Bitcoin ecdsa public key tokens

Part 2: Building a Transaction By Hand

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Elliptic Curve Cryptography ECC is one of the most powerful but least understood types of cryptography in wide use today. Fundamentally, we believe it's important to be able to understand the technology behind any security system in order to trust it. To that end, we looked around to find a good, relatively easy-to-understand primer on ECC in order to share with our users.

Finding none, we decided to write one ourselves. That is what follows. In other words, settle in for a bit of an epic because there's a lot to cover. If you just want bitcoin ecdsa public key tokens gist, the TL;DR is: ECC is the next generation of public key cryptography and, based on currently understood mathematics, provides a significantly more secure foundation than first generation public key cryptography systems like RSA.

If you're worried about ensuring the highest level of security while maintaining performance, ECC makes sense to adopt. If you're interested in the details, read on. The history of cryptography can be split into two eras: The turning point between the two occurred inwhen both the RSA algorithm and the Diffie-Hellman key exchange algorithm were introduced.

These new algorithms were revolutionary because they represented the first viable cryptographic schemes where security was based on the theory of bitcoin ecdsa public key tokens it was the first to enable secure communication between two parties without a shared secret.

Cryptography went from being about securely transporting secret codebooks around the world to being able to have provably secure communication between any two parties without worrying about someone listening in on the key exchange. Whitfield Diffie and Martin Hellman. Modern cryptography is founded on the idea that the key that you use to encrypt your data can be made public while the key that is used to to decrypt your data can be kept private.

As such, these systems are known as public key cryptographic systems. The first, and still most widely used of these systems, is known as RSA — named after the initials of the three men who first publicly described the algorithm: What you need for a public key cryptographic system to work is a set of algorithms that is easy to process in one direction, but difficult to undo.

In the case of RSA, the easy algorithm multiplies two prime numbers. If multiplication is the easy algorithm, its difficult pair algorithm is factoring the product bitcoin ecdsa public key tokens the multiplication into its two component primes. Algorithms that have this characteristic — easy in bitcoin ecdsa public key tokens direction, hard the other — are known as Tra door Functions. Finding a good Trapdoor Function is critical to making a secure public key cryptographic system.

The RSA algorithm is the bitcoin ecdsa public key tokens popular and best understood public key cryptography system. Its security relies on the fact that factoring is slow and multiplication is fast. What follows is a quick walk-through of what a small RSA system looks like and how it works.

In general, a public key encryption system has two components, a public key and a private key. Encryption works by taking a message and applying a mathematical operation to it to get a random-looking number.

Decryption takes the random looking number and applies a different operation to get back to the original number. Encryption with the public key can only be undone by decrypting with the private key. Computers don't do well with arbitrarily large numbers.

We can make sure that the numbers we are dealing with do not get too large by choosing a maximum number and only dealing with numbers less than the maximum. We can treat the numbers like the numbers on an analog clock.

Any calculation that results in a number larger than the maximum gets wrapped around to a number in the valid range. In RSA, this maximum value call it max is obtained by multiplying two random prime numbers. Bitcoin ecdsa public key tokens public and private keys are two specially chosen numbers that are greater than zero and less than the maximum value, call them pub and priv.

To encrypt a number you multiply it by itself pub times, making sure to wrap around when you hit the maximum. To decrypt a message, you multiply it by itself priv times and you get back to the original number. It sounds surprising, but it actually works.

This property was a big breakthrough when it was discovered. To create a RSA key pair, first randomly pick the two prime numbers to obtain the maximum max. Then pick bitcoin ecdsa public key tokens number to be the public key bitcoin ecdsa public key tokens. As long as you know the two prime numbers, you can compute a corresponding private key priv from this public key. This is how factoring relates to breaking RSA — factoring the maximum number into its component bitcoin ecdsa public key tokens allows you to compute someone's private key from the public key and decrypt their private messages.

Let's make this more concrete with an example. Take the prime numbers 13 and 7, their product gives us our maximum value of Let's take our public encryption bitcoin ecdsa public key tokens to be the number 5. Then using the fact that we know 7 and 13 are the factors of 91 and applying an algorithm called the Extended Euclidean Algorithmwe get that the private key is the number You can take a number and multiply it by itself 5 times to encrypt it, then take that number and multiply it by itself 29 times and you get the original number back.

In order to represent a message mathematically we have to turn the letters into numbers. A common representation of the Latin alphabet is UTF Each character corresponds to a number. Each of these digits are smaller than our maximum of 91, so we can encrypt them individually. Let's start with the first letter. We do that by dividing by 91 and taking the bitcoin ecdsa public key tokens.

Voila, we're back to This works with the rest of the digits, bitcoin ecdsa public key tokens in the original message. The takeaway is that you can bitcoin ecdsa public key tokens a number, multiply it by itself a number of times to get a random-looking number, then multiply that number by itself a secret number of times to get back to the original number.

