diff --git a/.gitignore b/.gitignore
index a9d37c5..2da6cde 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,2 +1,3 @@
 target
 Cargo.lock
+.idea
\ No newline at end of file
diff --git a/Cargo.toml b/Cargo.toml
index 6a2ada7..f74738b 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -20,6 +20,8 @@ rand = { version = "0.5", features = ["i128_support"] }
 rustc-serialize = { version = "0.3", optional = true }
 byteorder = { version = "1.0", features = ["i128"] }
 crunchy = "0.2.1"
+lazy_static = "*"
+rustc-hex = "2"
 
 [dev-dependencies.bincode]
 version = "0.6"
diff --git a/src/fields/fp.rs b/src/fields/fp.rs
index cf26e10..17856fa 100644
--- a/src/fields/fp.rs
+++ b/src/fields/fp.rs
@@ -240,6 +240,44 @@ field_impl!(
     0x9ede7d651eca6ac987d20782e4866389
 );
 
+lazy_static! {
+
+    static ref FQ: U256 = U256::from([
+        0x3c208c16d87cfd47,
+        0x97816a916871ca8d,
+        0xb85045b68181585d,
+        0x30644e72e131a029
+    ]);
+
+	static ref FQ_MINUS3_DIV4: Fq =
+		Fq::new(3.into()).expect("3 is a valid field element and static; qed").neg() *
+		Fq::new(4.into()).expect("4 is a valid field element and static; qed").inverse()
+			.expect("4 has inverse in Fq and is static; qed");
+
+	static ref FQ_MINUS1_DIV2: Fq =
+		Fq::new(1.into()).expect("1 is a valid field element and static; qed").neg() *
+		Fq::new(2.into()).expect("2 is a valid field element and static; qed").inverse()
+			.expect("2 has inverse in Fq and is static; qed");
+
+}
+
+impl Fq {
+    pub fn sqrt(&self) -> Option<Self> {
+        let a1 = self.pow(*FQ_MINUS3_DIV4);
+        let a1a = a1 * *self;
+        let a0 = a1 * (a1a);
+
+        let mut am1 = *FQ;
+        am1.sub(&1.into(), &*FQ);
+
+        if a0 == Fq::new(am1).unwrap() {
+            None
+        } else {
+            Some(a1a)
+        }
+    }
+}
+
 #[inline]
 pub fn const_fq(i: [u64; 4]) -> Fq {
     Fq(U256::from(i))
diff --git a/src/lib.rs b/src/lib.rs
index e680648..ce24d0d 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -4,6 +4,7 @@ extern crate crunchy;
 extern crate rand;
 #[cfg(feature = "rustc-serialize")]
 extern crate rustc_serialize;
+#[macro_use] extern crate lazy_static;
 
 pub mod arith;
 mod fields;
@@ -108,6 +109,19 @@ pub enum FieldError {
     NotMember,
 }
 
+#[derive(Debug)]
+pub enum CurveError {
+    InvalidEncoding,
+    NotMember,
+    Field(FieldError),
+}
+
+impl From<FieldError> for CurveError {
+    fn from(fe: FieldError) -> Self {
+        CurveError::Field(fe)
+    }
+}
+
 pub use groups::Error as GroupError;
 
 #[derive(Copy, Clone, Debug, PartialEq, Eq)]
@@ -166,6 +180,10 @@ impl Fq {
     pub fn modulus() -> arith::U256 {
         fields::Fq::modulus()
     }
+
+    pub fn sqrt(&self) -> Option<Self> {
+        self.0.sqrt().map(Fq)
+    }
 }
 
 impl Add<Fq> for Fq {
@@ -328,6 +346,24 @@ impl G1 {
     pub fn b() -> Fq {
         Fq(G1Params::coeff_b())
     }
+
+    pub fn from_compressed(bytes: &[u8]) -> Result<Self, CurveError> {
+        if bytes.len() != 33 { return Err(CurveError::InvalidEncoding); }
+
+        let sign = bytes[0];
+        let fq = Fq::from_slice(&bytes[1..])?;
+        let x = fq;
+        let y_squared = (fq * fq * fq) + Self::b();
+
+        let mut y = y_squared.sqrt().ok_or(CurveError::NotMember)?;
+
+        if sign == 2 && y.into_u256().get_bit(0).expect("bit 0 always exist; qed") { y = y.neg(); }
+        else if sign == 3 && !y.into_u256().get_bit(0).expect("bit 0 always exist; qed") { y = y.neg(); }
+        else if sign != 3 && sign != 2 {
+            return Err(CurveError::InvalidEncoding);
+        }
+        AffineG1::new(x, y).map_err(|_| CurveError::NotMember).map(Into::into)
+    }
 }
 
 impl Group for G1 {
@@ -580,3 +616,24 @@ impl From<AffineG2> for G2 {
         G2(affine.0.to_jacobian())
     }
 }
+
+#[cfg(test)]
+mod tests {
+    extern crate rustc_hex as hex;
+
+    use super::{G1, Fq};
+
+    fn hex(s: &'static str) -> Vec<u8> {
+        use self::hex::FromHex;
+        s.from_hex().unwrap()
+    }
+
+    #[test]
+    fn g1_from_compressed() {
+        let g1 = G1::from_compressed(&hex("0230644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd46"))
+            .expect("Invalid g1 decompress result");
+        assert_eq!(g1.x(), Fq::from_str("21888242871839275222246405745257275088696311157297823662689037894645226208582").unwrap());
+        assert_eq!(g1.y(), Fq::from_str("3969792565221544645472939191694882283483352126195956956354061729942568608776").unwrap());
+        assert_eq!(g1.z(), Fq::one());
+    }
+}