There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Data Mining Practical Machine Learning Tools and Techniques

We propose a fully homomorphic encryption scheme -- i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in three steps. First, we provide a general result -- that, to construct an encryption scheme that permits evaluation of arbitrary circuits, it suffices to construct an encryption scheme that can evaluate (slightly augmented versions of) its own decryption circuit; we call a scheme that can evaluate its (augmented) decryption circuit bootstrappable.Next, we describe a public key encryption scheme using ideal lattices that is almost bootstrappable.Lattice-based cryptosystems typically have decryption algorithms with low circuit complexity, often dominated by an inner product computation that is in NC1. Also, ideal lattices provide both additive and multiplicative homomorphisms (modulo a public-key ideal in a polynomial ring that is represented as a lattice), as needed to evaluate general circuits.Unfortunately, our initial scheme is not quite bootstrappable -- i.e., the depth that the scheme can correctly evaluate can be logarithmic in the lattice dimension, just like the depth of the decryption circuit, but the latter is greater than the former. In the final step, we show how to modify the scheme to reduce the depth of the decryption circuit, and thereby obtain a bootstrappable encryption scheme, without reducing the depth that the scheme can evaluate. Abstractly, we accomplish this by enabling the encrypter to start the decryption process, leaving less work for the decrypter, much like the server leaves less work for the decrypter in a server-aided cryptosystem.

/pdf/fully-homomorphic-encryption-using-ideal-lattices-3oirjo0huq.pdf

Fully homomorphic encryption using ideal lattices

In this paper, we define and explore proofs of retrievability (PORs). A POR scheme enables an archive or back-up service (prover) to produce a concise proof that a user (verifier) can retrieve a target file F, that is, that the archive retains and reliably transmits file data sufficient for the user to recover F in its entirety.A POR may be viewed as a kind of cryptographic proof of knowledge (POK), but one specially designed to handle a large file (or bitstring) F. We explore POR protocols here in which the communication costs, number of memory accesses for the prover, and storage requirements of the user (verifier) are small parameters essentially independent of the length of F. In addition to proposing new, practical POR constructions, we explore implementation considerations and optimizations that bear on previously explored, related schemes.In a POR, unlike a POK, neither the prover nor the verifier need actually have knowledge of F. PORs give rise to a new and unusual security definition whose formulation is another contribution of our work.We view PORs as an important tool for semi-trusted online archives. Existing cryptographic techniques help users ensure the privacy and integrity of files they retrieve. It is also natural, however, for users to want to verify that archives do not delete or modify files prior to retrieval. The goal of a POR is to accomplish these checks without users having to download the files themselves. A POR can also provide quality-of-service guarantees, i.e., show that a file is retrievable within a certain time bound.

PORs: Proofs of Retrievability for Large Files

Blockchain is a decentralized transaction and data management technology developed first for Bitcoin cryptocurrency. The interest in Blockchain technology has been increasing since the idea was coined in 2008. The reason for the interest in Blockchain is its central attributes that provide security, anonymity and data integrity without any third party organization in control of the transactions, and therefore it creates interesting research areas, especially from the perspective of technical challenges and limitations. In this research, we have conducted a systematic mapping study with the goal of collecting all relevant research on Blockchain technology. Our objective is to understand the current research topics, challenges and future directions regarding Blockchain technology from the technical perspective. We have extracted 41 primary papers from scientific databases. The results show that focus in over 80% of the papers is on Bitcoin system and less than 20% deals with other Blockchain applications including e.g. smart contracts and licensing. The majority of research is focusing on revealing and improving limitations of Blockchain from privacy and security perspectives, but many of the proposed solutions lack concrete evaluation on their effectiveness. Many other Blockchain scalability related challenges including throughput and latency have been left unstudied. On the basis of this study, recommendations on future research directions are provided for researchers.

/pdf/where-is-current-research-on-blockchain-technology-a-530we6hlvi.pdf

Where Is Current Research on Blockchain Technology?-A Systematic Review.

