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Efficiently Obfuscating Re-Encryption Program Under DDH Assumption [chapter]

Akshayaram Srinivasan, Chandrasekaran Pandu Rangan
2017 Lecture Notes in Computer Science  
security of our encryption -re-encryption system (in the strengthened model) under the DDH-assumption.  ...  A re-encryption program (or a circuit) transforms a ciphertext encrypted under Alice's public key pk1 to a ciphertext of the same message encrypted under Bob's public key pk2. Hohenberger et al.  ...  We prove the average case secure obfuscator property of our obfuscator and the security of our encryption -re-encryption sustem system under the standard DDH assumption.  ... 
doi:10.1007/978-3-319-61204-1_14 fatcat:2ya3pq33h5boho6f7k7gv52deu

On Strong Simulation and Composable Point Obfuscation [chapter]

Nir Bitansky, Ran Canetti
2010 Lecture Notes in Computer Science  
We show fully composable VGB-obfuscators for point programs under a strong variant of the Decision Diffie Hellman assumption.  ...  The Virtual Black Box (VBB) property for program obfuscators provides a strong guarantee: Anything computable by an efficient adversary given the obfuscated program can also be computed by an efficient  ...  Under a strong Decision Diffie Hellman (DDH) assumption, we show that this obfuscator is t-DI for any polynomial t and hence is a tcomposable VGB obfuscator.  ... 
doi:10.1007/978-3-642-14623-7_28 fatcat:r4i4dcrshjf3nlfq2jwwvqpnua

On Strong Simulation and Composable Point Obfuscation

Nir Bitansky, Ran Canetti
2013 Journal of Cryptology  
We show fully composable VGB-obfuscators for point programs under a strong variant of the Decision Diffie Hellman assumption.  ...  The Virtual Black Box (VBB) property for program obfuscators provides a strong guarantee: Anything computable by an efficient adversary given the obfuscated program can also be computed by an efficient  ...  Under a strong Decision Diffie Hellman (DDH) assumption, we show that this obfuscator is t-DI for any polynomial t and hence is a tcomposable VGB obfuscator.  ... 
doi:10.1007/s00145-013-9146-9 fatcat:blmu5whfmnfcnkyluagyqixt7a

Functional Re-encryption and Collusion-Resistant Obfuscation [chapter]

Nishanth Chandran, Melissa Chase, Vinod Vaikuntanathan
2012 Lecture Notes in Computer Science  
Informally, this functionality, for a public-key encryption scheme and a function F with n possible outputs, transforms ("re-encrypts") an encryption of a message m under an "input public key" pk into  ...  In many settings, one might require that the program implementing the functional re-encryption functionality should reveal nothing about both the input secret key sk as well as the function F .  ...  We wish to thank Markulf Kohlweiss for suggesting the use of the SXDH assumption which simplified our construction.  ... 
doi:10.1007/978-3-642-28914-9_23 fatcat:vsa5brlwnjbgrf3ygme2dw7eky

On Symmetric Encryption and Point Obfuscation [chapter]

Ran Canetti, Yael Tauman Kalai, Mayank Varia, Daniel Wichs
2010 Lecture Notes in Computer Science  
the DDH assumption and the latter under the LWE assumption).  ...  Obfuscators for point functions are constructed in [10, 25] under strong assumptions, and in [21] in the random oracle model.  ...  Under the strengthened DDH assumption, there exists a CPA-secure symmetric encryption scheme with security against fully-weak keys.  ... 
doi:10.1007/978-3-642-11799-2_4 fatcat:eb5ovyugj5e45erl2hzv26atsu

Obfuscating Re-encryption Algorithm With Flexible and Controllable Multi-Hop on Untrusted Outsourcing Server

Mingwu Zhang, Yan Jiang, Yi Mu, Willy Susilo
2017 IEEE Access  
show that the obfuscator is efficient and practical in use.  ...  show that the obfuscator is efficient and practical in use.  ...  From the XMD-DDH assumption, g c 1 and g c 2 are uniformly distributed in G 1 .  ... 
doi:10.1109/access.2017.2771335 fatcat:i2berlgkmvfjlf4nuzujyec2ji

Obfuscation of Hyperplane Membership [chapter]

Ran Canetti, Guy N. Rothblum, Mayank Varia
2010 Lecture Notes in Computer Science  
We prove the security of the obfuscator under a new strong variant of the Decisional Diffie-Hellman assumption.  ...  Previous work on program obfuscation gives strong negative results for general-purpose obfuscators, and positive results for obfuscating simple functions such as equality testing (point functions).  ...  Other formalizations of program obfuscation [3, 4] allow for the obfuscation of cryptographic tasks such as checking proximity to a hidden point [11] , vote mixing [12] , and re-encryption [4] .  ... 
doi:10.1007/978-3-642-11799-2_5 fatcat:dkgqfluipzhidctzssn4rzzowa

Secure Obfuscation for Encrypted Signatures [chapter]

Satoshi Hada
2010 Lecture Notes in Computer Science  
In TCC'07, Hohenberger et al. proposed an obfuscator for a re-encryption functionality, which takes a ciphertext for a message encrypted under Alice's public key and transforms it into a ciphertext for  ...  even when adversaries are given an obfuscated program.  ...  and obfuscator presented in Section 5.4, which are much simpler than my original ones, and Henri Gilbert for helping me to revise the submitted version.  ... 
doi:10.1007/978-3-642-13190-5_5 fatcat:f3eekwswszes3dwrki3y53nowy

