diff --git a/ecc/bls12-377/ecdsa/ecdsa.go b/ecc/bls12-377/ecdsa/ecdsa.go
index cc13e8ac60..452e7df2a3 100644
--- a/ecc/bls12-377/ecdsa/ecdsa.go
+++ b/ecc/bls12-377/ecdsa/ecdsa.go
@@ -37,6 +37,7 @@ var errInvalidSig = errors.New("invalid signature")
 
 const (
 	sizeFr         = fr.Bytes
+	sizeFrBits     = fr.Bits
 	sizeFp         = fp.Bytes
 	sizePublicKey  = sizeFp
 	sizePrivateKey = sizeFr + sizePublicKey
@@ -103,7 +104,7 @@ func HashToInt(hash []byte) *big.Int {
 		hash = hash[:sizeFr]
 	}
 	ret := new(big.Int).SetBytes(hash)
-	excess := len(hash)*8 - sizeFr
+	excess := ret.BitLen() - sizeFrBits
 	if excess > 0 {
 		ret.Rsh(ret, uint(excess))
 	}
diff --git a/ecc/bls12-378/ecdsa/ecdsa.go b/ecc/bls12-378/ecdsa/ecdsa.go
index 44c297cc82..f6a5d04f91 100644
--- a/ecc/bls12-378/ecdsa/ecdsa.go
+++ b/ecc/bls12-378/ecdsa/ecdsa.go
@@ -37,6 +37,7 @@ var errInvalidSig = errors.New("invalid signature")
 
 const (
 	sizeFr         = fr.Bytes
+	sizeFrBits     = fr.Bits
 	sizeFp         = fp.Bytes
 	sizePublicKey  = sizeFp
 	sizePrivateKey = sizeFr + sizePublicKey
@@ -103,7 +104,7 @@ func HashToInt(hash []byte) *big.Int {
 		hash = hash[:sizeFr]
 	}
 	ret := new(big.Int).SetBytes(hash)
-	excess := len(hash)*8 - sizeFr
+	excess := ret.BitLen() - sizeFrBits
 	if excess > 0 {
 		ret.Rsh(ret, uint(excess))
 	}
diff --git a/ecc/bls12-381/ecdsa/ecdsa.go b/ecc/bls12-381/ecdsa/ecdsa.go
index 9039ee3885..3374cabdda 100644
--- a/ecc/bls12-381/ecdsa/ecdsa.go
+++ b/ecc/bls12-381/ecdsa/ecdsa.go
@@ -37,6 +37,7 @@ var errInvalidSig = errors.New("invalid signature")
 
 const (
 	sizeFr         = fr.Bytes
+	sizeFrBits     = fr.Bits
 	sizeFp         = fp.Bytes
 	sizePublicKey  = sizeFp
 	sizePrivateKey = sizeFr + sizePublicKey
@@ -103,7 +104,7 @@ func HashToInt(hash []byte) *big.Int {
 		hash = hash[:sizeFr]
 	}
 	ret := new(big.Int).SetBytes(hash)
-	excess := len(hash)*8 - sizeFr
+	excess := ret.BitLen() - sizeFrBits
 	if excess > 0 {
 		ret.Rsh(ret, uint(excess))
 	}
diff --git a/ecc/bls24-315/ecdsa/ecdsa.go b/ecc/bls24-315/ecdsa/ecdsa.go
index e1309b2f36..deb4712a52 100644
--- a/ecc/bls24-315/ecdsa/ecdsa.go
+++ b/ecc/bls24-315/ecdsa/ecdsa.go
@@ -37,6 +37,7 @@ var errInvalidSig = errors.New("invalid signature")
 
 const (
 	sizeFr         = fr.Bytes
+	sizeFrBits     = fr.Bits
 	sizeFp         = fp.Bytes
 	sizePublicKey  = sizeFp
 	sizePrivateKey = sizeFr + sizePublicKey
@@ -103,7 +104,7 @@ func HashToInt(hash []byte) *big.Int {
 		hash = hash[:sizeFr]
 	}
 	ret := new(big.Int).SetBytes(hash)
-	excess := len(hash)*8 - sizeFr
+	excess := ret.BitLen() - sizeFrBits
 	if excess > 0 {
 		ret.Rsh(ret, uint(excess))
 	}
diff --git a/ecc/bls24-317/ecdsa/ecdsa.go b/ecc/bls24-317/ecdsa/ecdsa.go
index dfcbab66cb..eda1c88065 100644
--- a/ecc/bls24-317/ecdsa/ecdsa.go
+++ b/ecc/bls24-317/ecdsa/ecdsa.go
@@ -37,6 +37,7 @@ var errInvalidSig = errors.New("invalid signature")
 
