Add article on key image

docs/cryptography/asymmetric/key-image.md

@@ -0,0 +1,46 @@
+# Monero private key image
+
+!!! danger
+    Author is nowhere close to being a cryptographer. Be sceptical on accuracy.
+
+Private key image serves to detect double spending attempts.
+
+In Monero funds are always sent to a one-time public key `P`.
+Related one-time private key `x` is specific to unspent output.
+
+As output can be spent only once (in whole), the related private key can be used only once.
+
+Thus, specific private key image `I` being present on the blockchain means
+that related output was already spent, and subsequent attempts must not be allowed.
+
+This whole scheme is necessary because Monero uses Ring Signatures
+which make it impossible to know whom exactly signed the transaction.
+This is why a simple Bitcoin-like double spending check wouldn't work here. 
+
+## Definition
+
+    I = x*Hp(P)
+
+Where:
+
+* `I` - private key image (or "key image" for short)
+* `x` - one-time private key used to unlock an unspent output
+* `P` - one-time public key of an unspent output
+* `Hp()` - hash function accepting an EC point as an argument 
+
+The `P` comes from this:
+
+    P = xG
+    
+Where `G` is the [Ed25519](/cryptography/asymmetric/ed25519) base point. 
+
+Substitute `P` with `xG` and we get:
+
+    I = x*Hp(xG)
+    
+The key image `I` is a one-way function of the private key `x`.
+
+## Reference
+
+* [StackExchange answer](https://monero.stackexchange.com/questions/2883/what-is-a-key-image)
+* [Another SE answer](https://monero.stackexchange.com/questions/2158/what-is-moneros-mechanism-for-defending-against-a-double-spend-attack)

mkdocs.yml

@@ -17,6 +17,7 @@ pages:
       - Private keys: 'cryptography/asymmetric/private-key.md'
       - Public keys: 'cryptography/asymmetric/public-key.md'
       - Ed25519 curve: 'cryptography/asymmetric/ed25519.md'
+      - Key image: 'cryptography/asymmetric/key-image.md'
 #    - CryptoNight PoW: 'cryptography/cryptonight.md'
     - Base58: 'cryptography/base58.md'
 - Address: