The curve should be called "edwards25519" while "Ed25519" is name for the whole signature scheme

docs/cryptography/asymmetric/edwards25519.md

@@ -1,4 +1,4 @@
-# Ed25519 curve
+# Edwards25519 elliptic curve
 
 !!! note
     Author is nowhere close to being a cryptographer. Be sceptical on accuracy.
@@ -6,13 +6,15 @@
 !!! note
     This article is only about the underlying curve. Public key derivation and signing algorithm will be treated separately. 
 
-Monero employs Ed25519 elliptic curve as a basis for its key pair generation.
+Monero employs edwards25519 elliptic curve as a basis for its key pair generation.
- 
+
-However, Monero does not exactly follow EdDSA reference signature scheme.
+The curve comes from the Ed25519 signature scheme. While Monero takes the curve unchanged, it does not exactly follow rest of the Ed25519.
+
+The edwards25519 curve is [birationally equivalent to Curve25519](https://tools.ietf.org/html/rfc7748#section-4.1).
 
 ## Definition
 
-This is the standard Ed25519 curve definition, no Monero specific stuff here,
+This is the standard edwards25519 curve definition, no Monero specific stuff here,
 except the naming convention. The convention comes from the CryptoNote
 whitepaper and is widely used in Monero literature.
 
@@ -25,8 +27,7 @@ Note:
 * curve is in two dimensions (nothing fancy, like all the curves is high school)
 * curve is mirrored below y axis due to `y^2` part of the equation (not a polynomial)
 
-
+### Base point: `G`
-### Base point `G`
  
 The base point is a specific point on the curve. It is used
 as a basis for further calculations. It is an arbitrary choice
@@ -40,7 +41,7 @@ That's because the specific x can be calculated from the curve equation.
     # The hex representation of the base point
     5866666666666666666666666666666666666666666666666666666666666666    
 
-### Prime order of the base point `l`
+### Prime order of the base point: `l`
 
 In layment terms, the "canvas" where the curve is drawn is assumed
 to have a finite "resolution", so point coordinates must "wrap around"
@@ -48,6 +49,7 @@ at some point. This is achieved by modulo the `l` value (lowercase L).
 In other words, the `l` defines the maximum scalar we can use.
 
     l = 2^252 + 27742317777372353535851937790883648493
+    # => 7237005577332262213973186563042994240857116359379907606001950938285454250989
 
 The `l` is a prime number specified by the curve authors.
 
@@ -67,9 +69,10 @@ Monero uses (apparently modified) Ref10 implementation by Daniel J. Bernstein.
 
 ## Reference
 
+* [A (Relatively Easy To Understand) Primer on Elliptic Curve Cryptography](https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/)
+* [RFC 8032 defining EdDSA](https://tools.ietf.org/html/rfc8032)
 * [Understanding Monero Cryptography](https://steemit.com/monero/@luigi1111/understanding-monero-cryptography-privacy-introduction) - excellent writeup by Luigi
 * [StackOverflow answer](https://monero.stackexchange.com/questions/2290/why-how-does-monero-generate-public-ed25519-keys-without-using-the-standard-publ)
 * [Python implementation](https://github.com/monero-project/mininero/blob/master/ed25519.py) - not the reference one but easier to understand
 * [Encoding point to hex](https://monero.stackexchange.com/questions/6050/what-is-the-base-point-g-from-the-whitepaper-and-how-is-it-represented-as-a)
-* [Ed25519 on Wikipedia](https://en.wikipedia.org/wiki/EdDSA#Ed25519)
+* [EdDSA on Wikipedia](https://en.wikipedia.org/wiki/EdDSA)
-* [A (Relatively Easy To Understand) Primer on Elliptic Curve Cryptography](https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/)

docs/cryptography/asymmetric/introduction.md

@@ -15,4 +15,4 @@ Historically, asymmetric cryptography was based on the problem of factorization
 back into prime numbers (which is practically impossible for large enough integers).
 
