diff --git a/gf2n.cpp b/gf2n.cpp
index 452e6982..8993baae 100644
--- a/gf2n.cpp
+++ b/gf2n.cpp
@@ -135,6 +135,9 @@ PolynomialMod2 PolynomialMod2::Monomial(size_t i)
 
 PolynomialMod2 PolynomialMod2::Trinomial(size_t t0, size_t t1, size_t t2)
 {
+	CRYPTOPP_ASSERT(t0 > t1);
+	CRYPTOPP_ASSERT(t1 > t2);
+
 	PolynomialMod2 r((word)0, t0+1);
 	r.SetBit(t0);
 	r.SetBit(t1);
@@ -144,6 +147,11 @@ PolynomialMod2 PolynomialMod2::Trinomial(size_t t0, size_t t1, size_t t2)
 
 PolynomialMod2 PolynomialMod2::Pentanomial(size_t t0, size_t t1, size_t t2, size_t t3, size_t t4)
 {
+	CRYPTOPP_ASSERT(t0 > t1);
+	CRYPTOPP_ASSERT(t1 > t2);
+	CRYPTOPP_ASSERT(t2 > t3);
+	CRYPTOPP_ASSERT(t3 > t4);
+
 	PolynomialMod2 r((word)0, t0+1);
 	r.SetBit(t0);
 	r.SetBit(t1);
diff --git a/gf2n.h b/gf2n.h
index 4aef31ee..38e2a910 100644
--- a/gf2n.h
+++ b/gf2n.h
@@ -69,9 +69,11 @@ public:
 		static PolynomialMod2 CRYPTOPP_API Monomial(size_t i);
 		/// \brief Provides x^t0 + x^t1 + x^t2
 		/// \return x^t0 + x^t1 + x^t2
+		/// \pre The coefficients should be provided in descending order. That is, <pre>t0 > t1 > t2<pre>.
 		static PolynomialMod2 CRYPTOPP_API Trinomial(size_t t0, size_t t1, size_t t2);
 		/// \brief Provides x^t0 + x^t1 + x^t2 + x^t3 + x^t4
 		/// \return x^t0 + x^t1 + x^t2 + x^t3 + x^t4
+		/// \pre The coefficients should be provided in descending order. That is, <pre>t0 > t1 > t2 > t3 > t4<pre>.
 		static PolynomialMod2 CRYPTOPP_API Pentanomial(size_t t0, size_t t1, size_t t2, size_t t3, size_t t4);
 		/// \brief Provides x^(n-1) + ... + x + 1
 		/// \return x^(n-1) + ... + x + 1
diff --git a/gf2n.cpp b/gf2n.cpp
index 8993baae..87d9961b 100644
--- a/gf2n.cpp
+++ b/gf2n.cpp
@@ -135,9 +135,14 @@ PolynomialMod2 PolynomialMod2::Monomial(size_t i)
 
 PolynomialMod2 PolynomialMod2::Trinomial(size_t t0, size_t t1, size_t t2)
 {
+	// Asserts and checks due to Bing Shi
 	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.
+	if (t1 > t0 || t2 > t0)
+		throw InvalidArgument("PolynomialMod2: coefficients must be in descending order");
+
 	PolynomialMod2 r((word)0, t0+1);
 	r.SetBit(t0);
 	r.SetBit(t1);
@@ -147,11 +152,16 @@ PolynomialMod2 PolynomialMod2::Trinomial(size_t t0, size_t t1, size_t t2)
 
 PolynomialMod2 PolynomialMod2::Pentanomial(size_t t0, size_t t1, size_t t2, size_t t3, size_t t4)
 {
+	// Asserts and checks due to Bing Shi
 	CRYPTOPP_ASSERT(t0 > t1);
 	CRYPTOPP_ASSERT(t1 > t2);
 	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.
+	if (t1 > t0 || t2 > t0 || t3 > t0 || t4 > t0)
+		throw InvalidArgument("PolynomialMod2: coefficients must be in descending order");
+
 	PolynomialMod2 r((word)0, t0+1);
 	r.SetBit(t0);
 	r.SetBit(t1);
@@ -663,7 +673,12 @@ GF2NT::GF2NT(unsigned int c0, unsigned int c1, unsigned int c2)
 	, t0(c0), t1(c1)
 	, result((word)0, m)
 {
+	// 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.
+	if (c1 > c0 || c2 > c0)
+		throw InvalidArgument("GF2NT: coefficients must be in descending order");
 }
 
 const GF2NT::Element& GF2NT::MultiplicativeInverse(const Element &a) const
@@ -972,7 +987,12 @@ GF2NP * BERDecodeGF2NP(BufferedTransformation &bt)
 GF2NT233::GF2NT233(unsigned int c0, unsigned int c1, unsigned int c2)
 	: GF2NT(c0, c1, 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.
+	if (c1 > c0 || c2 > c0)
+		throw InvalidArgument("GF2NT: coefficients must be in descending order");
 }
 
 const GF2NT::Element& GF2NT233::Multiply(const Element &a, const Element &b) const