Glendinning and Sidorov discovered an important feature of the Komornik-Loreti constant q ≈ 1.787... more Glendinning and Sidorov discovered an important feature of the Komornik-Loreti constant q ≈ 1.78723 in non-integer base expansions on two-letter alphabets: in bases 1 < q < q only countably numbers have unique expansions, while for q ≥ q there is a continuum of such numbers. We investigate the analogous question for ternary alphabets.
Electronic Notes in Theoretical Computer Science, 1996
Last works in linear logic mark a trend that can be summarized as: studying of fragments of calcu... more Last works in linear logic mark a trend that can be summarized as: studying of fragments of calculi which have good logical properties and a quite powerful class of representable functions. ELL is a system derived from linear logic which presents several of such good properties: first ...
In this article we present the implementation of an environment supporting Lévy's optimal reducti... more In this article we present the implementation of an environment supporting Lévy's optimal reduction for the λ-calculus [Lév78] on parallel (or distributed) computing systems. In a similar approach to Lamping's one in [Lam90], we base our work on a graph reduction technique known as directed virtual reduction [DPR97] which is actually a restriction of Danos-Regnier virtual reduction . The environment, which we refer to as PELCR (Parallel Environment for optimal Lambda-Calculus Reduction) relies on a strategy for directed virtual reduction, namely half combustion. While developing PELCR we have adopted both a message aggregation technique, allowing a reduction of the communication overhead, and a fair policy for distributing dynamically originated load among processors. Additionally, we have used a set of other optimizations, e.g. allowing the maintenance of relatively low size for the manipulated data structures so not to incur problems related to their management at the application level or due to the management of large process memory images at the operating system level. We also present an experimental study demonstrating the ability of PELCR to definitely exploit parallelism intrinsic to λ-terms while performing the reduction. We show how PELCR allows achieving up to 70/80% of the ideal speedup on last generation multiprocessor computing systems. As a last note, the software modules have been developed with the C language and using a standard interface for message passing, i.e. MPI, thus making PELCR itself a highly portable software package.
Expansions in noninteger bases often appear in number theory and probability theory, and they are... more Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases in function of the alphabets.
What we will do in this thesis is to consider a particular class of ciphers and put ourselves in ... more What we will do in this thesis is to consider a particular class of ciphers and put ourselves in the shoes of an attacker, to try to understand how many informations are achievable about the cipher and the original message, with the knowledge of the only material available in quite big quantity: ciphertext.
Istituto Per Le Applicazioni Del Calcolo “M. Picone ”- CNR and
Abstract. In this article we present the implementation of an environment supporting Lévy’s optim... more Abstract. In this article we present the implementation of an environment supporting Lévy’s optimal reduction for the λ-calculus [Lév78] on parallel (or distributed) computing systems. In a similar approach to Lamping’s one in [Lam90], we base our work on a graph reduction technique known as directed virtual reduction [DPR97] which is actually a restriction of Danos-Regnier virtual reduction [DR93]. The environment, which we refer to as PELCR (Parallel Environment for optimal Lambda-Calculus Reduction) relies on a strategy for directed virtual reduction, namely half combustion, which we introduce in this article. While developing PELCR we have adopted both a message aggregation technique, allowing a reduction of the communication overhead, and a fair policy for distributing dynamically originated load among processors. Additionally, we have used a set of other optimizations, e.g. allowing the maintenance of relatively low size for the manipulated data structures so not to incur prob...
