is a mapping from readable text to gibberish, and back again. For instance, a simple cipher would be to add four to every letter in the text so A becomes E. Decoding then would involve simply subtracting four from each letter.

## What is Public-key Cryptography?

Asymmetric encryption, also called public-key infrastructure is one of the cornerstones of blockchain technology. It is based on conventional cryptographic methods — applied to modern computing. Therefore, in order to understand blockchain, we need to first understand cryptography and specifically asymmetric encryption. Cryptography is the study and practice of secure communication , concealing messages from third parties with logical and mathematical functions. During encryption, a piece of secret information is converted into a cypher — seemingly unreadable coded text.

## Elliptic Curve Cryptography In Online Voting

The difference between private keys and public keys is huge — find out what "not your keys, not your coins" really means. Private keys are an essential part of the underlying architecture of crypto networks because you need them to sign transactions. In this guide, you will learn about public key cryptography and the role of private keys in crypto wallets. A public key, as you may have guessed because of the name, is public and can be shared with anyone. A private key, however, must be kept secure to ensure the security of the framework.

## Public-Key Cryptography

For thousands of years the art of encryption consisted in hiding one secret from the enemy. By gaining access to this secret the opponent could decode the message and, perhaps, future messages encoded using the same key. The Nazis created a fabulous machine called Enigma, which would use a complex mechanical system of rotors to produce very strong encryption in the age before computers. In fact modern electronic computers were researched and developed greatly by Alan Turing and a team of allied codebreakers at Bletchley Park during the wartime efforts to break Enigma! Cryptography is at the heart of Computer Science and has been a major driving force for computer development throughout the years. Today games and entertainment are likely the greatest drivers of innovation, but cryptography will never lose its place at the birth of the computer. Breaking cryptography, then, for hundreds of years boiled down to guessing a key. But modern computers can break any historical cryptographic key in minutes.

## Asymmetric Cryptography

It uses two pairs of keys - public and private. A key is a some long binary number. The public key is distributed worldwide and is truly public as its name suggests.

## Digital signature scheme for information non-repudiation in blockchain: a state of the art review

Heng Kiong teaches Information Technology, including business analytics and management information systems, at a tertiary institute. An earlier article explored how symmetric key algorithm or private-key cryptography works. We learned that there are challenges with using the same private key to encrypt and decrypt data. These are summarised below:. Blockchain uses public-key cryptography which is an encryption based upon asymmetric key algorithms.

## Quantum Threat to Blockchains: Shor’s and Grover’s Algorithms

NET Applications. We help small teams achieve big things. Whether a global brand, or an ambitious scale-up, we help the small teams who power them, to achieve more. We love to share our hard won learnings, through blogs, talks or thought leadership. This is the good stuff! If you would like to ask us a question, talk about your requirements, or arrange a chat, we would love to hear from you. Want to know more about how endjin could help you?

## German Wear, Mokassins driving moc Freizeitschuhe lederschuhe Nubukleder Senffarben

At the end of the article, many people are still perplexed because the authors brush over a lot of complicated concepts without explaining them. Instead, they engrave the details of each transaction onto a stone block , then cement it in place in the center of the village. They engrave this information onto a block, then cement it in the town square. Since the information is public, there can be no disputes over who legally controls what.

Amusing topic

I hadn't heard about it yet

A fascinating message

I mean it's the wrong way.