ECC primitives for Julia

crypto.j

# Eliptic Curve Cryptography w/ Julia!

abstract EC

## The point O found at every horizontal line

type ECInf <: EC
end

## Points on the curve

type ECPoint <: EC
    x :: Int
    y :: Int
end

# Extended Euclidean Aglorithm

function extended_gcd(a, b)
    if b == 0
        return (1, 0)
    else
        q = div(a, b)
        r = a - b * q
        s, t = extended_gcd(b, r)
        return (t, s - (q * t))
    end
end

# Multiplicative Inverses over the Field Fp

function mod_inv(a :: Int, b :: Int, m :: Int)
    inver, dis = extended_gcd(b, m);
    x = (a - m*dis*a)/b
    return int(x % m)
end

## Eliptic Curve Addition over the Field Fp ##

addMod(a :: ECPoint, b :: ECInf, c :: Int) = a
addMod(a :: ECInf, b :: ECPoint, c :: Int) = b

addMod(a :: ECPoint, b :: ECPoint, c :: Int) = begin

    x1 = a.x
    x2 = b.x
    y1 = a.y
    y2 = b.y

    if x1 == x2 && y1 == -y2
        return ECInf()
    end

    if x1 == x2 && y1 == y2
        lambda = mod_inv(((3*(x1^2)) + A), 2*y1, c)
    else
        lambda = mod_inv((y2 - y1), (x2 - x1), c)
    end

    x3 = ((lambda)^2 - x1 - x2) % c
    y3 = (lambda*(x1 - x3) - y1) % c

    return ECPoint(x3, y3)
end

# the returned point R satisfied R = nP

double_add(p :: ECPoint, n :: Int, Fp :: Int) = begin
    q = p
    r = ECInf()
    while n > 0
        if n % 2 == 1
            r = addMod(r, q, Fp)
        end
        q = addMod(q, q, Fp)
        n = fld(n, 2)
    end
    return r
end

# Perform the computation and return R
A = 14
P = ECPoint(6, 730)
Fp = 3623
n = 947

R = double_add(P, n, Fp);
println(R);