Applicable Algebra in Engineering, Communication and Computing
Algebraic Cryptanalysis is a widely used technique that tackles the problem of breaking ciphers m... more Algebraic Cryptanalysis is a widely used technique that tackles the problem of breaking ciphers mainly relying on the ability to express a cryptosystem as a solvable polynomial system. Each output bit/word can be expressed as a polynomial equation in the cipher’s inputs—namely the key and the plaintext or the initialisation vector bits/words. A part of research in this area consists in finding suitable algebraic structures where polynomial systems can be effectively solved, e.g., by computing Gröbner bases. In 2009, Dinur and Shamir proposed the cube attack, a chosen plaintext algebraic cryptanalysis technique for the offline acquisition of an equivalent system by means of monomial reduction; interpolation on cubes in the space of variables enables retrieving a linear polynomial system, hence making it exploitable in the online phase to recover the secret key. Since its introduction, this attack has received both many criticisms and endorsements from the crypto community; this work ...
IEEE/ACM Transactions on Computational Biology and Bioinformatics
Drug repurposing is a highly active research area, aiming at finding novel uses for drugs that ha... more Drug repurposing is a highly active research area, aiming at finding novel uses for drugs that have been previously developed for other therapeutic purposes. Despite the flourishing of methodologies, success is still partial, and different approaches offer, each, peculiar advantages. In this composite landscape, we present a novel methodology focusing on an efficient mathematical procedure based on gene similarity scores and biased random walks which rely on robust drug-gene-disease association data sets. The recommendation mechanism is further unveiled by means of the Markov chain underlying the random walk process, hence providing explainability about how findings are suggested. Performances evaluation and the analysis of a case study on rheumatoid arthritis show that our approach is accurate in providing useful recommendations and is computationally efficient, compared to the state of the art of drug repurposing approaches.
In 2009, Dinur and Shamir proposed the cube attack, an algebraic cryptanalysis technique that onl... more In 2009, Dinur and Shamir proposed the cube attack, an algebraic cryptanalysis technique that only requires black box access to a target cipher. Since then, this attack has received both many criticisms and endorsements from crypto community; this work aims at revising and collecting the many attacks that have been proposed starting from it. We categorise all of these attacks in five classes; for each class, we provide a brief summary description along with the state-of-the-art references and the most recent cryptanalysis results. Furthermore, we extend and refine the new notation we proposed in 2021 and we use it to provide a consistent definition for each attack family. Finally, in the appendix, we provide an in-depth description of the kite attack framework, a cipher independent tool we firstly proposed in 2018 that implements the kite attack on GPUs. To prove its effectiveness, we use Mickey2.0 as a use case, showing how to embed it in the framework.
Computational biology aims at disentangling the complexity of biological phenomena by providing t... more Computational biology aims at disentangling the complexity of biological phenomena by providing tools/algorithms to analyse experimental data or models to predict outcomes of the biological system based on experimental and clinical data. Bioinformatics tools are used to analyse and interpret large scale experimental data and to distil useful information necessary to set up mathematical/computational models. In turn, computational models replicate the dynamics of complex biological systems thus offering in silico evaluations of a hypothesis. Models can be used to predict changes in the behaviour of a system over time and further unravel the complexity of the phenomena under study. Together, these methodologies have the potential to reshape our understanding of biology at all levels of details eventually allowing the optimization of existing therapies or even the formulation of new ones. In this article, we present succinct and informal descriptions of the main approaches or framework...
In this paper, we show how a construction of an implicit complexity model can be implemented usin... more In this paper, we show how a construction of an implicit complexity model can be implemented using concepts coming from the core of von Neumann algebras. Namely, our aim is to gain an understanding of classical computation in terms of the hyperfinite II 1 factor, starting from the class of Kalmar recursive functions. More methodologically, we address the problem of finding the right perspective from which to view the new relation between computation and combinatorial aspects in operator algebras. The rich structure of discrete invariants may provide a mathematical setting able to shed light on some basic combinatorial phenomena that are at the basis of our understanding of complexity.
