Separations in circular security for arbitrary length key cycles

While standard notions of security suffice to protect any message supplied by an adversary, in some situations stronger notions of security are required. One such notion is n-circular security, where ciphertexts Enc(pk₁, sk₂), Enc(pk₂, sk₃), . . . , Enc(pk_n, sk₁) should be indistinguishable from encryptions of zero. In this work we prove the following results for n-circular security, based upon recent candidate constructions of indistinguishability obfuscation [18,16] and one way functions: For any n there exists an encryption scheme that is IND-CPA secure but not n-circular secure. There exists a bit encryption scheme that is IND-CPA secure, but not 1-circular secure. If there exists an encryption system where an attacker can distinguish a key encryption cycle from an encryption of zeroes, then in a transformed cryptosystem there exists an attacker which recovers secret keys from the encryption cycles. The last result is generic and applies to any such cryptosystem.