Cryptography: A Brief History from Symmetry to Bitcoin


For people interested in the mathematical and theoretical side of modern cryptography

Bitcoin - The Currency of the Internet

A community dedicated to Bitcoin, the currency of the Internet. Bitcoin is a distributed, worldwide, decentralized digital money. Bitcoins are issued and managed without any central authority whatsoever: there is no government, company, or bank in charge of Bitcoin. You might be interested in Bitcoin if you like cryptography, distributed peer-to-peer systems, or economics. A large percentage of Bitcoin enthusiasts are libertarians, though people of all political philosophies are welcome.

Where Cryptography and Objectivism Collide

Discussion of cryptography, cryptocurrency, and the cypherpunk-inspired burbclave government system with relation to Ayn Rand's Objectivism.

Interview with Andrew Poelstra of Blockstream talking cryptography. Bitcoin is the next Bitcoin.

Interview with Andrew Poelstra of Blockstream talking cryptography. Bitcoin is the next Bitcoin. submitted by Capitalist_Dog to Bitcoin [link] [comments]

Anyone familiar with cryptography/bitcoin/bitwasp classes who can help with an issue?

edit: $100 btc reward for the resolution!
I have been following this guide:
to try and derive legacy bitcoin addresses from an xpub key from my electrum wallet which using the bitwasp classes as specified in the guide. With the latest repository changes, it seems to have broken this method of generation somehow and there are comments with the exact error i am getting on the guide article but no solutions anywhere. this is my error:
Fatal error: Uncaught InvalidArgumentException: Invalid fingerprint for BIP32 key, must be in range [0 - (231)-1] inclusive
after looking at where this error is thrown in: vendor\bitwasp\bitcoin\src\Key\Deterministic\HierarchicalKey.php (Line 82)
if ($parentFingerprint < 0 || $parentFingerprint > IntRange::U32_MAX) { throw new \InvalidArgumentException('Invalid fingerprint for BIP32 key, must be in range [0 - (2^31)-1] inclusive'); } 
$parentFingerprint is 0 when I echo it but i do not know how any of these classes work enough to debug it.
Can anyone follow this guide and see if they can replicate my issue please? I used the exact sample code provided for xpub keys.
Full stack trace:
Fatal error: Uncaught InvalidArgumentException: Invalid fingerprint for BIP32 key, must be in range [0 - (2^31)-1] inclusive in [path_redacted]\vendor\bitwasp\bitcoin\src\Key\Deterministic\HierarchicalKey.php:82 Stack trace: #0 [path_redacted]\vendor\bitwasp\bitcoin\src\Serializer\Key\HierarchicalKey\ExtendedKeySerializer.php(147): BitWasp\Bitcoin\Key\Deterministic\HierarchicalKey->__construct(Object(BitWasp\Bitcoin\Crypto\EcAdapter\Impl\PhpEcc\Adapter\EcAdapter), Object(BitWasp\Bitcoin\Key\KeyToScript\Factory\P2pkhScriptDataFactory), 0, 0, 0, Object(BitWasp\Buffertools\Buffer), Object(BitWasp\Bitcoin\Crypto\EcAdapter\Impl\PhpEcc\Key\PublicKey)) #1 [path_redacted]\vendor\bitwasp\bitcoin\src\Serializer\Key\HierarchicalKey\ExtendedKeySerializer.php(159): BitWasp\Bitcoin\Serializer\Key\HierarchicalKey\ExtendedKeySerializer->fromParser(Object(BitWasp\Bitcoin\Network\Networks\Bitcoin), Object(BitWasp\Bufferto in [path_redacted]\vendor\bitwasp\bitcoin\src\Key\Deterministic\HierarchicalKey.php on line 82 
Thank you for any knowledge that can be share for this!
submitted by Bolshoi-Booze to PHPhelp [link] [comments]

The Politics of Cryptography: Bitcoin and The Ordering Machines

The Politics of Cryptography: Bitcoin and The Ordering Machines submitted by BitcoinAllBot to BitcoinAll [link] [comments]

The Politics of Cryptography: Bitcoin and The Ordering Machines

The Politics of Cryptography: Bitcoin and The Ordering Machines submitted by siktha to Bitcoin [link] [comments]

12-12 13:53 - 'Arbitrary precision rational calculator by Andrew Birrell...using in cryptography...' (self.Bitcoin) by /u/bruseyujchbl removed from /r/Bitcoin within 245-255min

