Square root computation over even extension fields

This paper presents a comprehensive study of the computation of square roots over finite extension fields. We propose two novel algorithms for computing square roots over even field extensions of the form \F_{q^{2}}, with $q=p^n,$ $p$ an odd prime and $n\geq 1$. Both algorithms have an associate computational cost roughly equivalent to one exponentiation in \F_{q^{2}}. The first algorithm is devoted to the case when $q\equiv 1 \bmod 4$, whereas the second one handles the case when $q\equiv 3 \bmod 4$. Numerical comparisons show that the two algorithms presented in this paper are competitive and in some cases more efficient than the square root methods previously known

A note on the cost of computing odd degree isogenies

Finding an isogenous supersingular elliptic curve of a prescribed odd degree is an important building block for all the isogeny-based protocols proposed to date. In this note we present several strategies for the efficient construction of odd degree isogenies, which outperform previously reported methods when dealing with isogeny degrees in the range $[7, 2^{20}].

Optimal strategies for CSIDH

Since its proposal in Asiacrypt 2018, the commutative isogeny-based key exchange protocol (CSIDH) has spurred considerable attention to improving its performance and re-evaluating its classical and quantum security guarantees. In this paper we discuss how the optimal strategies employed by the Supersingular Isogeny Diffie-Hellman (SIDH) key agreement protocol can be naturally extended to CSIDH. Furthermore, we report a software library that achieves moderate but noticeable performance speedups when compared against state-of-the-art implementations of CSIDH-512, which is the most popular CSIDH instantiation. We also report an estimated number of field operations for larger instantiations of this protocol, namely, CSIDH-1024 and CSIDH-1792

Risk of SARS-CoV-2 exposure in a hospital-based allergy practice.

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Efecto de acondicionadores naturales y sintéticos sobre los cationes solubles y la infiltración del agua en un Aridisol

The objective of this work was to evaluate the effect of several conditioners on soluble cations and water infiltration on a fine clay Vertic Haplocambid soil collected on the Quibor depression, Venezuela. Solutions of two natural conditioners from dato cactus (Lemaireocereus griceus (Haw.) Br. & Rose) and lefaria cactus (Cereus deficiens Otto & Dietr), on concentrations of 2,000, 1,000 and 500 mg L-1, a synthetic polyacrilamide conditioner solution of 10 mg L-1 and local tap water were applied to the soil. All solutions and the tap water were poured in a mini flume to simulate the irrigation process on furrows. The natural conditioners increased the infiltration and produced a better Ca-Mg-Na relationship as compared with that produced by the polyacrilamide and the tap water without additives.The objective of this work was to evaluate the effect of several conditioners on soluble cations and water infiltration on a fine clay Vertic Haplocambid soil collected on the Quibor depression, Venezuela. Solutions of two natural conditioners from dato cactus (Lemaireocereus griceus (Haw.) Br. & Rose) and lefaria cactus (Cereus deficiens Otto & Dietr), on concentrations of 2,000, 1,000 and 500 mg L-1, a synthetic polyacrilamide conditioner solution of 10 mg L-1 and local tap water were applied to the soil. All solutions and the tap water were poured in a mini flume to simulate the irrigation process on furrows. The natural conditioners increased the infiltration and produced a better Ca-Mg-Na relationship as compared with that produced by the polyacrilamide and the tap water without additives.El objetivo del trabajo fue evaluar el efecto de diversos acondicionadores sobre los cationes solubles y la infiltración del agua en un suelo Vertic Haplocambid, arcilloso muy fino, de la depresión de Quibor, Venezuela. Fueron aplicadas soluciones de acondicionadores naturales de cardón dato (Lemaireocereus griceus (Haw.) Br. & Rose) y de cardón lefaria (Cereus deficiens Otto & Dietr), a concentraciones de 2.000, 1.000 y 500 mg L-1, solución de un acondicionador sintético, la poliacrilamida, en concentración de 10 mg L-1 y agua del acueducto local. Las soluciones de cada uno de esos tratamientos fueron vertidas sobre mini canales rellenos del suelo, para simular el flujo del agua en surcos. Los acondicionadores naturales incrementaron la infiltración y produjeron una relación Ca-Mg-Na en el suelo, mas adecuada que la producida con la aplicación de la poliacrilamida o el agua sin aditivos

Verifiable Isogeny Walks: Towards an Isogeny-based Postquantum VDF

In this paper, we investigate the problem of constructing postquantum-secure verifiable delay functions (VDFs), particularly based on supersingular isogenies. Isogeny-based VDF constructions have been proposed before, but since verification relies on pairings, they are broken by quantum computers. We propose an entirely different approach using succinct non-interactive arguments (SNARGs), but specifically tailored to the arithmetic structure of the isogeny setting to achieve good asymptotic efficiency. We obtain an isogeny-based VDF construction with postquantum security, quasi-logarithmic verification, and requiring no trusted setup. As a building block, we also construct non-interactive arguments for isogeny walks in the supersingular graph over Fp2 , which may be of independent interest

