How to construct random functions
Journal of the ACM (JACM)
Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Perfectly one-way probabilistic hash functions (preliminary version)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Towards Realizing Random Oracles: Hash Functions That Hide All Partial Information
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
On obfuscating point functions
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Correcting errors without leaking partial information
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On the Impossibility of Obfuscation with Auxiliary Input
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Obfuscation for cryptographic purposes
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Securely obfuscating re-encryption
TCC'07 Proceedings of the 4th conference on Theory of cryptography
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Transforming private-key encryption schemes into public-key encryption schemes is an interesting application of program obfuscation. The idea is that, given a private-key encryption scheme, an obfuscation of an encryption program with a private key embedded is used as a public key and the private key is used for decryption as it is. The security of the resulting public-key encryption scheme would be ensured because obfuscation is unintelligible and the public key is expected to leak no information on the private key. This paper investigates the possibility of general-purpose obfuscators for such a transformation, i.e., obfuscators that can transform an arbitrary private-key encryption scheme into a secure public-key encryption scheme. Barak et al. have shown a negative result, which says that there is a deterministic private-key encryption scheme that is unobfuscatable in the sense that, given any encryption program with a private key embedded, one can efficiently compute the private key. However, it is an open problem whether their result extends to probabilistic encryption schemes, where we should consider a relaxed notion of obfuscators, i.e., sampling obfuscators. Programs obfuscated by sampling obfuscators do not necessarily compute the same function as the original program, but produce the same distribution as the original program. In this paper, we show that there is a probabilistic private-key encryption scheme that can not be transformed into a secure public-key encryption scheme by sampling obfuscators which have a special property regarding input-output dependency of encryption programs. Our intention is not to claim that the required special property is reasonable. Rather, we claim that general-purpose obfuscators for the transformation, if they exist, must be a sampling obfuscator which does NOT have the special property.