Dinur and Shamir's cube attack has attracted significant attention in the literature. Nevertheles... more Dinur and Shamir's cube attack has attracted significant attention in the literature. Nevertheless, the lack of implementations achieving effective results casts doubts on its practical relevance. On the theoretical side, promising results have been recently achieved leveraging on division trails. The present paper follows a more practical approach and aims at giving new impetus to this line of research by means of a cipher-independent flexible framework that is able to carry out the cube attack on GPU/CPU clusters. We address all issues posed by a GPU implementation, providing evidence in support of parallel variants of the attack and identifying viable directions for solving open problems in the future. We report the results of running our GPU-based cube attack against round-reduced versions of three well-known ciphers: Trivium, Grain-128 and SNOW 3G. Our attack against Trivium improves the state of the art, permitting full key recovery for Trivium reduced to (up to) 781 initialization rounds (out of 1152) and finding the first-ever maxterm after 800 rounds. In this paper, we also present the first standard cube attack (i.e., neither dynamic nor tester) to yield maxterms for Grain-128 up to 160 initialization rounds on non-programmable hardware. We include a thorough evaluation of the impact of system parameters and GPU architecture on the performance. Moreover, we demonstrate the scalability of our solution on multi-GPU systems. We believe that our extensive set of results can be useful for the cryptographic engineering community at large and can pave the way to further results in the area. Keywords Cube attack • Algebraic attacks • Graphics processing unit 1 Introduction The cube attack is a chosen-plaintext attack in which linear equations binding key bits are extracted through exhaustive searches over selected public/I V bits-the edges of the B Marco Cianfriglia
In this paper, we propose and explore a new approach to abstract machines and optimal reduction v... more In this paper, we propose and explore a new approach to abstract machines and optimal reduction via streams, infinite sequences of elements. We first define a sequential abstract machine capable of performing directed virtual reduction (DVR) and then we extend it to its parallel version, whose equivalence is explained through the properties of DVR itself. The result is a formal definition of the λ-calculus interpreter called Parallel Environment for Lambda Calculus Reduction (PELCR), a software for λ-calculus reduction based on the Geometry of Interaction. In particular, we describe PELCR as a stream-processing abstract machine, which in principle can also be applied to infinite streams.
Glendinning and Sidorov discovered an important feature of the Komornik-Loreti constant q ≈ 1.787... more Glendinning and Sidorov discovered an important feature of the Komornik-Loreti constant q ≈ 1.78723 in non-integer base expansions on two-letter alphabets: in bases 1 < q < q only countably numbers have unique expansions, while for q ≥ q there is a continuum of such numbers. We investigate the analogous question for ternary alphabets.
Electronic Notes in Theoretical Computer Science, 1996
Last works in linear logic mark a trend that can be summarized as: studying of fragments of calcu... more Last works in linear logic mark a trend that can be summarized as: studying of fragments of calculi which have good logical properties and a quite powerful class of representable functions. ELL is a system derived from linear logic which presents several of such good properties: first ...
In this article we present the implementation of an environment supporting Lévy's optimal reducti... more In this article we present the implementation of an environment supporting Lévy's optimal reduction for the λ-calculus [Lév78] on parallel (or distributed) computing systems. In a similar approach to Lamping's one in [Lam90], we base our work on a graph reduction technique known as directed virtual reduction [DPR97] which is actually a restriction of Danos-Regnier virtual reduction . The environment, which we refer to as PELCR (Parallel Environment for optimal Lambda-Calculus Reduction) relies on a strategy for directed virtual reduction, namely half combustion. While developing PELCR we have adopted both a message aggregation technique, allowing a reduction of the communication overhead, and a fair policy for distributing dynamically originated load among processors. Additionally, we have used a set of other optimizations, e.g. allowing the maintenance of relatively low size for the manipulated data structures so not to incur problems related to their management at the application level or due to the management of large process memory images at the operating system level. We also present an experimental study demonstrating the ability of PELCR to definitely exploit parallelism intrinsic to λ-terms while performing the reduction. We show how PELCR allows achieving up to 70/80% of the ideal speedup on last generation multiprocessor computing systems. As a last note, the software modules have been developed with the C language and using a standard interface for message passing, i.e. MPI, thus making PELCR itself a highly portable software package.
