diff --git a/gf2n.cpp b/gf2n.cpp
index 87d9961b2..56c10de97 100644
--- a/gf2n.cpp
+++ b/gf2n.cpp
@@ -139,9 +139,9 @@ PolynomialMod2 PolynomialMod2::Trinomial(size_t t0, size_t t1, size_t t2)
 	CRYPTOPP_ASSERT(t0 > t1);
 	CRYPTOPP_ASSERT(t1 > t2);
 
-	// The test is odd because of ECIES<EC2N>. The basis is t0, but the other coefficients are not in descending order.
+	// The test is relaxed because of ECIES<EC2N>. The high order exponent is t0, but the other exponents are not in descending order.
 	if (t1 > t0 || t2 > t0)
-		throw InvalidArgument("PolynomialMod2: coefficients must be in descending order");
+		throw InvalidArgument("PolynomialMod2: exponents must be in descending order");
 
 	PolynomialMod2 r((word)0, t0+1);
 	r.SetBit(t0);
@@ -158,9 +158,9 @@ PolynomialMod2 PolynomialMod2::Pentanomial(size_t t0, size_t t1, size_t t2, size
 	CRYPTOPP_ASSERT(t2 > t3);
 	CRYPTOPP_ASSERT(t3 > t4);
 
-	// The test is odd because of ECIES<EC2N>. The basis is t0, but the other coefficients are not in descending order.
+	// The test is relaxed because of ECIES<EC2N>. The high order exponent is t0, but the other exponents are not in descending order.
 	if (t1 > t0 || t2 > t0 || t3 > t0 || t4 > t0)
-		throw InvalidArgument("PolynomialMod2: coefficients must be in descending order");
+		throw InvalidArgument("PolynomialMod2: exponents must be in descending order");
 
 	PolynomialMod2 r((word)0, t0+1);
 	r.SetBit(t0);
@@ -676,9 +676,9 @@ GF2NT::GF2NT(unsigned int c0, unsigned int c1, unsigned int c2)
 	// Asserts and checks due to Bing Shi
 	CRYPTOPP_ASSERT(c0 > c1 && c1 > c2 && c2==0);
 
-	// The test is odd because of ECIES<EC2N>. The basis is c0, but the other coefficients are not in descending order.
+	// The test is relaxed because of ECIES<EC2N>. The high order exponent is t0, but the other exponents are not in descending order.
 	if (c1 > c0 || c2 > c0)
-		throw InvalidArgument("GF2NT: coefficients must be in descending order");
+		throw InvalidArgument("GF2NT: exponents must be in descending order");
 }
 
 const GF2NT::Element& GF2NT::MultiplicativeInverse(const Element &a) const
@@ -990,9 +990,9 @@ GF2NT233::GF2NT233(unsigned int c0, unsigned int c1, unsigned int c2)
 	// Asserts and checks due to Bing Shi
 	CRYPTOPP_ASSERT(c0 > c1 && c1 > c2 && c2==0);
 
-	// The test is odd because of ECIES<EC2N>. The basis is c0, but the other coefficients are not in descending order.
+	// The test is relaxed because of ECIES<EC2N>. The high order exponent is t0, but the other exponents are not in descending order.
 	if (c1 > c0 || c2 > c0)
-		throw InvalidArgument("GF2NT: coefficients must be in descending order");
+		throw InvalidArgument("GF2NT233: exponents must be in descending order");
 }
 
 const GF2NT::Element& GF2NT233::Multiply(const Element &a, const Element &b) const