Add private and public key WiP articles

docs/cryptography/asymmetric/intro.md

@@ -3,7 +3,7 @@
 !!! danger
     Article author is nowhere close to being a cryptographer. Be sceptical on accuracy.
 
-Before we get to Monero, a little bit of context. We are talking asymmetric cryptography here.
+Before we get to Monero specific stuff, a little bit of context. We are talking asymmetric cryptography here.
 The "asymmetric" simply means the are two keys:
 
 * the private key (used primarily for signing data and for decrypting data)
@@ -16,15 +16,3 @@ back into prime numbers (which is practically impossible for large enough intege
 
 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.      
-
-## Private key
-
-Private key is a **large integer**, like:
-`115792089237316195423570985008687907853269984665640564039457584007913129639930`
-
-Private key is a **scalar**, meaning it is a single value.
-
-In equations scalars are represented by **lowercase letters**. 
-
-In user-facing contexts, private keys are encoded in little-endian hexadecimal form, like:
-`35187c5096d10db8a57be93885f28694ac9dcaa09d6b1fb1903aec07e168430a`

docs/cryptography/asymmetric/private-key.md

@@ -0,0 +1,33 @@
+# Private keys in Monero
+
+!!! danger
+    Article author is nowhere close to being a cryptographer. Be sceptical on accuracy.
+
+!!! warning
+    Article is a work in progress.
+
+Private key is generated [randomly](/cryptography/prng).
+
+Private key must be kept secret.
+
+Private key is a **large integer** impossible to guess, like:
+`108555083659983933209597798445644913612440610624038028786991485007418559037440`
+
+Private key is 256 bits long. 
+
+Private key is a **scalar**, meaning it is a single value.
+
+In equations scalars are represented by **lowercase letters**. 
+
+In user-facing contexts, private key is encoded in a [little-endian](https://en.wikipedia.org/wiki/Endianness#Little) hexadecimal form, like:
+`b3588a87056fb21dc4d052d59e83b54293882e646b543c29478e4cf45c28a402`
+
+## Relation to Ed25519
+
+Being a simple random integer, private key is not specific to any particular asymmetric cryptography scheme.
+
+However, before deriving Ed25519 public key, the private key is subject to modulo `l`,
+where `l` is the maximum scalar allowed by [Ed25519 scheme](/cryptography/asymmetric/ed25519).
+
+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 real concern.

docs/cryptography/asymmetric/public-key.md

@@ -0,0 +1,38 @@
+# Public keys in Monero
+
+!!! danger
+    Article author is nowhere close to being a cryptographer. Be sceptical on accuracy.
+
+!!! warning
+    Article is a work in progress.
+
+Public key is deterministically derived from private key based on [Ed25519 curve](/cryptography/asymmetric/ed25519) 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. 
+
+Public key is a **point (x,y)** on the elliptic curve.
+
+In equations points are represented by **uppercase letters**.
+
+In user-facing contexts, public key is encoded in a [little-endian](https://en.wikipedia.org/wiki/Endianness#Little) hexadecimal form, like:
+`016a941812293cf9a86071060fb090ab38d67945e659968cb8cf30e1bc725683` 
+
+## Deriving public key
+
+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
+ 
+Then:
+
+    P = xG
+
+The public key is simply the base point (G) multiplied by the private key (x).
+Multiplying the point is adding the point to itself a number of times.
+
+However, the addition is **not** a simple vector addition. It has a very specific
+definition nicely described in [this article](https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/).
+What is important is that result of addition is always a point on the curve.
+For example, G + G is another point on the curve.

mkdocs.yml

@@ -13,8 +13,10 @@ pages:
     - PRNG: 'cryptography/prng.md'
     - 'Keccak-256': 'cryptography/keccak-256.md'
     - Asymmetric:
-#      - Overview: 'cryptography/asymmetric/intro.md'
-      - 'Ed25519 curve': 'cryptography/asymmetric/ed25519.md'
+      - Overview: 'cryptography/asymmetric/intro.md'
+      - Private keys: 'cryptography/asymmetric/private-key.md'
+      - Public keys: 'cryptography/asymmetric/public-key.md'
+      - Ed25519 curve: 'cryptography/asymmetric/ed25519.md'
 #    - CryptoNight PoW: 'cryptography/cryptonight.md'
     - Base58: 'cryptography/base58.md'
 - Address: