RSA: The simplicity

Encryption, Decryption: Basic Demonstration

>>> p
'This is a really cool message'
>>> p_long = number.bytes_to_long(p)
>>> p_long
2275631377870141336578401759413355859292272041852979859542858975504229L
>>> p_str = number.long_to_bytes(p_long)
>>> p_str
'This is a really cool message'
>>> c_long = pow(p_long,Obj.e,Obj.n)
>>> c_str = number.long_to_bytes(c_long)
>>> c_long
3577359857149864104872582435988394681894692436564139372233149356497183396696626604420275454046346384499757690937676454298792444254247302261561478690808264L
>>> c_str
'DM\xc5OC\x06\xa4\x94a\xa55\x96\x14P|4k@\xc65\xd3\t\x8fiK\xcd\x85_Oy\xda\x86`\x80\x92^Z\xfb\x9e\xa2\xde\x80\x08\x15\xa6\xb1\x00\x1c\x15\xa4\x85\xaa&\xd1_<\xf5\xe9z\xc2\xd2\xa2\xa1\xc8'
>>> c_long_d = number.bytes_to_long(c_str)
>>> p_long_d = pow(c_long_d,Obj.d,Obj.n)
>>> Obj.e
65537L
>>> Obj.d
3099234778655942655587865702037601270973126650452005339672950395413703554490867017690953509681134585322799088009268155598839343071612819885580126249710113L
>>> Obj.n
6916892548570560661306383603420339672936005492616144183420607868694973262410116954423108364344944764719133340849158239328436916579807593845233379454432791L
>>> p_str_d = number.long_to_bytes(p_long_d)
>>> p_str_d
'This is a really cool message'
>>> 

Verification and Signatures

Verification

Hash

Hashing function: md5, SHA-1, etcetera...

Maps any sized input to a 64-bit number.

Which number is unpredictable.

Hash input files

When Alice send s a file to Bob, she includes a 64-bit hash number with the file.

Protection against random corruption
Little protection againdst evil-doers.

Authentication

RSA encoding scheme is bidirectional.

m^ed = m^de =m

Encrypt the hash

Alice encrypts the hash of the file being sent using Alice's SECRET key.

h = hash(m)
sig = h^d

Bob decrypts it using Alice's PUBLIC KEY:

desig = sig^e = h

ONLY Alice could have encrypted something that could be decrypted using HER public key.

Bob then hashes the file he received [after decrypting it using HIS private key]:

hash_m = hash(m)

And he checks that:

desig = hash_m