diff --git a/elgamal.py b/elgamal.py
index 7d2aee4..b3e8dba 100644
--- a/elgamal.py
+++ b/elgamal.py
@@ -206,9 +206,8 @@ def find_prime(iNumBits, iConfidence):
 						return p
 
 #encodes bytes to integers mod p.  reads bytes from file
-def encode(sPlaintext, iNumBits):
+def encode(sPlaintext, iNumBits, p):
 		byte_array = bytearray(sPlaintext, 'utf-16')
-
 		#z is the array of integers mod p
 		z = []
 
@@ -232,6 +231,9 @@ def encode(sPlaintext, iNumBits):
 				#add the byte multiplied by 2 raised to a multiple of 8
 				z[j//k] += byte_array[i]*(2**(8*(i%k)))
 
+		for i in range( len(z) ):
+				z[i] = modexp(z[i], 2, p)
+
 		#example
 				#if n = 24, k = n / 8 = 3
 				#z[0] = (summation from i = 0 to i = k)m[i]*(2^(8*i))
@@ -241,9 +243,11 @@ def encode(sPlaintext, iNumBits):
 		return z
 
 #decodes integers to the original message bytes
-def decode(aiPlaintext, iNumBits):
+def decode(aiPlaintext, iNumBits, p):
 		#bytes array will hold the decoded original message bytes
 		bytes_array = []
+		q = (p - 1) // 2
+		sqrtfactor = (q + 1) // 2
 
 		#same deal as in the encode function.
 		#each encoded integer is a linear combination of k message bytes
@@ -253,10 +257,14 @@ def decode(aiPlaintext, iNumBits):
 
 		#num is an integer in list aiPlaintext
 		for num in aiPlaintext:
+				#revnum = num
+				revnum = modexp(num, sqrtfactor, p)
+				if revnum > q:
+					revnum = p - revnum
 				#get the k message bytes from the integer, i counts from 0 to k-1
 				for i in range(k):
 						#temporary integer
-						temp = num
+						temp = revnum
 						#j goes from i+1 to k-1
 						for j in range(i+1, k):
 								#get remainder from dividing integer by 2^(8*j)
@@ -267,7 +275,7 @@ def decode(aiPlaintext, iNumBits):
 						bytes_array.append(letter)
 						#subtract the letter multiplied by the power of two from num so
 						#so the next message byte can be found
-						num = num - (letter*(2**(8*i)))
+						revnum = revnum - (letter*(2**(8*i)))
 
 		#example
 		#if "You" were encoded.
@@ -306,7 +314,7 @@ def generate_keys(iNumBits=256, iConfidence=32):
 
 #encrypts a string sPlaintext using the public key k
 def encrypt(key, sPlaintext):
-		z = encode(sPlaintext, key.iNumBits)
+		z = encode(sPlaintext, key.iNumBits - 2, key.p)
 
 	#cipher_pairs list will hold pairs (c, d) corresponding to each integer in z
 		cipher_pairs = []
@@ -349,7 +357,7 @@ def decrypt(key, cipher):
 				#add plain to list of plaintext integers
 				plaintext.append( plain )
 
-		decryptedText = decode(plaintext, key.iNumBits)
+		decryptedText = decode(plaintext, key.iNumBits - 2, key.p)
 
 	#remove trailing null bytes
 		decryptedText = "".join([ch for ch in decryptedText if ch != '\x00'])