# Encryption provably free of trapdoors

The ultimate cipher is one where the only attack open to an opponent is a
brute force attack. Designers of ciphers design their ciphers with this goal
in mind and attackers search for other easier ways to crack the cipher.

Can a cipher be devised such that the only possible means of attack is a
brute force attack? Can a cipher be mathematically proven to have such
security? i.e. Can a cipher be devised that is provably free of trapdoors?

Here is my attempt...

M=XOR(f(R,k1),g(P,k2))

M: ciphertext
P: plaintext
R: true random stream that is as long as P
k1 and k2: keys
f: a one to one transformation function
g: a one to one transformation function
XOR: xor function

Case 1: If R is unknown to the attacker, the algorithm is the equivalent of
the OTP and is secure against even a brute force attack.
Case 2: If R is known but P is unknown to the attacker, his only option is
to perform a brute force attack on k1 and k2.
Case 3: If R and P are known to the attacker, his only option is to perform
a brute force attack on k1 and k2.

A lot has been written on the difficulty of implementing the OTP, so it
would probably not be desirable to attempt to operate under case 1.

The use of R, a true random stream, means that there are no patterns in M so
analysing M by itself would be futile.

The algorithm would potentially be vulnerable to a chosen plaintext attack
(i.e. chosen P or chosen P and R).

Excluding a chosen plaintext attack, the only viable attack would seem to be
a brute force attack.

.

## Relevant Pages

• Re: Encryption provably free of trapdoors
... Can a cipher be mathematically proven to have such ... beginners and wannabe crypto tycoons obsess about it. ... I say use a 64 bit "unbreakable" RSA encryption to encrypt your one time pad ...
(sci.crypt)