RSA and Diffie-Hellman were so powerful because they came with rigorous security proofs. The authors proved that breaking the system is equivalent to solving a mathematical problem that is thought to be difficult to solve. Factoring is a very well known problem and has been studied since antiquity see Sieve of Eratosthenes. Any breakthroughs would be big news and would net the discoverer a significant financial windfall. That said, factoring is not the hardest problem on a bit for bit basis.

Specialized algorithms like the Quadratic Sieve and the General Number Field Sieve were created to tackle the problem of prime factorization and have been moderately successful. These algorithms are faster and less computationally intensive than the naive approach of just guessing pairs of known primes. These factoring algorithms get more efficient as the size of the numbers being factored get larger.

The gap between the difficulty of factoring large numbers and multiplying large numbers is shrinking as the number i. As the resources available to decrypt numbers increase, bitcoin ecdsa public key tokens size of the keys need to bitcoin ecdsa public key tokens even faster. This is not a sustainable situation for mobile and low-powered devices that have limited computational power. The gap between factoring and multiplying is not sustainable in the long term.

All this means is that RSA is not the ideal system for the future of cryptography. In an ideal Trapdoor Function, the easy way and the hard way get harder at the same rate with respect to the size of the numbers in bitcoin ecdsa public key tokens. We need a public key system based on a better Trapdoor. Building blocks of a better Trapdoor After the introduction of RSA and Diffie-Hellman, researchers explored other mathematics-based bitcoin ecdsa public key tokens solutions looking for other algorithms beyond factoring that would serve as good Trapdoor Functions.

Incryptographic algorithms were proposed based on an esoteric branch of mathematics called elliptic curves. But what exactly is an elliptic curve and how does the underlying Trapdoor Function work? Unfortunately, unlike factoring — something we all had to do for the first time in middle school — most people aren't as familiar with the math around elliptic curves. The math isn't as simple, nor is explaining it, but I'm going to give it a go over the next few sections. If your eyes start to glaze over, you can skip way down to the section: What does it all mean.

An elliptic curve is the set of points that satisfy a specific mathematical equation. The equation for an elliptic curve looks something bitcoin ecdsa public key tokens this:.

There are other representations of elliptic curves, but technically an elliptic curve is the set points satisfying an equation in two variables with degree two in one of the variables and three in the other. An elliptic curve is not just a pretty picture, it also has some properties that make it a good setting for cryptography. One of these is horizontal symmetry. Any point on the curve can be reflected over the x axis and remain the same curve.

A more interesting property is that any non-vertical line will intersect the curve in at most three places. Let's imagine this bitcoin ecdsa public key tokens as the setting for a bizarre game of billiards. Take any two points on the curve and draw a line through them, it will intersect the curve at exactly one more place.

In this game of billiards, you take a ball at point A, shoot it towards point B. When it hits the curve, the ball bounces either straight up if it's below the x-axis or straight down if it's above the x-axis to the other side of the curve. We can call this billiards move on two points "dot. It turns out that if you have two points, an initial point "dotted" with itself n times to arrive at a final point, finding out n when you only know the final point and the bitcoin ecdsa public key tokens point is hard.

To continue our bizzaro billiards metaphor, imagine one person plays our game alone in a room for a random period of time. It is easy for him to hit the ball over and over following the rules described above.

If someone walks into the room later and sees where the ball has ended up, even if they know all the rules of the game and where the ball started, they cannot determine the number of times the ball was struck to get there without running through the whole game again until the ball gets to the bitcoin ecdsa public key tokens point.

Easy to do, hard to undo: This simplified curve above is great to look at and explain bitcoin ecdsa public key tokens general concept of elliptic curves, but it doesn't represent what the curves used for cryptography look like. For this, we have to restrict ourselves to numbers in a fixed range, like in RSA.

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BitPay provides a standards-based REST interface which enables application developers to interact in a powerful, yet secure way with their BitPay account. Using the BitPay API, clients can create and manage invoices, issue refunds, manage bills, retrieve real-time rates information, view merchant ledger entries, and much more. Every Identity is represented in public form as a Client ID , which much like the Bitcoin protocol, is simply a hash of the identity's public key.

For your convenience, all of BitPay's Client Libraries support this functionality. API Tokens are analagous to a real-world event ticket, which grants access to a specific event when presented at the door. Also like tickets, they may grant broad or narrow privileges e.

New tokens are provided with each response from the API. For example, creating a new Invoice with one token will provide a new, second token that grants access to view and interact with that Invoice exclusively. If not using BitPay's Client Libraries , you will need to keep track of these tokens on your own. Facades named collections of capabilities that can be granted, such as the ability to create invoices or grant refunds.

In the ticket analogy, this corresponds to the ticket 'level', where a 'VIP' ticket would confer broader access than a 'Standard' level ticket. When registering an Identity, it is against a specific facade. Best practices suggest that the requested facade should be limited to the minimum level that grants the required capabilities. To use any non-public facade a token will need to be sent with the API request.

