A Practical Key Recovery Attack on Basic TCHo

Abstract

TCHo is a public key encryption scheme based on a stream cipher component, which is particular suitable for low cost devices like RFIDs. In its basic version, TCHo offers no IND-CCA2 security, but the authors suggest to use a generic hybrid construction to achieve this security level. The implementation of this method however, significantly increases the hardware complexity of TCHo and thus annihilates the advantage of being suitable for low cost devices. In this paper we show, that TCHo cannot be used without this construction. We present a chosen ciphertext attack on basic TCHo that recovers the secret key after approximately d 3/2 decryptions, where d is the number of bits of the secret key polynomial. The entropy of the secret key is $\log_2\binom{d}{w}$ , where w is the weight of the secret key polynomial, and w is usually small compared to d. In particular, we can break all of the parameters proposed for TCHo within hours on a standard PC.