We revisit the exact round complexity of secure computation in the multi-party and twoparty settings. For the special case of two-parties without a simultaneous message exchange channel, this question has been extensively studied and resolved. In particular, Katz and Ostrovsky (CRYPTO ’04) proved that five rounds are necessary and sufficient for securely realizing every two-party functionality ...

Privacy amplification is the task by which two cooperating parties transform a shared weak secret, about which an eavesdropper may have side information, into a uniformly random string uncorrelated from the eavesdropper. Privacy amplification against passive adversaries, where it is assumed that the communication is over a public but authenticated channel, can be achieved in the presence of cla...

We introduce a new notion flexible extractor. It is a generalization of the standard concept of a two-source-extractor which require each of a sources to have some entropy, flexible extractor requires the sum of sources entropy to exceed fixed value. We distinguish between a strong and a weak flexible extractors and (similarly to two-source-extractors case) prove that every weak flexible extrac...

The breakthrough result of Chattopadhyay and Zuckerman (2016) gives a reduction from the construction of explicit two-source extractors to the construction of explicit non-malleable extractors. However, even assuming the existence of optimal explicit nonmalleable extractors only gives a two-source extractor (or a Ramsey graph) for poly(logn) entropy, rather than the optimal O (logn). In this pa...

We describe very efficient protocols for non-malleable (interactive) proofs of plaintext knowledge for the RSA, Rabin, Paillier, and El-Gamal encryption schemes whose security can be proven in the standard model. We also highlight some important applications of these protocols, where we take care to ensure that our protocols remain secure when run in an asynchronous, concurrent environment: • C...

In a recent result, Dachman-Soled et al. (TCC ’15) proposed a new notion called locally decodable and updatable non-malleable codes, which informally, provides the security guarantees of a non-malleable code while also allowing for efficient random access. They also considered locally decodable and updatable non-malleable codes that are leakage-resilient, allowing for adversaries who continuall...

Error correcting codes, though powerful, are only applicable in scenarios where the adversarial channel does not introduce “too many” errors into the codewords. Yet, the question of having guarantees even in the face of many errors is well-motivated. Non-malleable codes, introduced by Dziembowski, Pietrzak and Wichs (ICS 2010), address precisely this question. Such codes guarantee that even if ...

M. Abdalla, M. Bellare and P. Rogaway proposed a variation of Diffie-Hellman assumption named as oracle Diffie-Hellman(ODH) assumption. They recommend to use a one-way cryptographic hash function for the ODH assumption. We notice that if the hash function is just one-way then there will be an attack. We show that if the the hash function is non-malleable then the computational version of ODH as...

We show a reduction from explicit two-source extractors with small error and arbitrarily small constant entropy rate to the existence of explicit t-non-malleable extractors with a small seed length. Previously, such a reduction was known either when one source had entropy rate above half [Raz05] or for general entropy rates but only for large error [CZ16]. As in previous reductions we start wit...