Abstract
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.
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- Encryption Scheme
- Homomorphic Encryption
- Cryptology ePrint Archive
- Security Game
- Polynomial Time Adversary
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Koppula, V., Ramchen, K., Waters, B. (2015). Separations in Circular Security for Arbitrary Length Key Cycles. In: Dodis, Y., Nielsen, J.B. (eds) Theory of Cryptography. TCC 2015. Lecture Notes in Computer Science, vol 9015. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46497-7_15
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