 const (
 	sizeFr         = fr.Bytes
+	sizeFrBits     = fr.Bits
 	sizeFp         = fp.Bytes
 	sizePublicKey  = sizeFp
 	sizePrivateKey = sizeFr + sizePublicKey
@@ -103,7 +104,7 @@ func HashToInt(hash []byte) *big.Int {
 		hash = hash[:sizeFr]
 	}
 	ret := new(big.Int).SetBytes(hash)
-	excess := len(hash)*8 - sizeFr
+	excess := ret.BitLen() - sizeFrBits
 	if excess > 0 {
 		ret.Rsh(ret, uint(excess))
 	}
diff --git a/ecc/bn254/ecdsa/ecdsa.go b/ecc/bn254/ecdsa/ecdsa.go
index 8593d6a721..b25cb4d9ea 100644
--- a/ecc/bn254/ecdsa/ecdsa.go
+++ b/ecc/bn254/ecdsa/ecdsa.go
@@ -37,6 +37,7 @@ var errInvalidSig = errors.New("invalid signature")
 
 const (
 	sizeFr         = fr.Bytes
+	sizeFrBits     = fr.Bits
 	sizeFp         = fp.Bytes
 	sizePublicKey  = sizeFp
 	sizePrivateKey = sizeFr + sizePublicKey
@@ -103,7 +104,7 @@ func HashToInt(hash []byte) *big.Int {
 		hash = hash[:sizeFr]
 	}
 	ret := new(big.Int).SetBytes(hash)
-	excess := len(hash)*8 - sizeFr
+	excess := ret.BitLen() - sizeFrBits
 	if excess > 0 {
 		ret.Rsh(ret, uint(excess))
 	}
diff --git a/ecc/bw6-633/ecdsa/ecdsa.go b/ecc/bw6-633/ecdsa/ecdsa.go
index f264a1e479..7bfa57467b 100644
--- a/ecc/bw6-633/ecdsa/ecdsa.go
+++ b/ecc/bw6-633/ecdsa/ecdsa.go
@@ -37,6 +37,7 @@ var errInvalidSig = errors.New("invalid signature")
 
 const (
 	sizeFr         = fr.Bytes
+	sizeFrBits     = fr.Bits
 	sizeFp         = fp.Bytes
 	sizePublicKey  = sizeFp
 	sizePrivateKey = sizeFr + sizePublicKey
@@ -103,7 +104,7 @@ func HashToInt(hash []byte) *big.Int {
 		hash = hash[:sizeFr]
 	}
 	ret := new(big.Int).SetBytes(hash)
-	excess := len(hash)*8 - sizeFr
+	excess := ret.BitLen() - sizeFrBits
 	if excess > 0 {
 		ret.Rsh(ret, uint(excess))
 	}
diff --git a/ecc/bw6-756/ecdsa/ecdsa.go b/ecc/bw6-756/ecdsa/ecdsa.go
index 11c7725b5c..092e08e799 100644
--- a/ecc/bw6-756/ecdsa/ecdsa.go
+++ b/ecc/bw6-756/ecdsa/ecdsa.go
@@ -37,6 +37,7 @@ var errInvalidSig = errors.New("invalid signature")
 
 const (
 	sizeFr         = fr.Bytes
+	sizeFrBits     = fr.Bits
 	sizeFp         = fp.Bytes
 	sizePublicKey  = sizeFp
 	sizePrivateKey = sizeFr + sizePublicKey
@@ -103,7 +104,7 @@ func HashToInt(hash []byte) *big.Int {
 		hash = hash[:sizeFr]
 	}
 	ret := new(big.Int).SetBytes(hash)
-	excess := len(hash)*8 - sizeFr
+	excess := ret.BitLen() - sizeFrBits
 	if excess > 0 {
 		ret.Rsh(ret, uint(excess))
 	}
diff --git a/ecc/bw6-761/ecdsa/ecdsa.go b/ecc/bw6-761/ecdsa/ecdsa.go
index 7a6669fcab..b556cca823 100644
--- a/ecc/bw6-761/ecdsa/ecdsa.go
+++ b/ecc/bw6-761/ecdsa/ecdsa.go
@@ -37,6 +37,7 @@ var errInvalidSig = errors.New("invalid signature")
 
