Papers by Juan Pedro Hecht
Computer Networks and Communications , 2025
Post-quantum cryptography is essential for securing digital communications against threats posed... more Post-quantum cryptography is essential for securing digital communications against threats posed by quantum computers. Researchers have focused on developing algorithms that can withstand attacks from both classical and quantum computers, thereby ensuring the security of data transmissions over public networks. A critical component of this security is the key agreement protocol, which allows two parties to establish a shared secret key over an insecure channel. This paper introduces two novel post-quantum key agreement protocols that can be easily implemented on standard computers using rectangular or rank-deficient matrices, exploiting the generalizations of the matrix power function, which is a generator of NP-hard problems. We provide basic concepts and proofs, pseudocodes, examples, and a discussion of complexity.
Journal of health science, Apr 28, 2019
Leptospirosis is a disease of worldwide distribution caused by spirochetes of the genus Leptospir... more Leptospirosis is a disease of worldwide distribution caused by spirochetes of the genus Leptospira. Rodents have been recognized as the most important and most widely distributed reservoirs of leptospirosis. In different regions of the world, there are outbreaks of leptospirosis that have a seasonal distribution and coincide with the rainy months. One way to study the spread of epidemics is through mathematical models. In the present work, the objective of the authors was to develop and explore a model of leptospirosis outbreak, combining the dynamics of propagation in human population with the dynamics of transmission from rodent reservoirs to humans. The authors designed a deterministic model based on differential equations. The dynamics of the model were explored through computational simulations. The typical evolution of prevalence observed in the model, qualitatively coincides with the dynamics of actual leptospirosis outbreaks. In the model, the peak prevalence was reduced when the transmission parameter and the number of rodents decreased, and when the lepospira decay rate increased. These results coincide with what was expected. The present development could be considered as a starting point for the generation of a more complex design.
Theoretical and Applied Informatics, Dec 12, 2017
Post-Quantum Cryptography (PQC) attempts to find cryptographic protocols resistant to attacks by ... more Post-Quantum Cryptography (PQC) attempts to find cryptographic protocols resistant to attacks by means of for instance Shor's polynomial time algorithm for numerical field problems like integer factorization (IFP) or the discrete logarithm (DLP). Other aspects are the backdoors discovered in deterministic random generators or recent advances in solving some instances of DLP. The use of alternative algebraic structures like non-commutative or non-associative partial groupoids, magmas, monoids, semigroups, quasigroups or groups, are valid choices for these new kinds of protocols. In this paper, we focus in an asymmetric cipher based on a generalized ElGamal non-arbitrated protocol using a non-commutative general linear group. The developed protocol forces a hard subgroup membership search problem into a non-commutative structure. The protocol involves at first a generalized Diffie-Hellman key interchange and further on the private and public parameters are recursively updated each time a new cipher session is launched. Security is based on a hard variation of the Generalized Symmetric Decomposition Problem (GSDP). Working with GF (251 8) a 64-bits security is achieved, and if GF (251 16) is chosen, the security rises to 127-bits. An appealing feature is that there is no need for big number libraries as all arithmetic if performed in Z 251 and therefore the new protocol is particularly useful for computational platforms with very limited capabilities like smartphones or smartcards.
arXiv (Cornell University), Mar 21, 2023
We present an improved post-quantum version of Sakalauskas matrix power function key agreement pr... more We present an improved post-quantum version of Sakalauskas matrix power function key agreement protocol, using rectangular matrices instead of the original square ones. Sakalauskas matrix power function is an efficient and secure way to generate a shared secret key, and using rectangular matrices provides additional flexibility and security. This method reduces the computational complexity by allowing smaller random integer matrices while maintaining a high level of security. We don't rely on matrices with special formatting to achieve commutativity; instead, we use full random values on those structures, increasing their entropy. Another advantage of using rectangular matrices over key agreement protocols is that they offer better protection against various linearization attacks.
arXiv (Cornell University), Jun 3, 2022
Although previous infection and vaccination provide protection against SARS-CoV-2 infection, both... more Although previous infection and vaccination provide protection against SARS-CoV-2 infection, both reinfection and breakthrough infection are possible events whose occurrence would increase with time after first exposure to the antigen and with the emergence of new variants of the virus. Periodic vaccination could counteract this decline in protection. In the present work, our aim was to develop and explore a model of SARS-CoV-2 spread with vaccination, reinfection and breakthrough infection. A modified deterministic SIS (Susceptible-Infected-Susceptible) model represented by a system of differential equations was designed. As in any SIS model, the population was divided into susceptible and infected individuals. But in our design, susceptible individuals were, in turn, grouped into three consecutive categories whose susceptibility increases with time after infection or vaccination. The model was studied by means of computer simulations, which were analysed qualitatively. The results obtained show that the prevalence, after oscillating between peaks and valleys, reaches a plateau phase. Moreover, as might be expected, the magnitude of the peaks and plateaus increases as the infection rate rises, the vaccination rate decreases and the rate of decay of protection conferred by vaccination or previous infection increases. Therefore, the present study suggests that, at least under certain conditions, the spread of SARS-CoV-2, although it could experience fluctuations, would finally evolve into an endemic form, with a more or less stable prevalence that would depend on the levels of infection and vaccination, and on the kinetics of post-infection and post-vaccination protection. However, it should be kept in mind that our development is a theoretical scheme with many limitations. For this reason, its predictions should be considered with great care.
