Semantic Security and Key-Privacy with Random Split of St-Gen Codes

Recently we have defined Staircase-Generator codes (St-Gen codes) and their variant with a random split of the generator matrix of the codes. One unique property of these codes is that they work with arbitrary error sets. In this paper we give a brief overview of St-Gen codes and the list decoding algorithm for their decoding. We also analyze the semantic security against chosen plaintext attack (IND-CPA) and key-privacy i.e. indistinguishability of public keys under chosen plaintext attack (IK-CPA) of the encryption scheme with random split of St-Gen codes. In a similar manner as it was done by Nojima et al., and later by Yamakawa et al., we show that padding the plaintext with a random bit-string provides IND-CPA and IK-CPA in the standard model. The difference with McEliece scheme is that with our scheme the length of the padded random string is significantly shorter.