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make message $M$ also an element in q-order subgroup #10

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make message $M$ also an element in q-order subgroup #10

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9e5f8d8
fix message space
weikengchen Sep 27, 2017
e469910
clean redundant variables
weikengchen Sep 27, 2017
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22 changes: 15 additions & 7 deletions elgamal.py
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Original file line number Diff line number Diff line change
Expand Up @@ -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 = []

Expand All @@ -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))
Expand All @@ -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
Expand All @@ -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)
Expand All @@ -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.
Expand Down Expand Up @@ -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 = []
Expand Down Expand Up @@ -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'])
Expand Down