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intro.md review (#202)

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Jeremy Bokobza
2017-10-31 22:50:36 +00:00
committed by Ignotus Peverell
parent 914810713d
commit 508349e799
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doc/intro.md
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@@ -27,7 +27,7 @@ The main goal and characteristics of the Grin project are:
This document is targeted at readers with a good
understanding of blockchains and basic cryptography. With that in mind, we attempt
to explain the technical buildup of MimbleWimble and how it's applied in Grin. We hope
this document is understandable to most technically minded readers. Our objective is
this document is understandable to most technically-minded readers. Our objective is
to encourage you to get interested in Grin and contribute in any way possible.
To achieve this objective, we will introduce the main concepts required for a good
@@ -41,7 +41,7 @@ MimbleWimble blockchain's transactions and blocks.
We start with a brief primer on Elliptic Curve Cryptography, reviewing just the
properties necessary to understand how MimbleWimble works and without
delving too much into the intricacies of ECC. For readers who would want to
dive deeper into those assumption, there are other opportunities to
dive deeper into those assumptions, there are other opportunities to
[learn more](http://andrea.corbellini.name/2015/05/17/elliptic-curve-cryptography-a-gentle-introduction/).
An Elliptic Curve for the purpose of cryptography is simply a large set of points that
@@ -59,7 +59,7 @@ In ECC, if we pick a very large number _k_ as a private key, `k*H` is
considered the corresponding public key. Even if one knows the
value of the public key `k*H`, deducing _k_ is close to impossible (or said
differently, while multiplication is trivial, "division" by curve points is
extremely difficult).
extremely difficult).
The previous formula `(k+j)*H = k*H + j*H`, with _k_ and _j_ both private
keys, demonstrates that a public key obtained from the addition of two private
@@ -79,7 +79,7 @@ The validation of MimbleWimble transactions relies on two basic properties:
proving that the transaction did not create new funds, _without revealing the actual amounts_.
* **Possession of private keys.** Like with most other cryptocurrencies, ownership of
transaction outputs is guaranteed by the possession of ECC private keys. However,
the proof that an entity own those private keys is not achieved by directly signing
the proof that an entity owns those private keys is not achieved by directly signing
the transaction.
The next sections on balance, ownership, change and proofs details how those two
@@ -90,7 +90,7 @@ fundamental properties are achieved.
Building up on the properties of ECC we described above, one can obscure the values
in a transaction.
If _v_ is the value of a transaction input or output and _H_ an ECC curve, we can simply
If _v_ is the value of a transaction input or output and _H_ an elliptic curve, we can simply
embed `v*H` instead of _v_ in a transaction. This works because using the ECC
operations, we can still validate that the sum of the outputs of a transaction equals the
sum of inputs:
@@ -102,8 +102,8 @@ transaction doesn't create money out of thin air, without knowing what the actua
values are. However, there are a finite number of usable values and one could try every single
one of them to guess the value of your transaction. In addition, knowing v1 (from
a previous transaction for example) and the resulting `v1*H` reveals all outputs with
value v1 across the blockchain. For these reasons, we introduce a second ECC curve
_G_ (practically G is just another generator point on the same curve group as H) and
value v1 across the blockchain. For these reasons, we introduce a second elliptic curve
_G_ (practically _G_ is just another generator point on the same curve group as _H_) and
a private key _r_ used as a *blinding factor*.
An input or output value in a transaction can then be expressed as:
@@ -112,9 +112,9 @@ An input or output value in a transaction can then be expressed as:
Where:
* _r_ is a private key used as a blinding factor, _G_ is an elliptical curve and
* _r_ is a private key used as a blinding factor, _G_ is an elliptic curve and
their product `r*G` is the public key for _r_ on _G_.
* _v_ is the value of an input or output and _H_ is another elliptical curve.
* _v_ is the value of an input or output and _H_ is another elliptic curve.
Neither _v_ nor _r_ can be deduced, leveraging the fundamental properties of Elliptic
Curve Cryptography. `r*G + v*H` is called a _Pedersen Commitment_.
@@ -162,9 +162,9 @@ should only be spendable by you:
_X_, the result of the addition, is visible by everyone. The value 3 is only known to you and Alice,
and 113 is only known to you.
To transfer those 3 coins again, the protocol needs to require 113 to be known somehow.
To transfer those 3 coins again, the protocol requires 113 to be known somehow.
To demonstrate how this works, let's say you want to transfer those 3 same coins to Carol.
You need build a simple transaction such that:
You need to build a simple transaction such that:
Xi => Y
@@ -280,19 +280,19 @@ outputs plus the fee, minus the inputs) and using it as a private key.
We've explained above how MimbleWimble transactions can provide
strong anonymity guarantees while maintaining the properties required for a valid
blockchain, i.e., a transaction does not create money and proof of ownership
blockchain, i.e., a transaction does not create money and proof of ownership
is established through private keys.
The MimbleWimble block format builds on this by introducing one additional
concept: _cut-through_. With this addition, a MimbleWimble chain gains:
* Extremely good scalability, as the great majority of transaction data can be
eliminated over time, without compromising security;
* Further anonymity by mixing and removing transaction data;
eliminated over time, without compromising security.
* Further anonymity by mixing and removing transaction data.
* And the ability for new nodes to sync up with the rest of the network very
efficiently.
### Cut-through
### Cut-through
Blocks let miners assemble multiple transactions into a single set that's added
to the chain. In the following block representations, containing 3 transactions,
@@ -388,4 +388,3 @@ blockchain. By using the addition properties of Elliptic Curve Cryptography, we'
able to build transactions that are completely opaque but can still be properly
validated. And by generalizing those properties to blocks, we can eliminate a large
amount of blockchain data, allowing for great scaling and fast sync of new peers.