 Recently, asymmetric cryptography is based on a mathematical notion of elliptic curves.
-Ed25519 is a specific, well researched and standardized elliptic curve used in Monero.      
+Edwards25519 is a specific, well researched and standardized elliptic curve used in Monero.

docs/cryptography/asymmetric/key-image.md

@@ -31,8 +31,8 @@ Where:
 The `P` comes from this:
 
     P = xG
-    
+
-Where `G` is the [Ed25519](/cryptography/asymmetric/ed25519) base point. 
+Where `G` is the [edwards25519](/cryptography/asymmetric/edwards25519) base point. 
 
 Substitute `P` with `xG` and we get:
 

docs/cryptography/asymmetric/private-key.md

@@ -27,8 +27,8 @@ See this [this guide](https://blog.cloudflare.com/a-relatively-easy-to-understan
 
 ### Key strength
 
-Before deriving Ed25519 public key, the private key is subject to modulo `l`,
+Before deriving the public key, private key is subject to modulo `l`,
-where `l` is the maximum scalar allowed by the [Ed25519 scheme](/cryptography/asymmetric/ed25519).
+where `l` is the maximum scalar allowed by the [edwards25519 curve](/cryptography/asymmetric/edwards25519).
 
 The `l` is on the order of 2^252, so the effective key strength is technically 252 bits, not 256 bits.
 This is standard for EC cryptography and is more of a cosmetic nuance than any concern.

docs/cryptography/asymmetric/public-key.md

@@ -3,7 +3,7 @@
 !!! note
     Author is nowhere close to being a cryptographer. Be sceptical on accuracy.
 
-Public key is deterministically derived from private key based on [Ed25519 curve](/cryptography/asymmetric/ed25519) with a little Monero-specific twist.
+Public key is deterministically derived from private key based on [edwards25519 curve](/cryptography/asymmetric/edwards25519) with a little Monero-specific twist.
 
 Public key is meant to be shared. Assuming correct implementation, it is not practically possible to recover private key from public key. 
 
@@ -20,7 +20,7 @@ Say:
 
 * P is a public key
 * x is a private key
-* G is a "base point"; this is simply a constant specific to [Ed25519](/cryptography/asymmetric/ed25519); this point lies on the elliptic curve
+* G is a "base point"; this is simply a constant specific to [edwards25519](/cryptography/asymmetric/edwards25519); this point lies on the elliptic curve
  
 Then:
 

docs/public-address/subaddress.md

@@ -45,20 +45,22 @@ Index       | Size in bytes    | Description
 Otherwise the data structure is the same as for [standard address](/public-address/standard-address/).
 
 Each subaddress conceptually has an index (with 0 being the base standard address).
-The index is not directly included in subaddress structure but is used as input to create the private spend key.
+The index is not directly included in subaddress structure but is used as input to create the private view key.
 
 ## Generating
 
-The private key `m` related to a subaddress is derived as follows:
+The private view key `m` for a subaddress is derived as follows:
     
     m = Hs(a || i)
     
 Where:
 
-* `Hs` is a Keccak-256 hash function interpreted as integer and modulo `l` (maximum Ed25519 scalar)
+* `Hs` is a Keccak-256 hash function interpreted as integer and modulo `l` (maximum edwards25519 scalar)
-* `a` is a private view key
+* `a` is a private view key of the base address
 * `i` is a subaddress index
 
+Deriving "sub view keys" from the "base view key" allows for creating a view only wallet that monitors entire wallet including subaddresses.
+
 TODO: describe rest of the procedure.
 
 ## Caveates

mkdocs.yml

@@ -16,7 +16,7 @@ nav:
       - Introduction: 'cryptography/asymmetric/introduction.md'
       - Private keys: 'cryptography/asymmetric/private-key.md'
       - Public keys: 'cryptography/asymmetric/public-key.md'
-      - Ed25519 curve: 'cryptography/asymmetric/ed25519.md'
+      - Edwards25519 curve: 'cryptography/asymmetric/edwards25519.md'
       - Key image: 'cryptography/asymmetric/key-image.md'
 #    - CryptoNight PoW: 'cryptography/cryptonight.md'
     - Base58: 'cryptography/base58.md'