Add diffie-hellman exercise (#119)

config.json

@@ -450,6 +450,14 @@
         "prerequisites": [],
         "difficulty": 5
       },
+      {
+        "slug": "diffie-hellman",
+        "name": "Diffie-Hellman",
+        "uuid": "b11e4b1a-09f7-4f10-83da-46cde3aed5b8",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5
+      },
       {
         "slug": "etl",
         "name": "ETL",

exercises/practice/diffie-hellman/.docs/instructions.md

@@ -0,0 +1,37 @@
+# Instructions
+
+Diffie-Hellman key exchange.
+
+Alice and Bob use Diffie-Hellman key exchange to share secrets.
+They start with prime numbers, pick private keys, generate and share public keys, and then generate a shared secret key.
+
+## Step 0
+
+The test program supplies prime numbers p and g.
+
+## Step 1
+
+Alice picks a private key, a, greater than 1 and less than p.
+Bob does the same to pick a private key b.
+
+## Step 2
+
+Alice calculates a public key A.
+
+    A = gᵃ mod p
+
+Using the same p and g, Bob similarly calculates a public key B from his private key b.
+
+## Step 3
+
+Alice and Bob exchange public keys.
+Alice calculates secret key s.
+
+    s = Bᵃ mod p
+
+Bob calculates
+
+    s = Aᵇ mod p
+
+The calculations produce the same result!
+Alice and Bob now share secret s.

exercises/practice/diffie-hellman/.meta/config.json

@@ -0,0 +1,19 @@
+{
+  "authors": [
+    "erikschierboom"
+  ],
+  "files": {
+    "solution": [
+      "diffie-hellman.ua"
+    ],
+    "test": [
+      "tests.ua"
+    ],
+    "example": [
+      ".meta/example.ua"
+    ]
+  },
+  "blurb": "Diffie-Hellman key exchange.",
+  "source": "Wikipedia, 1024 bit key from www.cryptopp.com/wiki.",
+  "source_url": "https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange"
+}

exercises/practice/diffie-hellman/.meta/example.ua

@@ -0,0 +1,4 @@
+PrivateKey ← ⍜(-2|⌊×)⊙⚂
+PowMod     ← ◿⊙(ⁿ:)
+PublicKey  ← PowMod
+Secret     ← PowMod

exercises/practice/diffie-hellman/.meta/tests.toml

@@ -0,0 +1,28 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[1b97bf38-4307-418e-bfd2-446ffc77588d]
+description = "private key is greater than 1 and less than p"
+
+[68b2a5f7-7755-44c3-97b2-d28d21f014a9]
+description = "private key is random"
+
+[b4161d8e-53a1-4241-ae8f-48cc86527f22]
+description = "can calculate public key using private key"
+
+[0d25f8d7-4897-4338-a033-2d3d7a9af688]
+description = "can calculate public key when given a different private key"
+
+[cd02ad45-3f52-4510-99cc-5161dad948a8]
+description = "can calculate secret using other party's public key"
+
+[17f13c61-a111-4075-9a1f-c2d4636dfa60]
+description = "key exchange"

exercises/practice/diffie-hellman/diffie-hellman.ua

@@ -0,0 +1,11 @@
+# Generate a private key
+# Key ? PrimeP
+PrivateKey ← |1 ⊙(⍤"Please implement PrivateKey" 0)
+
+# Calculate the public key
+# PublicKey ? PrimeP PrimeG PrivateKey 
+PublicKey ← |3 ⊙⋅⋅(⍤ "Please implement PublicKey" 0)
+
+# Calculate the secret
+# Secret ? PrimeP PublicKey PrivateKey
+Secret ← |3 ⊙⋅⋅(⍤ "Please implement Secret" 0)

exercises/practice/diffie-hellman/tests.ua

@@ -0,0 +1,38 @@
+~ "diffie-hellman.ua" ~ PrivateKey PublicKey Secret
+
+# Private key is greater than 1 and less than p
+P ← 7919
+⍤⤙≍ 1 /××⊃(≥2|<P) [⍥(PrivateKey P) 1000]
+
+# Private key is random
+P ← 7919
+⍤⤙≍ 1 >100 ⧻◴ [⍥(PrivateKey P) 1000]
+
+# Can calculate public key using private key
+P          ← 23
+G          ← 5
+PrivateKey ← 6
+⍤⤙≍ 8 PublicKey P G PrivateKey
+
+# Can calculate public key when given a different private key
+P          ← 23
+G          ← 5
+PrivateKey ← 15
+⍤⤙≍ 19 PublicKey P G PrivateKey
+
+# Can calculate secret using other party's public key
+P              ← 23
+TheirPublicKey ← 19
+MyPrivateKey   ← 6
+⍤⤙≍ 2 Secret P TheirPublicKey MyPrivateKey
+
+# Key exchange
+P               ← 23
+G               ← 5
+AlicePrivateKey ← PrivateKey P
+AlicePublicKey  ← PublicKey P G AlicePrivateKey
+BobPrivateKey   ← PrivateKey P
+BobPublicKey    ← PublicKey P G BobPrivateKey
+SecretA         ← Secret P BobPublicKey AlicePrivateKey
+SecretB         ← Secret P AlicePublicKey BobPrivateKey
+⍤⤙≍ SecretB SecretA