Universal Constructions and Robust Combiners for Indistinguishability Obfuscation and Witness Encryption [chapter]

Prabhanjan Ananth, Aayush Jain, Moni Naor, Amit Sahai, Eylon Yogev
2016 Lecture Notes in Computer Science  
In a recent paper, Goldwasser and Kalai posed as a challenge finding universal constructions for indistinguishability obfuscation and witness encryption.  ...  encryption (WE).  ...  Acknowledgements We thank Yuval Ishai for helpful discussions and for bringing to our notice the problem of universal obfuscation.  ... 
doi:10.1007/978-3-662-53008-5_17 fatcat:hodmwzkxl5g47esxgmjuipxzza

Patchable Indistinguishability Obfuscation: $$i\mathcal {O}$$ for Evolving Software [chapter]

Prabhanjan Ananth, Abhishek Jain, Amit Sahai
2017 Lecture Notes in Computer Science  
We show that sub-exponentially secure iO for circuits and sub-exponentially secure re-randomizable encryption schemes (Re-randomizable encryption schemes can be instantiated under standard assumptions  ...  DDH, LWE.) imply single-program patchable indistinguishability obfuscation; and we show that sub-exponentially secure iO for circuits and sub-exponentially secure DDH imply multi-program patchable indistinguishability  ...  Finally, we stress that while the security of iO remains an area of intense study, there are several known iO candidates and even universal iO candidates under well-studied assumptions [3] .  ... 
doi:10.1007/978-3-319-56617-7_5 fatcat:jl267kwoq5bndl3eepdi7nx6xm

Bootstrapping Obfuscators via Fast Pseudorandom Functions [chapter]

Benny Applebaum
2014 Lecture Notes in Computer Science  
Previously, such a bootstrapping procedure was known to exist under the assumption that there exists a fully-homomorphic encryption whose decryption algorithm can be computed in WEAK.  ...  Specifically, under standard intractability assumptions (e.g., hardness of factoring, Decisional Diffie-Hellman, or Learning with Errors), the existence of obfuscators for NC 1 or even TC 0 implies the  ...  First, we claim that, under the above assumption, any efficiently computable function F has an encoding F computable in WEAK.  ... 
doi:10.1007/978-3-662-45608-8_9 fatcat:6hnbeq7h3fabreqblfac2fsddq

Indistinguishability Obfuscation: From Approximate to Exact [chapter]

Nir Bitansky, Vinod Vaikuntanathan
2015 Lecture Notes in Computer Science  
This is achieved based on various types of secure computation protocols that can be obtained from different standard assumptions.  ...  As a step towards our results, which is of independent interest, we also obtain an approximate-to-exact transformation for functional encryption.  ...  Introduction Program obfuscation, the science of making programs "unintelligible" while preserving functionality, has been a holy grail in cryptography for over a decade.  ... 
doi:10.1007/978-3-662-49096-9_4 fatcat:kwblzro4bnhdbdwb6zvrhp4cye

The Magic of ELFs

Mark Zhandry
2018 Journal of Cryptology  
The only known positive example [CCR16] relies on extremely strong cryptographic assumptions such as general-purpose program obfuscation.  ...  Our results are as follows: • (Section 3) We give a practical construction of ELFs assuming the exponential hardness of the decisional Diffie-Hellman (DDH) problem: roughly, that the best attack on DDH  ...  Notice that by injectivity of f , y has a pre-image under H = f • h if and only if z = f −1 (y) has a pre-image under h.  ... 
doi:10.1007/s00145-018-9289-9 fatcat:aox3v4ow5nhf3mohas7dhotopa

The Magic of ELFs [chapter]

Mark Zhandry
2016 Lecture Notes in Computer Science  
The only known positive example [CCR16] relies on extremely strong cryptographic assumptions such as general-purpose program obfuscation.  ...  Our results are as follows: • (Section 3) We give a practical construction of ELFs assuming the exponential hardness of the decisional Diffie-Hellman (DDH) problem: roughly, that the best attack on DDH  ...  Notice that by injectivity of f , y has a pre-image under H = f • h if and only if z = f −1 (y) has a pre-image under h.  ... 
doi:10.1007/978-3-662-53018-4_18 fatcat:xaay2rqylvdalagbnibfol76va

Spooky Encryption and Its Applications [chapter]

Yevgeniy Dodis, Shai Halevi, Ron D. Rothblum, Daniel Wichs
2016 Lecture Notes in Computer Science  
Our first result shows that, under the LWE assumption, there exist encryption schemes supporting a large class of "spooky" relationships, which we call additive function sharing (AFS) spooky.  ...  Our second result shows that, assuming sub-exponentially hard indistinguishability obfuscation (iO) (and additional more standard assumptions), we can remove the common randomness and choose the public  ...  The second author was supported in part by the Defense Advanced Research Projects Agency (DARPA) and Army Research Office(ARO) under Contract No. W911NF-15-C-0236.  ... 
doi:10.1007/978-3-662-53015-3_4 fatcat:oey3p4bthvasnd3bksxsy4imi4
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