Calculator: [link]1 Do you think that with this calculator someone can crack cryptography (bitcoin private keys)? That possible or impossible?
If you send link "RSA" on page...then you can see interesting math thing. See boxes "v" and "z"...
Arbitrary precision rational calculator by Andrew Birrell...using in cryptography...
Go1dfish undelete link
unreddit undelete link
Author: bruseyujchbl
1: birr**ndr**/rat*al*
Unknown links are censored to prevent spreading illicit content.
submitted by removalbot to removalbot [link] [comments]


A cryptocurrency is merely a currency that relies on cryptography. Bitcoin, for example, leverages cryptography in order to verify transactions.
submitted by FredFreer05 to Buttcoin [link] [comments]

Quantum Resistance

Before jumping to conclusions about this post, know that I am not looking to spread any FUD but rather am trying to understand a forthcoming risk and potential solutions from an unbiased standpoint. My research has not yielded any definitive answer so I am turning here to seek direction from those more knowledgable than me.
When it comes to predicting quantum computing's ability to break Bitcoin cryptographically, I've seen estimates as small as two years and as large as 25 years. Either way, it is easily conceivable that quantum processors will improve to the point of threatening Bitcoin as a reliable form of currency and store of value.
One way to prevent vulnerability to quantum threats is by storing Bitcoin in an address that has only ever received Bitcoin and never sent it. Although, this is an unrealistic mitigant for an asset/currency that is intended to be bought and sold, for all trust will be lost in the network once quantum computing becomes powerful enough to hack Bitcoin. Nobody will place any value in a currency that can be hacked by sending a transaction.
Another argument I've seen is that once quantum computing is strong enough to hack Bitcoin's cryptography, Bitcoin will be a non-factor compared to the other digital security breakdowns that will have transpired. For example, nuclear codes, bank accounts, digital privacy, etc. However, those centralized networks will have the ability to preemptively update their internal security to the standard required in a quantum computing world. In a similar manner, cryptocurrency and blockchain as a whole will survive such transition via improved cryptography.
But when it comes to Bitcoin specifically, will it be possible to generate consensus among the miners to switch to a quantum resistant protocol? My research has found conflicting perspectives - one side being that in order to upgrade Bitcoin's security, it would require manual movement of coins to a new address by all users, and a burning of the coins that did not move after a "sufficient" amount of time. Burning one's assets would undoubtedly not hold in a court of law. Even if we are still several years away, an unsolvable existential threat on the horizon would be priced into the value of Bitcoin and drive it down to zero.
With that being said, are there any feasible solutions to bring Bitcoin to quantum resistance? How can Bitcoin survive this threat in the long run? What is being done currently to resolve such problem?
submitted by fuegoblue to Bitcoin [link] [comments]

Bitcoin’s Security and Hash Rate Explained

Bitcoin’s Security and Hash Rate Explained
As the Bitcoin hash rate reaches new all-time highs, there’s never been a better time to discuss blockchain security and its relation to the hashing power and the Proof of Work (PoW) that feed the network. The Bitcoin system is based on a form of decentralized trust, heavily relying on cryptography. This makes its blockchain highly secure and able to be used for financial transactions and other operations requiring a trustless ledger.
Far from popular belief, cryptography dates back to thousands of years ago. The same root of the word encryption — crypt — comes from the Greek word ‘kryptos’, meaning hidden or secret. Indeed, humans have always wanted to keep some information private. The Assyrians, the Chinese, the Romans, and the Greeks, they all tried over the centuries to conceal some information like trade deals or manufacturing secrets by using symbols or ciphers carved in stone or leather. In 1900 BC, Egyptians used hieroglyphics and experts often refer to them as the first example of cryptography.
Back to our days, Bitcoin uses cryptographic technologies such as:
  1. Cryptographic hash functions (i.e. SHA-256 and RIPEMD-160)
  2. Public Key Cryptography (i.e. ECDSA — the Elliptic Curve Digital Signature Algorithm)
While Public Key Cryptography, bitcoin addresses, and digital signatures are used to provide ownership of bitcoins, the SHA-256 hash function is used to verify data and block integrity and to establish the chronological order of the blockchain. A cryptographic hash function is a mathematical function that verifies the integrity of data by transforming it into a unique unidentifiable code.
Here is a graphic example to make things more clear:

– Extract from the MOOC (Massive Open Online Course) in Digital Currencies at the University of Nicosia.
Furthermore, hash functions are used as part of the PoW algorithm, which is a prominent part of the Bitcoin mining algorithm and this is what is of more interest to understand the security of the network. Mining creates new bitcoins in each block, almost like a central bank printing new money and creates trust by ensuring that transactions are confirmed only when enough computational power is devoted to the block that contains them. More blocks mean more computation, which means more trust.
With PoW, miners compete against each other to complete transactions on the network and get rewarded. Basically they need to solve a complicated mathematical puzzle and a possibility to easily prove the solution. The more hashing power, the higher the chance to resolve the puzzle and therefore perform the proof of work. In more simple words, bitcoins exist thanks to a peer to peer network that helps validate transactions in the ledger and provides enough trust to avoid that a third party is involved in the process. It also exists because miners give it life by resolving that computational puzzle, through the mining reward incentive they are receiving.
For more info, contact directly or email at [email protected].
Tel +357 70007828
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submitted by BlockDotCo to u/BlockDotCo [link] [comments]

Every Wednesday there is a hosted Bitcoin Core Pull Request Review Club on IRC. All welcome to join. Tomorrow's topic: PR19055 - Add MuHash3072 implementation (cryptography)

Every Wednesday there is a hosted Bitcoin Core Pull Request Review Club on IRC. All welcome to join. Tomorrow's topic: PR19055 - Add MuHash3072 implementation (cryptography) submitted by TheGreatMuffin to Bitcoin [link] [comments]

@cz_binance: I believe the first versions of CBDC are all likely going to be fairly centralized. Even as they use blockchain and cryptography technologies, they will be fairly different from #bitcoin.

@cz_binance: I believe the first versions of CBDC are all likely going to be fairly centralized. Even as they use blockchain and cryptography technologies, they will be fairly different from #bitcoin. submitted by rulesforrebels to BinanceTrading [link] [comments]

Every Wednesday there is a hosted Bitcoin Core Pull Request Review Club on IRC. All welcome to join. Tomorrow's topic: PR19055 - Add MuHash3072 implementation (cryptography) (x-post from /r/Bitcoin)

Every Wednesday there is a hosted Bitcoin Core Pull Request Review Club on IRC. All welcome to join. Tomorrow's topic: PR19055 - Add MuHash3072 implementation (cryptography) (x-post from /Bitcoin) submitted by ASICmachine to CryptoCurrencyClassic [link] [comments]

What the Department of Justices Recent Obession with Cryptography and Crypto is About (x-post from /r/Bitcoin)

submitted by ASICmachine to CryptoCurrencyClassic [link] [comments]

Solving Quantum Cryptography (x-post from /r/Bitcoin)

Solving Quantum Cryptography (x-post from /Bitcoin) submitted by ASICmachine to CryptoCurrencyClassic [link] [comments]

PBS Space Time segment on quantum cryptography (youtube link) (x-post from /r/Bitcoin)

PBS Space Time segment on quantum cryptography (youtube link) (x-post from /Bitcoin) submitted by ASICmachine to CryptoCurrencyClassic [link] [comments]

Why is it impossible to hack bitcoin?

No one has been able to hack Bitcoin because of its advanced blockchain technology. Yes, there have been many instances of theft, but mostly because of the lack of the precaution by the owners, problems with two-way authentication and other similar issues.
Any hack would probably involve generating fake transactions, but since they are fake, they wouldn’t generate a solvable hash, so miners would spot them immediately, and plenty of people have tried and failed.
Lets have a look at some precedents that could be considered "hacking bitcoin" but they don't look encouraging.
· CRACKING CRYPTOGRAPHY: Bitcoin utilizes SHA-256 for encryption. In the event that this algorthim is split, bitcoin is damned.
My conjecture is that when SHA-256 will split, new calculation gauges will rise and bitcoin would embrace them.
· ALTERING BITCOIN RULES: You might need to tackle hinders with lower trouble, make bitcoins after the 21 millionth bitcoin is mined in 2140 or change any of the principles of bitcoin.
You may well change them, and a few diggers can even process your exchanges, yet these coins would never again be Bitcoin, yet Bitcoin Hack. Just in case, you will be able to keep your bitcoins.
Adding bitcoins to your balance without proving ownership, it’s impossible.You need to show the miners that there is a previous transaction to your address.
If you fake it, miners will reject the transaction and the network won’t accept any block they that includes that transaction.
Bitcoin is pretty safe from hackers, but we can’t say the same for those companies built around Bitcoin. Isn't unordinary to heard that Bitcoin trades have been hacked and their clients bitcoins lost. It has happened to a large number of them before and will keep on occurring but as Bitcoin grows older, its ecosystem matures as well.
Thanks for reading!
submitted by Proassetz_exchange to Bitcoin [link] [comments]