Expansions in noninteger bases often appear in number theory and probability theory, and they are... more Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases in function of the alphabets.
What we will do in this thesis is to consider a particular class of ciphers and put ourselves in ... more What we will do in this thesis is to consider a particular class of ciphers and put ourselves in the shoes of an attacker, to try to understand how many informations are achievable about the cipher and the original message, with the knowledge of the only material available in quite big quantity: ciphertext.
Istituto Per Le Applicazioni Del Calcolo “M. Picone ”- CNR and
Abstract. In this article we present the implementation of an environment supporting Lévy’s optim... more Abstract. In this article we present the implementation of an environment supporting Lévy’s optimal reduction for the λ-calculus [Lév78] on parallel (or distributed) computing systems. In a similar approach to Lamping’s one in [Lam90], we base our work on a graph reduction technique known as directed virtual reduction [DPR97] which is actually a restriction of Danos-Regnier virtual reduction [DR93]. The environment, which we refer to as PELCR (Parallel Environment for optimal Lambda-Calculus Reduction) relies on a strategy for directed virtual reduction, namely half combustion, which we introduce in this article. While developing PELCR we have adopted both a message aggregation technique, allowing a reduction of the communication overhead, and a fair policy for distributing dynamically originated load among processors. Additionally, we have used a set of other optimizations, e.g. allowing the maintenance of relatively low size for the manipulated data structures so not to incur prob...
Applicable Algebra in Engineering, Communication and Computing
Algebraic Cryptanalysis is a widely used technique that tackles the problem of breaking ciphers m... more Algebraic Cryptanalysis is a widely used technique that tackles the problem of breaking ciphers mainly relying on the ability to express a cryptosystem as a solvable polynomial system. Each output bit/word can be expressed as a polynomial equation in the cipher’s inputs—namely the key and the plaintext or the initialisation vector bits/words. A part of research in this area consists in finding suitable algebraic structures where polynomial systems can be effectively solved, e.g., by computing Gröbner bases. In 2009, Dinur and Shamir proposed the cube attack, a chosen plaintext algebraic cryptanalysis technique for the offline acquisition of an equivalent system by means of monomial reduction; interpolation on cubes in the space of variables enables retrieving a linear polynomial system, hence making it exploitable in the online phase to recover the secret key. Since its introduction, this attack has received both many criticisms and endorsements from the crypto community; this work ...
IEEE/ACM Transactions on Computational Biology and Bioinformatics
Drug repurposing is a highly active research area, aiming at finding novel uses for drugs that ha... more Drug repurposing is a highly active research area, aiming at finding novel uses for drugs that have been previously developed for other therapeutic purposes. Despite the flourishing of methodologies, success is still partial, and different approaches offer, each, peculiar advantages. In this composite landscape, we present a novel methodology focusing on an efficient mathematical procedure based on gene similarity scores and biased random walks which rely on robust drug-gene-disease association data sets. The recommendation mechanism is further unveiled by means of the Markov chain underlying the random walk process, hence providing explainability about how findings are suggested. Performances evaluation and the analysis of a case study on rheumatoid arthritis show that our approach is accurate in providing useful recommendations and is computationally efficient, compared to the state of the art of drug repurposing approaches.
In 2009, Dinur and Shamir proposed the cube attack, an algebraic cryptanalysis technique that onl... more In 2009, Dinur and Shamir proposed the cube attack, an algebraic cryptanalysis technique that only requires black box access to a target cipher. Since then, this attack has received both many criticisms and endorsements from crypto community; this work aims at revising and collecting the many attacks that have been proposed starting from it. We categorise all of these attacks in five classes; for each class, we provide a brief summary description along with the state-of-the-art references and the most recent cryptanalysis results. Furthermore, we extend and refine the new notation we proposed in 2021 and we use it to provide a consistent definition for each attack family. Finally, in the appendix, we provide an in-depth description of the kite attack framework, a cipher independent tool we firstly proposed in 2018 that implements the kite attack on GPUs. To prove its effectiveness, we use Mickey2.0 as a use case, showing how to embed it in the framework.
