International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: On Symmetric Encryption and Point Obfuscation

Ran Canetti
Yael Tauman Kalai
Mayank Varia
Daniel Wichs
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Abstract: We show tight connections between several cryptographic primitives, namely encryption with weakly random keys, encryption with key-dependent messages (KDM), and obfuscation of point functions with multi-bit output(which we call multi-bit point functions, or MBPFs, for short). These primitives, which have been studied mostly separately in recent works, bear some apparent similarities, both in the flavor of their security requirements and in the flavor of their constructions and assumptions. Still, rigorous connections have not been drawn. Our results can be interpreted as indicating that MBPF obfuscators imply a very strong form of encryption that simultaneously achieves security for weakly-random keys and key-dependent messages as special cases. Similarly, each one of the other primitives implies a certain restricted form of MBPF obfuscation. Our results carry both constructions and impossibility results from one primitive to others. In particular: The recent impossibility result for KDM security of Haitner and Holenstein (TCC ’09) carries over to MBPF obfuscators. The Canetti-Dakdouk construction of MBPF obfuscators based on a strong variant of the DDH assumption (EC ’08) gives an encryption scheme which is secure w.r.t. any weak key distribution of super-logarithmic min-entropy (and in particular, also has very strong leakage resilient properties). All the recent constructions of encryption schemes that are secure w.r.t. weak keys imply a weak form of MBPF obfuscators. 
  title={On Symmetric Encryption and Point Obfuscation},
  booktitle={IACR Eprint archive},
  keywords={foundations / Obfuscation, Leakage-Resilience, Key-Dependent Messages, Symmetric-Key Encryption},
  note={Full version of TCC 2010 paper 14640 received 30 Jan 2010},
  author={Ran Canetti and Yael Tauman Kalai and Mayank Varia and Daniel Wichs},