feature: implement textbook DH

Author: NegaScout

src/ToyPublicKeys.jl

@@ -5,5 +5,6 @@ include("utils/random.jl")
 include("utils/number_theory.jl")
 include("padding/pkcs_1_v1_5.jl")
 include("rsa.jl")
+include("dh.jl")
 export RSAKey, RSAPrivateKey, RSAPublicKey, encrypt, decrypt, sign, verify_signature
 end

src/dh.jl

@@ -0,0 +1,22 @@
+struct DHPrivateKey
+    modulus::BigInt
+    public_component::BigInt
+    private_component::BigInt
+end
+
+struct DHPublicKey
+    modulus::BigInt
+    public_component::BigInt
+end
+
+function DHStep(key::DHPrivateKey)
+    return Base.GMP.MPZ.powm(key.public_component, key.private_component, key.modulus)
+end
+
+function DHStep(intermidiary::BigInt, key::DHPrivateKey)
+    return Base.GMP.MPZ.powm(intermidiary, key.private_component, key.modulus)
+end
+
+function generate_DHKeyPair(modulus::BigInt, public::BigInt, private::BigInt)
+    return (DHPrivateKey(modulus, public, private), DHPublicKey(modulus, public))
+end

test/dh.jl

@@ -0,0 +1,15 @@
+
+@testset "dh basics" begin
+    s_modulus = big"23"
+    s_public = big"5"
+    a_priv = big"4"
+    b_priv = big"3"
+    a_private_key, a_public_key = ToyPublicKeys.generate_DHKeyPair(s_modulus, s_public, a_priv)
+    b_private_key, b_public_key = ToyPublicKeys.generate_DHKeyPair(s_modulus, s_public, b_priv)
+    
+    a_interm = ToyPublicKeys.DHStep(a_private_key)
+    b_interm = ToyPublicKeys.DHStep(b_private_key)
+    a_shared_s = ToyPublicKeys.DHStep(b_interm, a_private_key)
+    b_shared_s = ToyPublicKeys.DHStep(a_interm, b_private_key)
+    @test a_shared_s == b_shared_s
+end

test/runtests.jl

@@ -2,3 +2,4 @@ using ToyPublicKeys
 using Test
 
 include("rsa.jl")
+include("dh.jl")