 const (
 	sizeFr         = fr.Bytes
+	sizeFrBits     = fr.Bits
 	sizeFp         = fp.Bytes
 	sizePublicKey  = sizeFp
 	sizePrivateKey = sizeFr + sizePublicKey
@@ -103,7 +104,7 @@ func HashToInt(hash []byte) *big.Int {
 		hash = hash[:sizeFr]
 	}
 	ret := new(big.Int).SetBytes(hash)
-	excess := len(hash)*8 - sizeFr
+	excess := ret.BitLen() - sizeFrBits
 	if excess > 0 {
 		ret.Rsh(ret, uint(excess))
 	}
diff --git a/ecc/secp256k1/ecdsa/ecdsa.go b/ecc/secp256k1/ecdsa/ecdsa.go
index de7c735da8..929592a46e 100644
--- a/ecc/secp256k1/ecdsa/ecdsa.go
+++ b/ecc/secp256k1/ecdsa/ecdsa.go
@@ -37,6 +37,7 @@ var errInvalidSig = errors.New("invalid signature")
 
 const (
 	sizeFr         = fr.Bytes
+	sizeFrBits     = fr.Bits
 	sizeFp         = fp.Bytes
 	sizePublicKey  = 2 * sizeFp
 	sizePrivateKey = sizeFr + sizePublicKey
@@ -103,7 +104,7 @@ func HashToInt(hash []byte) *big.Int {
 		hash = hash[:sizeFr]
 	}
 	ret := new(big.Int).SetBytes(hash)
-	excess := len(hash)*8 - sizeFr
+	excess := ret.BitLen() - sizeFrBits
 	if excess > 0 {
 		ret.Rsh(ret, uint(excess))
 	}
diff --git a/ecc/stark-curve/ecdsa/ecdsa.go b/ecc/stark-curve/ecdsa/ecdsa.go
index 4707f32195..55b0e09050 100644
--- a/ecc/stark-curve/ecdsa/ecdsa.go
+++ b/ecc/stark-curve/ecdsa/ecdsa.go
@@ -37,6 +37,7 @@ var errInvalidSig = errors.New("invalid signature")
 
 const (
 	sizeFr         = fr.Bytes
+	sizeFrBits     = fr.Bits
 	sizeFp         = fp.Bytes
 	sizePublicKey  = sizeFp
 	sizePrivateKey = sizeFr + sizePublicKey
@@ -103,7 +104,7 @@ func HashToInt(hash []byte) *big.Int {
 		hash = hash[:sizeFr]
 	}
 	ret := new(big.Int).SetBytes(hash)
-	excess := len(hash)*8 - sizeFr
+	excess := ret.BitLen() - sizeFrBits
 	if excess > 0 {
 		ret.Rsh(ret, uint(excess))
 	}
diff --git a/internal/generator/ecdsa/template/ecdsa.go.tmpl b/internal/generator/ecdsa/template/ecdsa.go.tmpl
index fd953cdf42..17234c557c 100644
--- a/internal/generator/ecdsa/template/ecdsa.go.tmpl
+++ b/internal/generator/ecdsa/template/ecdsa.go.tmpl
@@ -19,6 +19,7 @@ var errInvalidSig = errors.New("invalid signature")
 
 const (
 	sizeFr         = fr.Bytes
+	sizeFrBits     = fr.Bits
 	sizeFp         = fp.Bytes
 {{- if eq .Name "secp256k1"}}
 	sizePublicKey  = 2 * sizeFp
@@ -94,7 +95,7 @@ func HashToInt(hash []byte) *big.Int {
 		hash = hash[:sizeFr]
     }
 	ret := new(big.Int).SetBytes(hash)
-	excess := len(hash)*8 - sizeFr
+	excess := ret.BitLen() - sizeFrBits
 	if excess > 0 {
 		ret.Rsh(ret, uint(excess))
 	}