An algebraic attack is a method for cryptanalysis which is based on finding and solving a system of nonlinear equations Recently, algebraic attacks where found helpful in cryptanalysing LFSR-based stream ciphers The efficiency of these attacks greatly depends on the degree of the nonlinear equations At Crypto 2003, Courtois [8] proposed Fast Algebraic Attacks His main idea is to decrease the degree of the equations using a precomputation algorithm Unfortunately, the correctness of the precomputation step was neither proven, nor was it obvious The three main results of this paper are the following: First, we prove that Courtois' precomputation step is applicable for cryptographically reasonable LFSR-based stream ciphers Second, we present an improved precomputation algorithm Our new precomputation algorithm is parallelisable, in contrast to Courtois' algorithm, and it is more efficient even when running sequentially Third, we demonstrate the improved efficiency of our new algorithm by applying it to the key stream generator E 0 from the Bluetooth standard In this case, we get a theoretical speed-up by a factor of about 8, even without any parallelism This improves the fastest attack known Practical tests confirm the advantage of our new precomputation algorithm for the test cases considered

Improving fast algebraic attacks

Recently, algebraic attacks were proposed to attack several cryptosystems, e.g. AES, LILI-128 and Toyocrypt. This paper extends the use of algebraic attacks to combiners with memory. A (k,l)-combiner consists of k parallel linear feedback shift registers (LFSRs), and the nonlinear filtering is done via a finite automaton with k input bits and l memory bits. It is shown that for (k,l)-combiners, nontrivial canceling relations of degree at most ⌈k(l+1)/2⌉ exist. This makes algebraic attacks possible. Also, a general method is presented to check for such relations with an even lower degree. This allows to show the invulnerability of certain (k,l)-combiners against this kind of algebraic attacks. On the other hand, this can also be used as a tool to find improved algebraic attacks.

/pdf/algebraic-attacks-on-combiners-with-memory-4ha5engnu6.pdf

Algebraic Attacks on Combiners with Memory

An algebraic attack is a method for cryptanalysis which is based on finding and solving a system of nonlinear equations. Recently, algebraic attacks where found helpful in cryptanalysing LFSR-based stream ciphers. The efficiency of these attacks greatly depends on the degree of the nonlinear equations. At Crypto 2003, Courtois [8] proposed Fast Algebraic Attacks. His main idea is to decrease the degree of the equations using a precomputation algorithm. Unfortunately, the correctness of the precomputation step was neither proven, nor was it obvious.

/pdf/improving-fast-algebraic-attacks-408n74r7oc.pdf

Improving Fast Algebraic Attacks

Recently, algebraic attacks were proposed to attack several cryptosystems, e.g. AES, LILI-128 and Toyocrypt. This paper extends the use of algebraic attacks to combiners with memory. A (k,l)-combiner consists of k parallel linear feedback shift registers (LFSRs), and the nonlinear filtering is done via a finite automaton with k input bits and l memory bits. It is shown that for (k, l)-combiners, nontrivial canceling relations of degree at most [k(l+1)/2] exist. This makes algebraic attacks possible. Also, a general method is presented to check for such relations with an even lower degree. This allows to show the invulnerability of certain (k,l)-combiners against this kind of algebraic attacks. On the other hand, this can also be used as a tool to find improved algebraic attacks. Inspired by this method, the E 0 keystream generator from the Bluetooth standard is analyzed. As it turns out, a secret key can be recovered by solving a system of linear equations with 2 23.07 unknowns. To our knowledge, this is the best published attack on the E 0 keystream generator yet.

Algebraic attacks on combiners with memory

Ripple is a payment system and a digital currency which evolved completely independently of Bitcoin. Although Ripple holds the second highest market cap after Bitcoin, there are surprisingly no studies which analyze the provisions of Ripple.

Frederik Armknecht

Papers

Improving fast algebraic attacks

Algebraic Attacks on Combiners with Memory

Improving Fast Algebraic Attacks

Algebraic attacks on combiners with memory

Ripple: Overview and Outlook