Stream cipher based on quasigroup string transformations in Zp∗Z_p^*

In this paper we design a stream cipher that uses the algebraic structure of the multiplicative group \bbbz_p^* (where p is a big prime number used in ElGamal algorithm), by defining a quasigroup of order $p-1$ and by doing quasigroup string transformations. The cryptographical strength of the proposed stream cipher is based on the fact that breaking it would be at least as hard as solving systems of multivariate polynomial equations modulo big prime number $p$ which is NP-hard problem and there are no known fast randomized or deterministic algorithms for solving it. Unlikely the speed of known ciphers that work in \bbbz_p^* for big prime numbers $p$, the speed of this stream cipher both in encryption and decryption phase is comparable with the fastest symmetric-key stream ciphers.Comment: Small revisions and added reference

POPE: Partial Order Preserving Encoding

Recently there has been much interest in performing search queries over encrypted data to enable functionality while protecting sensitive data. One particularly efficient mechanism for executing such queries is order-preserving encryption/encoding (OPE) which results in ciphertexts that preserve the relative order of the underlying plaintexts thus allowing range and comparison queries to be performed directly on ciphertexts. In this paper, we propose an alternative approach to range queries over encrypted data that is optimized to support insert-heavy workloads as are common in "big data" applications while still maintaining search functionality and achieving stronger security. Specifically, we propose a new primitive called partial order preserving encoding (POPE) that achieves ideal OPE security with frequency hiding and also leaves a sizable fraction of the data pairwise incomparable. Using only O(1) persistent and $O(n^\epsilon)$ non-persistent client storage for $0<\epsilon<1$, our POPE scheme provides extremely fast batch insertion consisting of a single round, and efficient search with O(1) amortized cost for up to $O(n^{1-\epsilon})$ search queries. This improved security and performance makes our scheme better suited for today's insert-heavy databases.Comment: Appears in ACM CCS 2016 Proceeding

Affine Determinant Programs: A Framework for Obfuscation and Witness Encryption

An affine determinant program ADP: {0,1}^n &#8594; {0,1} is specified by a tuple (A,B_1,...,B_n) of square matrices over F_q and a function Eval: F_q &#8594; {0,1}, and evaluated on x \in {0,1}^n by computing Eval(det(A + sum_{i \in [n]} x_i B_i)). In this work, we suggest ADPs as a new framework for building general-purpose obfuscation and witness encryption. We provide evidence to suggest that constructions following our ADP-based framework may one day yield secure, practically feasible obfuscation. As a proof-of-concept, we give a candidate ADP-based construction of indistinguishability obfuscation (iO) for all circuits along with a simple witness encryption candidate. We provide cryptanalysis demonstrating that our schemes resist several potential attacks, and leave further cryptanalysis to future work. Lastly, we explore practically feasible applications of our witness encryption candidate, such as public-key encryption with near-optimal key generation

Revisiting Shared Data Protection Against Key Exposure

This paper puts a new light on secure data storage inside distributed systems. Specifically, it revisits computational secret sharing in a situation where the encryption key is exposed to an attacker. It comes with several contributions: First, it defines a security model for encryption schemes, where we ask for additional resilience against exposure of the encryption key. Precisely we ask for (1) indistinguishability of plaintexts under full ciphertext knowledge, (2) indistinguishability for an adversary who learns: the encryption key, plus all but one share of the ciphertext. (2) relaxes the "all-or-nothing" property to a more realistic setting, where the ciphertext is transformed into a number of shares, such that the adversary can't access one of them. (1) asks that, unless the user's key is disclosed, noone else than the user can retrieve information about the plaintext. Second, it introduces a new computationally secure encryption-then-sharing scheme, that protects the data in the previously defined attacker model. It consists in data encryption followed by a linear transformation of the ciphertext, then its fragmentation into shares, along with secret sharing of the randomness used for encryption. The computational overhead in addition to data encryption is reduced by half with respect to state of the art. Third, it provides for the first time cryptographic proofs in this context of key exposure. It emphasizes that the security of our scheme relies only on a simple cryptanalysis resilience assumption for blockciphers in public key mode: indistinguishability from random, of the sequence of diferentials of a random value. Fourth, it provides an alternative scheme relying on the more theoretical random permutation model. It consists in encrypting with sponge functions in duplex mode then, as before, secret-sharing the randomness

Polynomial-Time, Semantically-Secure Encryption Achieving the Secrecy Capacity

In the wiretap channel setting, one aims to get information-theoretic privacy of communicated data based only on the assumption that the channel from sender to receiver is noisier than the one from sender to adversary. The secrecy capacity is the optimal (highest possible) rate of a secure scheme, and the existence of schemes achieving it has been shown. For thirty years the ultimate and unreached goal has been to achieve this optimal rate with a scheme that is polynomial-time. (This means both encryption and decryption are proven polynomial time algorithms.) This paper finally delivers such a scheme. In fact it does more. Our scheme not only meets the classical notion of security from the wiretap literature, called MIS-R (mutual information security for random messages) but achieves the strictly stronger notion of semantic security, thus delivering more in terms of security without loss of rate