On the Security of Mexican Digital Fiscal Documents De la Seguridad de Documentos Fiscales Mexicanos

Abstract In January 2005, the Mexican Tributary Administration System (SAT) introduced an official norm that stipulates how to generate electronic invoices that were termed by SAT, Comprobante Fiscal Digital (CFD). Supporting the CFD service implies the exchange of confidential information over Internet and other communication channels that are intrinsically highly vulnerable. Therefore, it becomes indispensable to incorporate to this service reliable and sound information security mechanisms. In the case of SAT's CFD, its security guarantees depend on customary cryptographic mechanisms such as, digital signatures, hash functions, etc. In this paper we point out several security flaws in the procedure specified by SAT for generating such electronic invoices. Furthermore, we provide recommendations for avoiding the security problems detected, which include the usage of more robust cryptographic mechanisms, alternative authentication protocols, time stamps authorities and a safe storage system. Keywords: Information Security, Digital Certificates, Digital Notary, Mexican Tributary Administration System. Resumen En enero de 2005, el Gobierno mexicano a través del Servicio de Administración Tributaria (SAT), presentó una norma oficial que estipula cómo generar facturas electrónicas, las cuales recibieron el nombre oficial de Comprobante Fiscal Digital (CFD). El hecho de ofrecer el servicio de CFD implica el intercambio de información confidencial que debe viajar por Internet y otros canales de comunicación que son intrínsecamente altamente vulnerables. Por lo tanto, es indispensable incorporar a dicho servicio, herramientas de seguridad confiables y técnicamente sólidas. En el caso de los comprobantes fiscales digitales del SAT, su seguridad depende de mecanismos criptográficos tradicionales tales como, firmas digitales, funciones picadillo, etc. En este artículo se señalan fallas de seguridad en el procedimiento especificado por el SAT para la generación de sus facturas electrónicas. Aunado a esto, en este trabajo se dan algunas recomendaciones para eliminar los problemas de seguridad detectados, lo cual incluye, el uso de mecanismos criptográficos más robustos, protocolos de autentificación alternativos, autoridades que emitan estampillas de tiempo y un sistema de almacenamiento a largo plazo seguro. Palabras clave: Seguridad informática, certificados digitales, notaría digital, servicio de administración tributaria

Low Complexity Bit-Parallel Square Root Computation over GF(2m2^m) for all Trinomials

In this contribution we introduce a low-complexity bit-parallel algorithm for computing square roots over binary extension fields. Our proposed method can be applied for any type of irreducible polynomials. We derive explicit formulae for the space and time complexities associated to the square root operator when working with binary extension fields generated using irreducible trinomials. We show that for those finite fields, it is possible to compute the square root of an arbitrary field element with equal or better hardware efficiency than the one associated to the field squaring operation. Furthermore, a practical application of the square root operator in the domain of field exponentiation computation is presented. It is shown that by using as building blocks squarers, multipliers and square root blocks, a parallel version of the classical square-and-multiply exponentiation algorithm can be obtained. A hardware implementation of that parallel version may provide a speedup of up to 50\% percent when compared with the traditional version

eSIDH: the revenge of the SIDH

The Supersingular Isogeny-based Diffie-Hellman key exchange protocol (SIDH) was introduced by Jao an De Feo in 2011. SIDH operates on supersingular elliptic curves defined over quadratic extension fields of the form GF($p^2$), where $p$ is a large prime number of the form $p = 4^{e_A} 3^{e_B} - 1,$ where $e_A, e_B$ are positive integers such that $4^{e_A} \approx 3^{e_B}.$ In this paper, a variant of the SIDH protocol that we dubbed extended SIDH (eSIDH) is presented. The eSIDH variant makes use of primes of the form, $p = 4^{e_A} \ell_B^{e_B}\ell_C^{e_C} f - 1.$ Here $\ell_B, \ell_C$ are two small prime numbers; $f$ is a cofactor; and $e_A, e_B$ and $e_C$ are positive integers such that $4^{e_A} \approx \ell_B^{e_B}\ell_C^{e_C}.$ We show that for many relevant instantiations of the SIDH protocol, this new family of primes enjoys a faster field arithmetic than the one associated to traditional SIDH primes. Furthermore, the proposed eSIDH protocol preserves the length and format of SIDH private/public keys, and its richer opportunities for parallelism yields a noticeable speedup factor when implemented on multi-core platforms. Using a single-core SIDH $p_{751}$ implementation as a baseline, a parallel eSIDH $p_{765}$ instantiation yields an acceleration factor of $1.05, 1.30$ and $1.41,$ when implemented on $k = \{1, 2, 3\}$-core processors. In addition, eSIDH $p_{765}$ yields an acceleration factor of $1.050, 1.160$ and $1.162.$ when both protocols are implemented on $k = \{1, 2, 3\}$-core processors. To our knowledge, this work reports the first multi-core implementation of SIDH