Prediction for 2018: Bitcoin will crash

As usual predictions usually fail it seems, and this one is speculative so it's just a hedge just in case. The prediction is that Bitcoin has on purpose been designed to crash in 2018, either through the cryptography it uses becomes broken or its proof of work algorithm will stop functioning.
The purpose for the crash is to destroy the chance of currencies emerging as a competition and threat to the fiat currencies.
Notice that the NSA has already moved away from the kind of cryptography Bitcoin uses:
"The National Security Agency has long cuddled up to Elliptic Curve Cryptography, swaying standards bodies away from RSA crypto and toward ECC in the late 1990s, as well as recommending it as a strong enough solution for sensitive government agencies to use in guarding their biggest secrets.
In August, however, the NSA let it publicly slip, in relatively hushed tones, that it was divorcing itself from Suite B, a 20-year-old public crypto standard that relied on ECC and was certified for top secret data protection. The agency suggests concerns over advances in quantum computing as the reason for its about-face in support of Suite-B. ...
Cryptographers, however, aren’t buying that reasoning." --
submitted by MrNeoson to conspiracy [link] [comments]

How I Met Satoshi. Jon Matonis on Craig wright as Satoshi.
During the London proof sessions, I had the opportunity to review the relevant data along three distinct lines: cryptographic, social, and technical. Based on what I witnessed, it is my firm belief that Craig Steven Wright satisfies all three categories. For cryptographic proof in my presence, Craig signed and verified a message using the private key from block #1 newly-generated coins and from block #9 newly-generated coins (the first transaction to Hal Finney). The social evidence, including his unique personality, early emails that I received, and early drafts of the Bitcoin white paper, points to Craig as the creator. I also received satisfactory explanations to my questions about registering the domain and the various time-of-day postings to the BitcoinTalk forum. Additionally, Craig’s technical working knowledge of public key cryptography, Bitcoin’s addressing system, and proof-of-work consensus in a distributed peer-to-peer environment is very strong.
According to me, the proof is conclusive and I have no doubt that Craig Steven Wright is the person behind the Bitcoin technology, Nakamoto consensus, and the Satoshi Nakamoto name
submitted by fookingroovin to btc [link] [comments]

Cryptography is at the heart of bitcoin and other digital currencies . learn the basics

Cryptography is at the heart of bitcoin and other digital currencies . learn the basics submitted by orangehello1 to Bitcoin [link] [comments]

The Great Uncoined... biggest myths in Crypto

Throughout the history of Bitcoin and cryptocurrency there have been a myriad of myths and fallacies that have propagated to hinder mass adoption from the great 'uncoined'. I wanted to make this article to look back and dispel some of the more common ones.
Quantum computers could crack Bitcoin’s cryptography
Bitcoin uses an Elliptic Curve Digital Signature Algorithm (ECDSA) as part of its security. In theory quantum computers could potentially crack this cryptography (and all other cryptography used in fiat and other services). However, quantum computers do not exist, and realistically won’t exist for a significant period. Furthermore, Bitcoin has been designed to be upgraded if it were ever a potential threat in the future.
The risk of quantum computers is also there for financial institutions, like banks, because they heavily rely on cryptography when doing transactions.
Bitcoin can’t scale due to having a 21 million coin cap
Due to the divisibility of Bitcoin there are approximately 2 quadrillion possible units. Each BTC is divisible by 8.
Bitcoin is a ponzi scheme
A ponzi scheme works by promising a client a profit at little to no risk. People that spruik ponzi schemes aim to attract new clients and have them invest in the ‘business’. Those investment returns are then given to the earlier investors. Without new investors, the flow of money runs out to the previous investors, usually resulting in a collapse of the scheme. Bitcoin is different in that it promises no return, new investors do not pay older investors to access the system, and new investors do not have to rely on more new investors to make money (if that is even their goal).
You can’t control inflation
Due to the inability for anyone to increase the total supply of Bitcoin past its 21 million cap, as a currency it can’t be inflated. It is much more likely that Bitcoin will increase in value as demand increases.
Bitcoin is full of scammers
Bitcoin, like any financial instrument, has those with nefarious intentions drawn to it. However 99% of users have not had any issues, if they use due diligence and do their research prior to purchase. Knowledge is power for any newcomer to the cryptocurrency world.
Fiat already fulfills our monetary needs
Fiat has evolved over time, but still follows an outdated process and has enjoyed the relative safety of avoiding innovation. Economic disruption is needed to bring our money systems into the globalized and open society demanded by today’s citizens. Bitcoin has unique traits, that could make Fiat obsolete. It has shaken up the industry and that can only benefit everyone.

