diff --git a/src/common/finite_field.rs b/src/common/finite_field.rs
index 231a2a0..6fc57fd 100644
--- a/src/common/finite_field.rs
+++ b/src/common/finite_field.rs
@@ -1,4 +1,4 @@
-use std::{ops::{Add, Sub, Mul}, fmt::{self, Display}};
+use std::{ops::{Add, Sub, Mul, Div, Neg}, fmt::{self, Display}};
 
 use bigdecimal::{BigDecimal, Zero};
 
@@ -16,10 +16,17 @@ macro_rules! ffe {
     };
 }
 
+#[macro_export]
+macro_rules! ffeb {
+    ( $value: expr, $p: expr ) => {
+        FiniteFieldElement::new($value, $p)
+    };
+}
+
 #[derive(Debug, Clone, PartialEq)]
 pub struct FiniteFieldElement {
     pub value: BigDecimal,
-    p: BigDecimal
+    pub p: BigDecimal
 }
 
 fn pmod(x: BigDecimal, y: BigDecimal) -> BigDecimal {
@@ -73,6 +80,22 @@ impl Mul for FiniteFieldElement {
     }
 }
 
+impl Div for FiniteFieldElement {
+    type Output = Self;
+
+    fn div(self, rhs: Self) -> Self::Output {
+        Self::new(self.value / rhs.value, self.p)
+    }
+}
+
+impl Neg for FiniteFieldElement {
+    type Output = Self;
+
+    fn neg(self) -> Self::Output {
+        Self::new(-self.value, self.p)
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
diff --git a/src/elliptic_curve/elliptic_curve.rs b/src/elliptic_curve/elliptic_curve.rs
index df75b50..bef7caa 100644
--- a/src/elliptic_curve/elliptic_curve.rs
+++ b/src/elliptic_curve/elliptic_curve.rs
@@ -1,23 +1,85 @@
-use bigdecimal::BigDecimal;
-use crate::common::finite_field::*;
+use bigdecimal::{BigDecimal, FromPrimitive};
+use crate::{common::finite_field::*, b, ffeb, ffe};
 
+#[derive(Debug, Clone, PartialEq)]
 pub struct EllipticCurve {
     pub a: BigDecimal,
     pub b: BigDecimal,
     pub p: BigDecimal
 }
 
+#[derive(Debug, Clone, PartialEq)]
 pub struct EllipticCurvePoint {
     pub x: FiniteFieldElement,
-    pub y: FiniteFieldElement
+    pub y: FiniteFieldElement,
+    pub infinity: bool
 }
 
 impl EllipticCurve {
-    pub fn add(lhs: EllipticCurvePoint, rhs: EllipticCurvePoint) -> EllipticCurvePoint {
-        lhs
+    pub fn add(self, lhs: EllipticCurvePoint, rhs: EllipticCurvePoint) -> EllipticCurvePoint {
+        if lhs.clone().x == rhs.x && rhs.y == -lhs.clone().y {
+            return EllipticCurvePoint {
+                x: ffe!(0, 1),
+                y: ffe!(0, 1),
+                infinity: true
+            }
+        }
+
+        if lhs.infinity {
+            return rhs
+        }
+
+        if rhs.infinity {
+            return lhs
+        }
+
+        let (psi, phi) = if lhs == rhs {
+            let phi = Self::twice_phi(lhs.clone(), self.clone());
+            let psi = Self::twice_psi(lhs.clone(), self);
+
+            (phi, psi)
+        } else {
+            let phi = Self::add_phi(lhs.clone(), rhs.clone());
+            let psi = Self::add_psi(lhs.clone(), rhs.clone());
+
+            (phi, psi)
+        };
+
+        EllipticCurvePoint {
+            x: phi.clone() * phi - lhs.x.clone() - rhs.x.clone(),
+            y: todo!(),
+            infinity: todo!(), 
+        }
     }
 
     fn add_phi(a: EllipticCurvePoint, b: EllipticCurvePoint) -> FiniteFieldElement {
-        
+        (a.y - b.y) / (a.x - b.x)
+    }
+
+    fn add_psi(a: EllipticCurvePoint, b: EllipticCurvePoint) -> FiniteFieldElement {
+        (a.x.clone() * b.y - b.x.clone() * a.y) / (a.x - b.x)
+    }
+
+    fn twice_phi(a: EllipticCurvePoint, c: EllipticCurve) -> FiniteFieldElement {
+        let x = a.x.clone();
+        let y = a.y.clone();
+        let p = a.x.p.clone();
+        (
+            ffeb!(b!(3), p.clone()) * x.clone() * x
+             + ffeb!(c.a, p.clone())
+        ) / (
+            ffeb!(b!(2), p) * y
+        )
+    }
+
+    fn twice_psi(a: EllipticCurvePoint, c: EllipticCurve) -> FiniteFieldElement {
+        let p = a.x.p.clone();
+        (
+            ffeb!(b!(3), p.clone()) * a.x.clone() * a.x.clone()
+             + ffeb!(c.a, p.clone()) * a.x.clone()
+             - ffeb!(b!(2), p.clone()) * a.y.clone() * a.y.clone()
+        ) / (
+            ffeb!(b!(2), p) * a.y
+        )
     }
 }