Resistencia a la torsión de los instrumentos endodónticos PathFile sometidos a fatiga cíclica
Rev. Asoc. Odontol. Argent, 2014
Journal of Life Sciences, 2016
The aim of this study was to develop and explore a stochastic lattice gas cellular automata (LGCA... more The aim of this study was to develop and explore a stochastic lattice gas cellular automata (LGCA) model for epidemics. A computer program was development in order to implement the model. An irregular grid of cells was used. A susceptible-infected-recovered (SIR) scheme was represented. Stochasticity was generated by Monte Carlo method. Dynamics of model was explored by numerical simulations. Model achieves to represent the typical SIR prevalence curve. Performed simulations also show how infection, mobility and distribution of infected individuals may influence the dynamics of propagation. This simple theoretical model might be a basis for developing more realistic designs.
Alteraciones morfológicas en instrumentos endodónticos rotatorios ante la fatiga cíclica
Rev Asoc Odontol Argent, Dec 1, 2013
“Criptografía no conmutativa usando un grupo general lineal de orden primo de Mersenne”
Resumen—este trabajo presenta un protocolo de cifrado seguro y compacto basado en el grupo genera... more Resumen—este trabajo presenta un protocolo de cifrado seguro y compacto basado en el grupo general lineal GL (d, F2) donde d es un exponente primo de Mersenne tal que 2^d-1 también es primo. Por compacto queremos significar que solo usa álgebra Booleana que puede ser implementada en plataformas de escasos recursos como procesadores de 8 y 16 bits. El aspecto atrayente de este enfoque es que para este tipo de primitivas algebraicas no conmutativas, se desconocen ataques de complejidad en tiempo sub exponencial ni algoritmos cuánticos como ocurre en los tradicionales campos numéricos. En GL (d, F2), toda matriz cuyo polinomio característico sea irreducible es generadora de un subgrupo multiplicativo cíclico Md de orden (2^d-1) del grupo GL (d, F2). Para desarrollar un protocolo de cifrado de clave pública, se usa como función trampa de una vía el problema de búsqueda del conjugador (CSP) en Md el que por ahora es de complejidad NP. Si d fuese suficientemente grande (como ser 89), la b...
Determination of the specific rate constants for the phagocytosis of radiogold colloids by the reticuloendothelial system in the rat
International Journal of Nuclear Medicine and Biology, 1984
ABSTRACT Previous works demonstrated that the phagocytosis of radiogold colloidal particles follo... more ABSTRACT Previous works demonstrated that the phagocytosis of radiogold colloidal particles follows Michaelis-Menten kinetics and that the process can be visualized as a two-stage phenomenon, consisting in the adsorption of the colloidal particle on the reticuloendothelial cell's surface and its posterior engulfment. Each stage is accounted for by the specific rate constants k1 and k2, respectively. Heretofore it was only possible to determine and the maximal rate of phagocytosis, Vm. In the present work we propose a relatively simple method for the determination of k1, which allows the calculation of k2 and the number of active adsorption “loci” per kg body, (R). The comparison of the kinetic data for the gelatine or polyvinylpyrrolidone protected radiogold colloids shows that the corresponding (R) values are not significantly different. Therefore, the differences between the respective Ks and Vm values should be attributed to changes of k1 and principally of k2.Our method and experimental results allow a deeper comprehension of the phenomenon of phagocytosis, which will be useful for the study of the influence of immunomodulating drugs on either stage of this process.