What do you think is the biggest crypto myth is out there?
submitted by EasyCryptoAU to BitcoinAUS [link] [comments]

a very nice and short cryptography course (x-post from /r/Bitcoin)

a very nice and short cryptography course (x-post from /Bitcoin) submitted by ASICmachine to CryptoCurrencyClassic [link] [comments]

Satoshi Nakamoto Had Outside Cryptography Help, Says Early Bitcoin Dev

Satoshi Nakamoto Had Outside Cryptography Help, Says Early Bitcoin Dev submitted by that-crypto-dude to CryptoCurrency [link] [comments]

on this date, 26 years ago - The Cypherpunk's Manifesto was published and set the beginning of a whole new movement.

Favourite quote 1 - The need of anonymous p2p payments over the internet:
privacy in an open society requires anonymous transaction systems. Until now, cash has been the primary such system. An anonymous transaction system is not a secret transaction system. An anonymous system empowers individuals to reveal their identity when desired and only when desired; this is the essence of privacy.
Favourite quote 2 - The solution: open source software, cryptography, bitcoin
We the Cypherpunks are dedicated to building anonymous systems. We are defending our privacy with cryptography, with anonymous mail forwarding systems, with digital signatures, and with electronic money.
Cypherpunks write code. We know that someone has to write software to defend privacy, and since we can't get privacy unless we all do, we're going to write it. We publish our code so that our fellow Cypherpunks may practice and play with it. Our code is free for all to use, worldwide. We don't much care if you don't approve of the software we write. We know that software can't be destroyed and that a widely dispersed system can't be shut down.

Full text of the Cypherpunk's Manifesto HERE
submitted by BibzMibz to aeVentures [link] [comments]

Introduction to Cryptography of Bitcoin, Explained! Bob Cowles: Introduction to Cryptography and the Bitcoin Protocol 2/2 - CERN What is Cryptography and how it is used in Bitcoin - In ... Cryptography: How Bitcoin Works? How cryptography formed the basis of bitcoin? - YouTube

ECDSA (‘Elliptical Curve Digital Signature Algorithm’) is the cryptography behind private and public keys used in Bitcoin. It consists of combining the math behind finite fields and elliptic ... Cryptography is the process of communicating securely in an insecure environment – i.e. where other people can listen in and control the communication channel. The message you wish to send is converted to a cipher text that appears to be gibberish unless you know the secret to unlocking it. There are two main types of cryptography – symmetric and asymmetric. The Bitcoin Network mainly uses hashes in combination with digital signatures to protect the integrity of the data owing through the blockchain, using public-key cryptography. Hashes are furthermore used in the context of the consensus protocol “Proof-of-Work.” Bitcoin uses public-key cryptography, and more especially, elliptic-curve cryptography. Please note that alternative blockchains ... The history of cryptography from Whitfield-Diffie to Bitcoin and beyond continues to progress. Math provides the foundation. Modern math unlocks possibilities unheard of before the middle of the twentieth century. Mathematical research continues, and when quantum computing becomes common, new mathematical possibilities will emerge. Beyond math, decentralization drives the history of modern ... Signatures in Bitcoin. In many ways, this is the traditional cryptography in Bitcoin. We ask the question, “How do we know that Alice was authorized to transfer 100 Bitcoins to Bob,” and anyone who has used public-key cryptography knows the answer is, “Alice signs the transaction with her private key and publishes this signature for the Bitcoin network to verify with her public key.”

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Introduction to Cryptography of Bitcoin, Explained!

Bitcoin 101 - Elliptic Curve Cryptography - Part 4 - Generating the Public Key (in Python) - Duration: 21:22. CRI 25,030 views. 21:22. Elliptic Curve Diffie Hellman - Duration: 17:49. The Cryptography Behind Bitcoin - Duration: 29:28. CSBreakdown 22,923 views. 29:28. 1. Introduction to Human Behavioral Biology - Duration: 57:15. Stanford Recommended for you. 57:15 . Will ... 📌 Read the full article here: _____ Taklimakan Network is an ALL-IN-ONE Crypto Social Network. Grow your ... Description: You can understand this video much better if you watch the earlier videos. You can click on the playlist below to watch them - https://www.youtu... This video describes the inner-workings of Bitcoin. It provides three different versions, to highlight the drawbacks of each version and then presents the solutions given by Bitcoin. The last ...