In the era of big data, reducing the computational complexity of servers in data centers will be an important goal. We propose Low Complexity Secure Codes (LCSCs) that are specifically designed to provide information theoretic security in cloud distributed storage systems. Unlike traditional coding schemes that are designed for error correction capabilities, these codes are only designed to provide security with low decoding complexity. These sparse codes are able to provide (asymptotic) perfect secrecy similar to Shannon cipher. The simultaneous promise of low decoding complexity and perfect secrecy make these codes very desirable for cloud storage systems with large amount of data. The design is particularly suitable for large size archival data such as movies and pictures. The complexity of these codes are compared with traditional encryption techniques.
Our final goal is to demonstrate that perfect secrecy as defined by Shannon in @cite_29 can be achieved without any need to store keys. Note that the original approach of Shannon cipher system @cite_29 is not practical since for each bit of information, we need to store one bit of key which practically doubles the storage capacity requirement. We demonstrate that without generating any key, it is feasible to achieve perfect secrecy asymptotically. Since in this work we generate equivalent of key by means of combining of contents together (encoding function), it is clear that this encoding function cannot be shared by Alice with the cloud or Eve. This is one fundamental difference between this work and common problem of wiretap channel. One can consider this as the private key that is generated by Alice to secure the contents and won't be shared with anyone.
@cite_29
2211831180 60616127 2167765756 2140805804
Suppose that Alice wishes to send messages to Bob through a communication channel C1, but her transmissions also reach an eavesdropper Eve through another channel C2. This is the wiretap channel model introduced by Wyner in 1975. The goal is to design a coding scheme that makes it possible for Alice to communicate both reliably and securely. Reliability is measured in terms of Bob's probability of error in recovering the message, while security is measured in terms of the mutual information between the message and Eve's observations. Wyner showed that the situation is characterized by a single constant Cs, called the secrecy capacity, which has the following meaning: for all e >; 0, there exist coding schemes of rate R ≥ Cs-e that asymptotically achieve the reliability and security objectives. However, his proof of this result is based upon a random-coding argument. To date, despite consider able research effort, the only case where we know how to construct coding schemes that achieve secrecy capacity is when Eve's channel C2 is an erasure channel, or a combinatorial variation thereof. Polar codes were recently invented by Arikan; they approach the capacity of symmetric binary-input discrete memoryless channels with low encoding and decoding complexity. In this paper, we use polar codes to construct a coding scheme that achieves the secrecy capacity for a wide range of wiretap channels. Our construction works for any instantiation of the wiretap channel model, as long as both C1 and C2 are symmetric and binary-input, and C2 is degraded with respect to C1. Moreover, we show how to modify our construction in order to provide strong security, in the sense defined by Maurer, while still operating at a rate that approaches the secrecy capacity. In this case, we cannot guarantee that the reliability condition will also be satisfied unless the main channel C1 is noiseless, although we believe it can be always satisfied in practice. Consider the following scenario: Alice and Bob, two parties who share no secret key initially but whose goal it is to generate a (large amount of) information-theoretically secure (or unconditionally secure) shared secret key, are connected only by an insecure public channel to which an eavesdropper Eve has perfect (read) access. Moreover, there exists a satelite broadcasting random bits at a very low signal power. Alice and Bob can receive these bits with certain bit error probabilities ?A and ?B, respectively (e.g. ?A = ?B = 30 ) while Eve is assumed to receive the same bits much more reliably with bit error probability ?E ? ?A, ?B (e.g. ?E = 1 ). The errors on the three channels are assumed to occur at least partially independently. Practical protocols are discussed by which Alice and Bob can generate a secret key despite the facts that Eve possesses more information than both of them and is assumed to have unlimited computational resources as well as complete knowledge of the protocols.The described scenario is a special case of a much more general setup in which Alice, Bob and Eve are assumed to know random variables X, Y and Z jointly distributed according to some probability distribution PXYZ, respectively. The results of this paper suggest to build cryptographic systems that are provably secure against enemies with unlimited computing power under realistic assumptions about the partial independence of the noise on the involved communication channels. Privacy amplification allows two parties Alice and Bob knowing a partially secret string S to extract, by communication over a public channel, a shorter, highly secret string S'. Bennett, Brassard, Crepeau, and Maurer showed that the length of S' can be almost equal to the conditional Renyi entropy of S given an opponent Eve's knowledge. All previous results on privacy amplification assumed that Eve has access to the public channel but is passive or, equivalently, that messages inserted by Eve can be detected by Alice and Bob. In this paper we consider privacy amplification secure even against active opponents. First it is analyzed under what conditions information-theoretically secure authentication is possible even though the common key is only partially secret. This result is used to prove that privacy amplification can be secure against an active opponent and that the size of S' can be almost equal to Eve's min-entropy about S minus 2n 3 if 5 is an n-bit string. Moreover, it is shown that for sufficiently large n privacy amplification is possible when Eve's min-entropy about S exceeds only n 2 rather than 2n 3. We study the question of basing symmetric key cryptography on weak secrets. In this setting, Alice and Bob share an n-bit secret W, which might not be uniformly random, but the adversary has at least k bits of uncertainty about it (formalized using conditional min-entropy). Since standard symmetric-key primitives require uniformly random secret keys, we would like to construct an authenticated key agreement protocol in which Alice and Bob use W to agree on a nearly uniform key R, by communicating over a public channel controlled by an active adversary Eve. We study this question in the information theoretic setting where the attacker is computationally unbounded. We show that single-round (i.e. one message) protocols do not work when k ≤ n 2, and require poor parameters even when n 2 On the other hand, for arbitrary values of k, we design a communication efficient two-round (challenge-response) protocol extracting nearly k random bits. This dramatically improves the previous construction of Renner and Wolf [32], which requires Θ(λ + log(n)) rounds where λ is the security parameter. Our solution takes a new approach by studying and constructing "non-malleable" seeded randomness extractors -- if an attacker sees a random seed X and comes up with an arbitrarily related seed X', then we bound the relationship between R= Ext(W;X) and R' = Ext(W;X'). We also extend our two-round key agreement protocol to the "fuzzy" setting, where Alice and Bob share "close" (but not equal) secrets WA and WB, and to the Bounded Retrieval Model (BRM) where the size of the secret W is huge.