Tokens can require authentication, which would requiring cryptographically signing each request. This will respond with a new token that will include a pairingCode. This pairing code can then be shared with a merchant organization administrator to approve access.

A token without a Client ID authentication restriction can be made, and a token can then be copied directly to make API calls, such as creating invoices. It is also important to note that pairing codes will expire after 24 hours , however once a token is approved or claimed the expiration is cleared. Once again the mechanics of this exchange may be simplified through the use of one of the BitPay libraries. For more information about specific resource URIs, please visit the resource documentation.

So if you are sending a request to:. The result should be included as the value of the x-signature request header. If your key becomes compromised, you will want to disable your old Client ID and register a new one. API sessions are an optional feature of our API which can be utilized to provide even greater security and reliability.

In particular it protects against replay attacks and ensures api requests are processed in the same order they are received. The server responds with a sessionId. The sessionId is used in each subsequent request along with a requestNumber.

On the first request, the requestNumber should be 1. Each additional request should increment the requestNumber by 1. If the server receives a request out of order it will return an error.

If the client does not hear back from the server because of an interruption in network connectivity or some other problem, the client may retry by sending the same request with the same requestNumber. The server will then respond with a cached copy of the data if it had already serviced that request but was interrupted when delivering it to the client. API sessions timeout after 15 minutes of inactivity. After 15 minutes, clients will get an error, and must create a new session.

Clients can be programmed to handle creation of new sessions and timeouts automatically. Please see the Node. Codes marked as deprecated may have been used in the past, but are no longer used for newly written ledger entries. Bills are payment requests addressed to specific buyers.

Bill line items have fixed prices, typically denominated in fiat currency. A client is identified by its access key id. A client is associated with a token via a pairing process. Invoices are time-sensitive payment requests addressed to specific buyers. An invoice has a fixed price, typically denominated in fiat currency. It also has a BTC equivalent price, calculated by BitPay, with an expiration time of about 15 minutes.

Retrieves invoices for the calling merchant filtered by query. Payouts are batches of bitcoin payments to employees, customers, partners, etc. Rates are exchange rates, representing the number of fiat currency units equivalent to one BTC. Creates an API session to protect against replay attacks and ensure requests are received in the same order they are sent.

Settlements are transfers of payment profits from BitPay to bank accounts and bitcoin wallets owned by merchants, partners, etc. This endpoint exposes reports detailing these settlements. Retrieves settlement reports for the calling merchant filtered by query. Gets a detailed reconciliation report of the activity within the settlement period. Subscriptions are repeat billing agreements with specific buyers. BitPay sends bill emails to buyers identified in active subscriptions according to the specified schedule.

Tokens are API access identifiers which are associated with a set of capabilities. A capability may be very broad, for example, retrieve the list of all exchange rates. Or a capability may be very specific, for example, update bill Overview BitPay provides a standards-based REST interface which enables application developers to interact in a powerful, yet secure way with their BitPay account.

Facades Facades named collections of capabilities that can be granted, such as the ability to create invoices or grant refunds. Facade Capabilities Description public The implicit facade applied when no token is provided. Provides access to public methods for generating merchant applications, generating and claiming tokens, or checking exchange rates. Allows for create, search, and view actions for Invoices and Bills; ledger download, as well as the creation of new merchant or pos tokens associated with the account.

My BitPay Client id e. Each request should include in the HTTP headers: So if you are sending a request to: US wallet provider names used for payouts BitPay Code Name bitgo uphold circle coinbase gdax gemini itbit kraken. Bills Resource Bills are payment requests addressed to specific buyers. Indicates whether corresponding invoice web page should display equivalent fiat amount. Default is current time.

Required Parameters description price quantity Facades merchant. Parameters status Facades merchant. Parameters none Facades merchant. Required Parameters none Facades public. Parameters none Facades client. Required Parameters none Facades client public. Parameters none Facades public.

Resource Invoices are time-sensitive payment requests addressed to specific buyers. ISO 3-character currency code. This is the currency associated with the price field, supported currencies are listed on https: Can be used by the merchant to assign their own internal Id to an invoice. If used, there should be a direct match between an orderId and an invoiceId.

Contact for notification of invoice status change. If missing, then account notification email address is notified. URL to redirect your shopper back to your website after a successful purchase.

Be sure to include "http: The URIs for sending a transaction to the invoice. The first key is the transaction currency.

The transaction currency maps to an object containing the payment URIs. Order reference number from the point-of-sale POS. It should be a unique identifer for each order that you submit.

Field is a passthru-variable returned in the payment notification post, without any modifications, for you to match up the BitPay payment notification with the request that was sent to BitPay. HIGH speed confirmations typically take seconds, and can be used for digital goods or low-risk items. LOW speed confirmations take about 1 hour, and should be used for high-value items.

If missing, then account transaction speed is used. Indicates whether email and IPN notifications should be sent for this invoice. If missing, then account notification settings are used. Indicates whether IPN notifications should be sent for this invoice when the invoice expires or is refunded.

If true, then fullNotifications is automatically set to true.

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