diff --git a/src/fields/fp.rs b/src/fields/fp.rs
index bbbfeada..625be0c0 100644
--- a/src/fields/fp.rs
+++ b/src/fields/fp.rs
@@ -69,6 +69,16 @@ macro_rules! field_impl {
                 }
             }
 
+            /// Converts a U256 to an Fr regardless of modulus.
+            pub fn new_mul_factor(mut a: U256) -> Option<Self> {
+                if true {
+                    a.mul(&U256($rsquared), &U256($modulus), $inv);
+                    Some($name(a))
+                } else {
+                    None
+                }
+            }
+
             pub fn interpret(buf: &[u8; 64]) -> Self {
                 $name::new(U512::interpret(buf).divrem(&U256($modulus)).1).unwrap()
             }
@@ -80,6 +90,12 @@ macro_rules! field_impl {
                 U256($modulus)
             }
 
+            #[inline]
+            #[allow(dead_code)]
+            pub fn inv(&self) -> u64 {
+                $inv
+            }
+
             pub fn raw(&self) -> &U256 {
                 &self.0
             }
diff --git a/src/lib.rs b/src/lib.rs
index 984c1334..84ca22d3 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -2,7 +2,7 @@ extern crate rand;
 extern crate rustc_serialize;
 extern crate byteorder;
 
-mod arith;
+pub mod arith;
 mod fields;
 mod groups;
 
@@ -30,7 +30,7 @@ impl Fr {
     pub fn from_slice(slice: &[u8]) -> Result<Self, FieldError> {
         arith::U256::from_slice(slice)
             .map_err(|_| FieldError::InvalidSliceLength) // todo: maybe more sensful error handling
-            .and_then(|x| fields::Fr::new(x).ok_or(FieldError::NotMember))
+            .and_then(|x| fields::Fr::new_mul_factor(x).ok_or(FieldError::NotMember))
             .map(|x| Fr(x))
     }
     pub fn to_big_endian(&self, slice: &mut [u8]) -> Result<(), FieldError> {
@@ -92,8 +92,11 @@ impl Fq {
             .map(|x| Fq(x))
     }
     pub fn to_big_endian(&self, slice: &mut [u8]) -> Result<(), FieldError> {
-        self.0.raw().to_big_endian(slice).map_err(|_| FieldError::InvalidSliceLength)
-    }    
+        let mut a: arith::U256 = self.0.into();
+        // convert from Montgomery representation
+        a.mul(&fields::Fq::one().raw(), &fields::Fq::modulus(), self.0.inv());
+        a.to_big_endian(slice).map_err(|_| FieldError::InvalidSliceLength)
+    }
 }
 
 impl Add<Fq> for Fq {