Computational biology aims at disentangling the complexity of biological phenomena by providing t... more Computational biology aims at disentangling the complexity of biological phenomena by providing tools/algorithms to analyse experimental data or models to predict outcomes of the biological system based on experimental and clinical data. Bioinformatics tools are used to analyse and interpret large scale experimental data and to distil useful information necessary to set up mathematical/computational models. In turn, computational models replicate the dynamics of complex biological systems thus offering in silico evaluations of a hypothesis. Models can be used to predict changes in the behaviour of a system over time and further unravel the complexity of the phenomena under study. Together, these methodologies have the potential to reshape our understanding of biology at all levels of details eventually allowing the optimization of existing therapies or even the formulation of new ones. In this article, we present succinct and informal descriptions of the main approaches or framework...
In this paper, we show how a construction of an implicit complexity model can be implemented usin... more In this paper, we show how a construction of an implicit complexity model can be implemented using concepts coming from the core of von Neumann algebras. Namely, our aim is to gain an understanding of classical computation in terms of the hyperfinite II 1 factor, starting from the class of Kalmar recursive functions. More methodologically, we address the problem of finding the right perspective from which to view the new relation between computation and combinatorial aspects in operator algebras. The rich structure of discrete invariants may provide a mathematical setting able to shed light on some basic combinatorial phenomena that are at the basis of our understanding of complexity.
Dinur and Shamir's cube attack has attracted significant attention in the literature. Nevertheles... more Dinur and Shamir's cube attack has attracted significant attention in the literature. Nevertheless, the lack of implementations achieving effective results casts doubts on its practical relevance. On the theoretical side, promising results have been recently achieved leveraging on division trails. The present paper follows a more practical approach and aims at giving new impetus to this line of research by means of a cipher-independent flexible framework that is able to carry out the cube attack on GPU/CPU clusters. We address all issues posed by a GPU implementation, providing evidence in support of parallel variants of the attack and identifying viable directions for solving open problems in the future. We report the results of running our GPU-based cube attack against round-reduced versions of three well-known ciphers: Trivium, Grain-128 and SNOW 3G. Our attack against Trivium improves the state of the art, permitting full key recovery for Trivium reduced to (up to) 781 initialization rounds (out of 1152) and finding the first-ever maxterm after 800 rounds. In this paper, we also present the first standard cube attack (i.e., neither dynamic nor tester) to yield maxterms for Grain-128 up to 160 initialization rounds on non-programmable hardware. We include a thorough evaluation of the impact of system parameters and GPU architecture on the performance. Moreover, we demonstrate the scalability of our solution on multi-GPU systems. We believe that our extensive set of results can be useful for the cryptographic engineering community at large and can pave the way to further results in the area. Keywords Cube attack • Algebraic attacks • Graphics processing unit 1 Introduction The cube attack is a chosen-plaintext attack in which linear equations binding key bits are extracted through exhaustive searches over selected public/I V bits-the edges of the B Marco Cianfriglia
In this paper, we propose and explore a new approach to abstract machines and optimal reduction v... more In this paper, we propose and explore a new approach to abstract machines and optimal reduction via streams, infinite sequences of elements. We first define a sequential abstract machine capable of performing directed virtual reduction (DVR) and then we extend it to its parallel version, whose equivalence is explained through the properties of DVR itself. The result is a formal definition of the λ-calculus interpreter called Parallel Environment for Lambda Calculus Reduction (PELCR), a software for λ-calculus reduction based on the Geometry of Interaction. In particular, we describe PELCR as a stream-processing abstract machine, which in principle can also be applied to infinite streams.
Uploads
Papers by Marco Pedicini