arXiv (Cornell University), Feb 19, 2020
Post-Quantum Cryptography (PQC) attempts to find cryptographic protocols resistant to attacks usi... more Post-Quantum Cryptography (PQC) attempts to find cryptographic protocols resistant to attacks using Shor's polynomial time algorithm for numerical field problems or Grover's algorithm to find the unique input to a black-box function that produces a particular output value. The use of nonstandard algebraic structures like non-commutative or nonassociative structures, combined with one-way trapdoor functions derived from combinatorial group theory, are mainly unexplored choices for these new kinds of protocols and overlooked in current PQC solutions. In this paper, we develop an algebraic extension ring framework who could be applied to different asymmetric protocols (i.e. key exchange, key transport, enciphering, digital signature, zero-knowledge authentication, oblivious transfer, secret sharing etc.). A valuable feature is that there is no need for big number libraries as all arithmetic is performed in extension field operations (precisely the AES field). We assume that the new framework is cryptographical secure against strong classical attacks like the sometimes-useful length-based attack, Roman'kov's linearization attacks and Tsaban's algebraic span attack. This statement is based on the non-linear structure of the selected platform which proved to be useful protecting the AES protocol. Otherwise, it could resist post-quantum attacks (Grover, Shor) and be particularly useful for computational platforms with limited capabilities like USB cryptographic keys or smartcards. Semantic security (IND-CCA2) could also be inferred for this new platform.
PQC: Elgamal GF(251^8) Benchmark
Theoretical and Applied Informatics, Dec 12, 2017
PQC: Elgamal GF(251^8) Cipher Sample
Theoretical and Applied Informatics, Dec 12, 2017
CIBSI-TIBETS-20_paper_2-v2.pdf
<i>Abstract—</i>Shor's quantum numerical field algorithm or Grover's quantum ... more <i>Abstract—</i>Shor's quantum numerical field algorithm or Grover's quantum search algorithm promoted the development of Post-Quantum Cryptography (PQC), an attempt to find cryptographic protocols resistant to quantum attacks. NIST is currently searching future standards of this kind. A mostly overlooked but valuable line of solutions, not present into the proposed PQC solutions (as for the 2nd standardization search round, 2019), is provided by non-commutative algebraic structures, specifically canonical protocols that rely on one-way trapdoor functions (OWTF). The canonical trapdoor one-way function here selected is a fortified version of the Triple Decomposition Problem (TDP) developed by Kurt. The original protocol relies on two linear and one quadratic algebraic public equation. An Algebraic Span Attack (ASA) developed by Tsaban, focus on the linear equations, and as claimed, provides a successful attack on the original TDP protocol. As a strong countermeasure, we present an evolved and almost symmetrically designed full non-linear version. This is accomplished transforming those linear equations into quadratic ones (XTDP) and the same is accomplished for public exchanged tokens between any entities. Furthermore, a KEM/PKE (Key Encapsulation Mechanism combined with Public Key Encryption) is provided using the <i>GL(d, F<sub>251</sub>)</i> group. A detailed step-by-step toy sample, with source code, is presented in Appendix A.<br>Related Preprint: arXiv:1812.05454 <b> </b>
Equilibrium and steady state thermodynamics of active transport systems studied on simple models simulating Ca2+ transport through sarcoplasmic reticulum membranes
Journal of Theoretical Biology, May 1, 1986
Equilibrium and steady state conditions of primary active transport systems are analyzed in model... more Equilibrium and steady state conditions of primary active transport systems are analyzed in models simulating well known characteristics of calcium transport through sarcoplasmic reticulum membranes. The model for the equilibrium simulations is a closed system with two compartments and a vectorial chemical reaction coupling Ca transport and ATP breakdown. The chemical potential difference for Ca (delta mu Ca) is calculated as a function of the total amount of Ca (Cat) and nucleotides (Nt) in the system. Results are obtained by successive approximations along the thermodynamic pathway of the reaction, up to minimizing free energy of the system, since the solution of the explicit equations cannot be obtained with computers of current precision for data within physiological ranges. delta mu Ca and [Caout] are extremely dependent on Cat and Nt for certain combinations of the variables, i.e. [Caout] can be raised from 10(-8) to 10(-6) M when Cat varies from 0.998 to 1.002 mM, therefore, the running force of the spontaneous reaction is largely shifted by tiny changes in the parameters of the system. For steady state simulations, ATP supply to the system, ADP and Pi drainage, and Ca diffusion through the barrier, are assumed. Again, conditions within physiological ranges can be found where tiny changes in Cat, the rate of ATP supply, diffusion, the ratio between the volumes of the compartments, or a relative uncoupling between the transport and hydrolytic reactions, largely shifts delta mu Ca and [Caout], thus making the steady state highly unstable and therefore well designed to operate as an amplifier of physiological signals. The equilibrium model describes some physicochemical characteristics of the system; the steady state model is more useful to simulate several physiological situations.
