p38.fsx

#load "utils.fs"
#load "sha1.fs"

open Utils
open Sha1
open System
open System.Numerics
open System.Security.Cryptography

let N_hex = "ffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c245e485b576625e7ec6f44c42e9a637ed6b0bff5cb6f406b7edee386bfb5a899fa5ae9f24117c4b1fe649286651ece45b3dc2007cb8a163bf0598da48361c55d39a69163fa8fd24cf5f83655d23dca3ad961c62f356208552bb9ed529077096966d670c354e4abc9804f1746c08ca237327ffffffffffffffff"

let SHA256ToBigInt (bs: byte []) : BigInteger =
    (new SHA256Managed()).ComputeHash bs |> Array.toList |> Utils.bytesToBigInt

let SHA256AndHMAC (s: BigInteger) (salt: BigInteger) =
    let K = (new SHA256Managed()).ComputeHash (s.ToByteArray()) 
    (new HMACSHA256(K)).ComputeHash (salt.ToByteArray())

(* Client and Server Pre-Agreed *) 

let N = Utils.hexToBigInt N_hex
let g = BigInteger 2
let k = BigInteger 3
let I = "test@test.com" |> Utils.strToBytes
let P = "abaissed" |> Utils.strToBytes

(* Secrets *)

let r = new Random()
let a = r.Next(100) |> BigInteger
let b = r.Next(100) |> BigInteger

(* Server Computation *) 

let salt = r.Next(1000) |> BigInteger
let v =
    let x = Array.append (salt.ToByteArray()) P |> SHA256ToBigInt
    BigInteger.ModPow (g, x, N)
let u = Utils.randKey 16 |> Array.toList |> Utils.bytesToBigInt

(* Normal Exchange *)

let keyCToS A = (I, A)
let keySToC (I, A) = (I, A, salt, (BigInteger.ModPow (g, b, N)), u)

let HMACCToS (I, A: BigInteger, salt: BigInteger, B: BigInteger, u) =
    let x = Array.append (salt.ToByteArray()) P |> SHA256ToBigInt
    let s = BigInteger.ModPow (B, (a + (u * x)), N)
    let h = SHA256AndHMAC s salt
    (I, A, salt, B, u, h)

let HMACSToC (I, A: BigInteger, salt: BigInteger, B: BigInteger, u, h) =
    let s = BigInteger.ModPow (A * BigInteger.ModPow(v, u, N), b, N)
    let h' = SHA256AndHMAC s salt
    if h = h' then "ok" else "password incorrect"

let exchange =
    keyCToS (BigInteger.ModPow (g, a, N)) |> keySToC |> HMACCToS |> HMACSToC

(* MITM Password Crack *)

let HMACSToC' (I, A: BigInteger, salt: BigInteger, B: BigInteger, u, h) =
    let rec guess words =
        if Seq.length words = 0 then "no valid password guessed"
        else let p = Seq.head words |> Utils.strToBytes
             let x = Array.append (salt.ToByteArray()) p |> SHA256ToBigInt
             let v = BigInteger.ModPow (g, x, N)
             let s = BigInteger.ModPow (A * BigInteger.ModPow(v, u, N), b, N)
             let h' = SHA256AndHMAC s salt
             if h = h' then (p |> Utils.bytesToStr) else guess (Seq.tail words)
    Utils.readLines "words.txt" |> guess

let exchangeHack =
    keyCToS (BigInteger.ModPow (g, a, N)) |> keySToC |> HMACCToS |> HMACSToC'