We present STeP-archives, a novel and practical data archival architecture, where an attacker who wants to censor or tamper with a data object must cause obvious collateral damage to a large number of other objects in the system. We use maximum distance separable erasure codes to entangle unrelated data blocks and provide redundancy against storage failures, which results in an archive with constant time read-write operations. We show a tradeoff for the attacker between attack complexity, irrecoverability, and collateral damage. We also show that the problem is asymmetric between attackers and defenders; while a defender can efficiently recover from imperfect attacks, an attacker must solve an NP-hard problem to find a perfect (irrecoverable) attack that minimizes collateral damage to other data objects, or even approximate its size. We then study efficient sample-heuristic attack algorithms that lead to irrecoverable but large damage and demonstrate how some strategies and parameter choices allow to resist these sample attacks. Finally, we provide empirical evidence that an attacker who wants to irrecoverably tamper with a document archived long enough must destroy a constant fraction of the archive.

We provide a new family of elliptic curves that results in a one to two percent performance improvement of the elliptic curve integer factorization method. The speedup is confirmed by extensive tests for factors ranging from 15 to 63 bits.

We present STEP-archives, a model for censorship-resistant storage systems where an attacker cannot censor or tamper with data without causing a large amount of obvious collateral damage. MDS erasure codes are used to entangle unrelated data blocks, in addition to providing redundancy against storage failures. We show a tradeoff for the attacker between attack complexity, irrecoverability, and collateral damage. We also show that the system can efficiently recover from attacks with imperfect irrecoverability, making the problem asymmetric between attackers and defenders. Finally, we present sample heuristic attack algorithms that are efficient and irrecoverable (but not collateral-damage-optimal), and demonstrate how some strategies and parameter choices allow to resist these sample attacks.

We present work in progress to completely factor seventeen Mersenne numbers using a variant of the special number field sieve where sieving on the algebraic side is shared among the numbers. It is expected that it reduces the overall factoring effort by more than 50%. As far as we know this is the first practical application of Coppersmith’s “factorization factory” idea. Most factorizations used a new double-product approach that led to additional savings in the matrix step.

This paper describes carry-less arithmetic operations modulo an integer 2^M-1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implementation on a cluster of PlayStation 3 game consoles a new record was set for the elliptic curve method for integer factorization.

At the IPCO VI conference Cornuéjols and Dawande proposed a set of 0-1 linear programming instances that proved to be very hard to solve by traditional methods, and in particular by linear programming-based branch-and-bound. They offered these market split instances as a challenge to the integer programming community. The market split problem can be formulated as a system of linear diophantine equations in 0-1 variables. In our study we use the algorithm of Aardal, Hurkens, and Lenstra (1998) based on lattice basis reduction. This algorithm is not restricted to deal with market split instances only but is a general method for solving systems of linear diophantine equations with bounds on the variables. We show computational results from solving both feasibility and optimization versions of the market split instances with up to 7 equations and 60 variables and discuss various branching strategies and their effect on the number of enumerated nodes. To our knowledge, the largest feasibility and optimization instances solved before had 6 equations and 50 variables, and 4 equations and 30 variables, respectively. We also present a probabilistic analysis describing how to compute the probability of generating infeasible market split instances. By generating instances the way prescribed by Cornuéjols and Dawande, one obtains relatively many feasible instances for sizes larger than 5 equations and 40 variables.

The number field sieve is an algorithm to factor integers of the form r, 4-s for small positive r and s.This note is intended as a 'report on work in progress' on this algorithm.We informally describe the algorithm, discuss several implementation related aspects, and present some of the factorizations obtained so far.We also mention some solutions to the problems encountered when generalizing the algorithm to general integers using an idea of Buhler and Pomerance.It is not unlikely that this leads to a general purpose factoring algorithm that is asymptotically substantially faster than the fastest factoring algorithms known so far, like the multiple polynomial quadratic sieve.

We present an algorithm to factor multivariate polynomials over algebraic number fields that is polynomial-time in the degrees of the polynomial to be factored. The algorithm is an immediate generalization of the polynomial-time algorithm to factor univariate polynomials with rational coefficients.

It is shown that the binary expansions of algebraic numbers do not form secure pseudorandom sequences, given sufficiently many initial bits of an algebraic number, its minimal polynomial can be reconstructed, and therefore the further bits of the algebraic number can be computed. This also enables the authors to devise a simple algorithm to factorise polynomials with rational coefficients. All algorithms work in polynomial time

This paper describes an algorithm for the factorization of multivariate polynomials with coefficients in a finite field that is polynomial-time in the degrees of the polynomial to be factored. The algorithm makes use of a new basis reduction algorithm for lattices over IFq.