From 0f0fa69c8d5fec8c7507e27ba8f618018db1ee78 Mon Sep 17 00:00:00 2001
From: tomsmeding <tom.smeding@gmail.com>
Date: Thu, 13 Oct 2016 18:51:38 +0200
Subject: Comment gf28.{cpp,h}

---
 aes.cpp  |   2 +-
 gf28.cpp | 143 +++++++++++++++++----------------------------------------------
 gf28.h   |  37 ++++-------------
 3 files changed, 47 insertions(+), 135 deletions(-)

diff --git a/aes.cpp b/aes.cpp
index f36a69f..6d9163d 100644
--- a/aes.cpp
+++ b/aes.cpp
@@ -31,7 +31,7 @@ namespace AES{
 		}
 
 		for(int i=0;i<256;i++){
-			uint8_t inv=(uint8_t)GF28(i).inverse();
+			uint8_t inv=GF28::inverse(i);
 			uint8_t res=0;
 			for(int j=0;j<8;j++){
 				uint8_t bit=((inv>>j)&1)^
diff --git a/gf28.cpp b/gf28.cpp
index 9513818..fbf7daa 100644
--- a/gf28.cpp
+++ b/gf28.cpp
@@ -3,117 +3,52 @@
 
 using namespace std;
 
-int GF28::reduce(int v,int m){
-	assert(m);
-	while(true){
-		int sh=__builtin_clz(m)-__builtin_clz(v);
-		if(sh<0)break;
-		v^=m<<sh;
-		if(v==0)break;
-	}
-	return v;
-}
-
-uint8_t GF28::multiply(uint8_t x,uint8_t y){
-	if(x==0||y==0)return 0;
-	int res=0;
-	int addend=x;
-	while(y){
-		if(y&1)res^=addend;
-		addend<<=1;
-		if(addend&0x100)addend^=modulus;
-		y>>=1;
-	}
-	return res;
-}
-
-GF28::GF28()
-		:value(0){}
-
-GF28::GF28(int v)
-		:value(reduce(v,modulus)){}
-
-GF28::operator uint8_t() const {
-	return value;
-}
-
-GF28& GF28::operator+=(GF28 o){
-	value^=o.value;
-	return *this;
-}
-
-GF28& GF28::operator-=(GF28 o){
-	value^=o.value;
-	return *this;
-}
+namespace GF28 {
 
-GF28& GF28::operator<<=(int n){
-	assert(n>=0);
-	value<<=n;
-	if(value&0x100)value^=modulus;
-	return *this;
-}
-
-GF28 GF28::operator+(GF28 o) const {
-	return GF28(value^o.value);
-}
+	const int modulus=0x11b;
 
-GF28 GF28::operator-(GF28 o) const {
-	return GF28(value^o.value);
-}
-
-GF28 GF28::operator*(GF28 o) const {
-	if(value==0||o.value==0)return GF28(0);
-	GF28 res;
-	GF28 addend(*this);
-	while(o.value){
-		if(o.value&1)res+=addend;
-		addend<<=1;
-		o.value>>=1;
+	uint8_t reduce(int v,int m){
+		assert(v&&m);
+		while(true){
+			int sh=__builtin_clz(m)-__builtin_clz(v);
+			if(sh<0)break;
+			v^=m<<sh;
+			if(v==0)break;
+		}
+		return (uint8_t)(unsigned int)v;
 	}
-	return res;
-}
-GF28 GF28::operator<<(int n) const {
-	return GF28(*this)<<=n;
-}
-
-bool GF28::operator==(GF28 o) const {
-	return value==o.value;
-}
 
-GF28 GF28::inverse() const {
-	if(value==0)return *this;
-	int x=1,y=0,x2=0,y2=1,r=modulus,r2=value;
-	while(r2!=0){
-		assert(r!=0);
-		int ex=__builtin_clz(r2)-__builtin_clz(r);
-		if(ex<0){
-			swap(x,x2);
-			swap(y,y2);
-			swap(r,r2);
-		} else {
-			int xn=x^(x2<<ex); x=x2; x2=xn;
-			int yn=y^(y2<<ex); y=y2; y2=yn;
-			int rn=r^(r2<<ex); r=r2; r2=rn;
+	uint8_t multiply(uint8_t x,uint8_t y){
+		if(x==0||y==0)return 0;
+		int res=0;
+		int addend=x;
+		while(y){
+			if(y&1)res^=addend;
+			addend<<=1;
+			if(addend&0x100)addend^=modulus;
+			y>>=1;
 		}
+		return res;
 	}
-	assert(r==1);
-	return GF28(y);
-}
 
-ostream& operator<<(ostream &os,GF28 p){
-	if(os.flags()&ios_base::hex){
-		return os<<p.value;
-	}
-	if(p.value==0)return os<<'0';
-	bool first=true;
-	for(int m=1<<16,i=16;m!=0;m>>=1,i--){
-		if(p.value&m){
-			if(!first)os<<'+';
-			first=false;
-			if(i==0)os<<'1';
-			else os<<"x^"<<i;
+	uint8_t inverse(uint8_t value){
+		if(value==0)return value;
+		int x=1,y=0,x2=0,y2=1,r=modulus,r2=value;
+		while(r2!=0){
+			assert(r!=0);
+			int ex=__builtin_clz(r2)-__builtin_clz(r);
+			if(ex<0){
+				swap(x,x2);
+				swap(y,y2);
+				swap(r,r2);
+			} else {
+				int xn=x^(x2<<ex); x=x2; x2=xn;
+				int yn=y^(y2<<ex); y=y2; y2=yn;
+				int rn=r^(r2<<ex); r=r2; r2=rn;
+			}
 		}
+		assert(r==1);
+		return reduce(y,modulus);
 	}
-	return os;
+
 }
diff --git a/gf28.h b/gf28.h
index 194cd57..2f3401b 100644
--- a/gf28.h
+++ b/gf28.h
@@ -4,36 +4,13 @@
 #include <cstdint>
 
 //The GF(2^8) field used in AES
+//Elements are represented by unsigned 8-bit ints, as is their nature.
+//Since addition in GF(2^8) is more simply written as just '^', only
+//multiplication and taking inverses is necessary to implement separately.
 
-class GF28{
-	int value;
+namespace GF28 {
 
-	static int reduce(int v,int m);
+	uint8_t multiply(uint8_t x,uint8_t y);
+	uint8_t inverse(uint8_t value);
 
-public:
-	static const int modulus=0x11b;
-
-	static uint8_t multiply(uint8_t x,uint8_t y); //for when the class is overkill
-
-	GF28();
-	explicit GF28(int v);
-
-	explicit operator uint8_t() const;
-
-	GF28& operator+=(GF28 o);
-	GF28& operator-=(GF28 o);
-	GF28& operator<<=(int n); //multiplication by x^n
-
-	GF28 operator+(GF28 o) const;
-	GF28 operator-(GF28 o) const;
-	GF28 operator*(GF28 o) const;
-	GF28 operator<<(int n) const; //multiplication by x^n
-
-	bool operator==(GF28 o) const;
-
-	GF28 inverse() const;
-
-	friend std::ostream& operator<<(std::ostream&,GF28);
-};
-
-std::ostream& operator<<(std::ostream &os,GF28 p);
+}
-- 
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