Computer Methods and Programs in Biomedicine, Sep 1, 1990
A highly optimized software for the kinetic analysis of complex chemical models is presented. The... more A highly optimized software for the kinetic analysis of complex chemical models is presented. The program is applied to the analysis of a vectorial biochemical reaction, where many species are linked by multiple equilibria of any order. The reaction simulates the CaE+-transport-linked ATPase reaction taking place in a suspension of vesicular fragments of isolated sarcoplasmic reticulum membranes, as described in many experimental reports. The model includes 12 reactants and intermediate chemical species, 14 kinetic constants, compartmentalization, and thermodynamic adjustment. The concentrations of all the model components, at any time, starting from a known initial condition, are calculated. The transient concentrations of the species are obtained by numerical integration of the appropriate differential equations, using an optimized version of the Runge-Kutta-GiU algorithm, with the aid of a Digital PDP11/23 computer and a standard BASIC-11 software, which could be fast and easily fitted to work with any microcomputer and/or alternative language or faster working compiled BASIC version. The errors of the calculations are evaluated.
International Journal of Advanced Engineering Research and Science, 2017
Currently there is an active Post-Quantum Cryptography (PQC) solutions search, which attempts to ... more Currently there is an active Post-Quantum Cryptography (PQC) solutions search, which attempts to find cryptographic protocols resistant to attacks by means of for instance Shor's polynomial time algorithm for numerical field problems like integer factorization (IFP) or the discrete logarithm (DLP). The use of non-commutative or non-associative structures are, among others, valid choices for these kinds of protocols. In our case, we focus on a permutation subgroup of high order and belonging to the symmetric group S381. Using adequate one-way functions (OWF), we derived a Diffie-Hellman key exchange and an ElGamal ciphering procedure that only relies on combinatorial operations. Both OWF pose hard search problems which are assumed as not belonging to BQP time-complexity class. Obvious advantages of present protocols are their conceptual simplicity, fast throughput implementations, high cryptanalytic security and no need for arithmetic operations and therefore extended precision l...
arXiv (Cornell University), Jan 4, 2023
We present in this paper an algorithm for exchanging session keys, coupled with a hashing encrypt... more We present in this paper an algorithm for exchanging session keys, coupled with a hashing encryption module. We show schemes designed for their potential invulnerability to classical and quantum attacks. In turn, if the parameters included were appropriate, brute-force attacks exceed the (five) security levels used in the NIST competition of new post-quantum standards. The original idea consists of products of rectangular matrices in ℤp as public values and whose factorization is proved to be an NP-complete problem. We present running times as a function of the explored parameters and their link with operational safety. To our knowledge there are no classical and quantum attacks of polynomial complexity available at hand, remaining only the systematic exploration of the private-key space.
Post-quantum cryptography (PQC) is a trend that has a deserved NIST status, and which aims to be ... more Post-quantum cryptography (PQC) is a trend that has a deserved NIST status, and which aims to be resistant to quantum computers attacks like Shor and Grover algorithms. In this paper, we propose a method for designing post-quantum provable IND-CPA/IND-CCA2 public key cryptosystems based on polynomials over a non-commutative algebraic extension ring. The key ideas of our proposal is that (a) for a given non-commutative ring of rank-3 tensors, we can define polynomials and take them as the underlying work structure (b) we replace all numeric field arithmetic with GF(2 8) field operations. By doing so, it is easy to implement Rpropped Diffie-Helman-like key exchange protocol and consequently ElGamal-like cryptosystems. Here R stands for Rijndael as we work over the AES field. This approach yields secure post-quantum protocols since the resulting multiplicative monoid is immune against quantum algorithms and resist classical linearization attacks like Tsaban's Algebraic Span or Roman'kov. The protocols have been proved to be semantically secure. Finally, we present numerical examples of the proposed R-Propped protocols.
Post-quantum cryptography (PQC) is a trend that has a deserved NIST status, and which aims to be ... more Post-quantum cryptography (PQC) is a trend that has a deserved NIST status, and which aims to be resistant to quantum computer attacks like Shor and Grover algorithms [1]. We choose to follow a non-standard way to achieve PQC: taking any standard asymmetric protocol and replacing numeric field arithmetic with GF(2 8) field operations [2]. By doing so, it is easy to implement R-propped asymmetric systems as present and former papers show [3,4,5]. Here R stands for Rijndael as we work over the AES field. This approach yields secure postquantum protocols since the resulting multiplicative monoid resists known quantum algorithm and classical linearization attacks like Tsaban's Algebraic Span [6] or Roman'kov linearization attacks [7]. Here we develop an original group-based digital signature protocol and R-propped it. The protocol security relies on the intractability of a generalized discrete log problem, combined with the power sets of algebraic ring extension tensors [2]. The semantic security and classical and quantum security levels are discussed. Finally, we present a numerical example of the proposed protocol.
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Papers by Juan Pedro Hecht