Indistinguishability Obfuscation Without Multilinear Maps: New Paradigms via Low Degree Weak Pseudorandomness and Security Amplification

Author(s):  
Prabhanjan Ananth ◽  
Aayush Jain ◽  
Huijia Lin ◽  
Christian Matt ◽  
Amit Sahai
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Huige Wang ◽  
Kefei Chen ◽  
Tianyu Pan ◽  
Yunlei Zhao

Functional encryption (FE) can implement fine-grained control to encrypted plaintext via permitting users to compute only some specified functions on the encrypted plaintext using private keys with respect to those functions. Recently, many FEs were put forward; nonetheless, most of them cannot resist chosen-ciphertext attacks (CCAs), especially for those in the secret-key settings. This changed with the work, i.e., a generic transformation of public-key functional encryption (PK-FE) from chosen-plaintext (CPA) to chosen-ciphertext (CCA), where the underlying schemes are required to have some special properties such as restricted delegation or verifiability features. However, examples for such underlying schemes with these features have not been found so far. Later, a CCA-secure functional encryption from projective hash functions was proposed, but their scheme only applies to inner product functions. To construct such a scheme, some nontrivial techniques will be needed. Our key contribution in this work is to propose CCA-secure functional encryptions in the PKE and SK environment, respectively. In the existing generic transformation from (adaptively) simulation-based CPA- (SIM-CPA-) secure ones for deterministic functions to (adaptively) simulation-based CCA- (SIM-CCA-) secure ones for randomized functions, whether the schemes were directly applied to CCA settings for deterministic functions is not implied. We give an affirmative answer and derive a SIM-CCA-secure scheme for deterministic functions by making some modifications on it. Again, based on this derived scheme, we also propose an (adaptively) indistinguishable CCA- (IND-CCA-) secure SK-FE for deterministic functions. The final results show that our scheme can be instantiated under both nonstandard assumptions (e.g., hard problems on multilinear maps and indistinguishability obfuscation (IO)) and under standard assumptions (e.g., DDH, RSA, LWE, and LPN).


2020 ◽  
Vol 14 (1) ◽  
pp. 5-14
Author(s):  
Dan Boneh ◽  
Darren Glass ◽  
Daniel Krashen ◽  
Kristin Lauter ◽  
Shahed Sharif ◽  
...  

AbstractWe describe a framework for constructing an efficient non-interactive key exchange (NIKE) protocol for n parties for any n ≥ 2. Our approach is based on the problem of computing isogenies between isogenous elliptic curves, which is believed to be difficult. We do not obtain a working protocol because of a missing step that is currently an open mathematical problem. What we need to complete our protocol is an efficient algorithm that takes as input an abelian variety presented as a product of isogenous elliptic curves, and outputs an isomorphism invariant of the abelian variety.Our framework builds a cryptographic invariant map, which is a new primitive closely related to a cryptographic multilinear map, but whose range does not necessarily have a group structure. Nevertheless, we show that a cryptographic invariant map can be used to build several cryptographic primitives, including NIKE, that were previously constructed from multilinear maps and indistinguishability obfuscation.


2020 ◽  
Vol 33 (3) ◽  
pp. 1080-1113 ◽  
Author(s):  
Martin R. Albrecht ◽  
Pooya Farshim ◽  
Shuai Han ◽  
Dennis Hofheinz ◽  
Enrique Larraia ◽  
...  

AbstractWe provide constructions of multilinear groups equipped with natural hard problems from indistinguishability obfuscation, homomorphic encryption, and NIZKs. This complements known results on the constructions of indistinguishability obfuscators from multilinear maps in the reverse direction. We provide two distinct, but closely related constructions and show that multilinear analogues of the $${\text {DDH}} $$DDH assumption hold for them. Our first construction is symmetric and comes with a $$\kappa $$κ-linear map $$\mathbf{e }: {{\mathbb {G}}}^\kappa \longrightarrow {\mathbb {G}}_T$$e:Gκ⟶GT for prime-order groups $${\mathbb {G}}$$G and $${\mathbb {G}}_T$$GT. To establish the hardness of the $$\kappa $$κ-linear $${\text {DDH}} $$DDH problem, we rely on the existence of a base group for which the $$\kappa $$κ-strong $${\text {DDH}} $$DDH assumption holds. Our second construction is for the asymmetric setting, where $$\mathbf{e }: {\mathbb {G}}_1 \times \cdots \times {\mathbb {G}}_{\kappa } \longrightarrow {\mathbb {G}}_T$$e:G1×⋯×Gκ⟶GT for a collection of $$\kappa +1$$κ+1 prime-order groups $${\mathbb {G}}_i$$Gi and $${\mathbb {G}}_T$$GT, and relies only on the 1-strong $${\text {DDH}} $$DDH assumption in its base group. In both constructions, the linearity $$\kappa $$κ can be set to any arbitrary but a priori fixed polynomial value in the security parameter. We rely on a number of powerful tools in our constructions: probabilistic indistinguishability obfuscation, dual-mode NIZK proof systems (with perfect soundness, witness-indistinguishability, and zero knowledge), and additively homomorphic encryption for the group $$\mathbb {Z}_N^{+}$$ZN+. At a high level, we enable “bootstrapping” multilinear assumptions from their simpler counterparts in standard cryptographic groups and show the equivalence of PIO and multilinear maps under the existence of the aforementioned primitives.


1970 ◽  
Vol 23 (02) ◽  
pp. 261-275 ◽  
Author(s):  
G Zbinden ◽  
J. N Mehrishi ◽  
S Tomlin

SummaryThe severity of platelet damage induced by hyper- and hypotonic NaCl solutions and freezing and thawing was assessed by microscopic evaluation and measuring inhibition of 5-HT uptake. The same techniques were used to quantitate the effects of aggregating agents. The positively charged macromolecules PS, Poly-L und Poly-O reduced the net negative surface charge as determined by microelectrophoresis, caused platelet aggregation and inhibited 5-HT uptake. The damaging effects of Poly-L and Poly-O were more severe and more closely related to concentration than that of PS. The negatively charged macromolecules Poly-IC and NaPS increased the anodic electrophoretic mobility. Poly-IC and heparin caused a low degree of platelet clumping and no inhibition of 5-HT uptake. NaPS produced severe platelet damage with extensive clumping and complete inhibition of 5-HT uptake. Na laurate had the same effect, but did not alter electrophoretic mobility. ADP caused concentration-dependent platelet aggregation and inhibition of 5-HT uptake. The effects of ADP and NaPS were compared in agitated and non-agitated platelet samples containing identical concentrations of the 2 compounds. Agitation was found to increase the degree of platelet clumping and to reduce 5-HT uptake.


GEOgraphia ◽  
2018 ◽  
Vol 19 (41) ◽  
pp. 123
Author(s):  
Gustavo Souza Valladares ◽  
Cláudia Maria Sabóia de Aquino ◽  
Renê Pedro de Aquino ◽  
Raphael Moreira Beirigo

Resumo: O Parque Nacional da Serra da Capivara (PNSC) tem alguns dos sítios arqueológicos mais importantes das Américas. A área onde os solos foram amostrados corresponde ao Parque Nacional da Serra da Capivara (PNSC) e uma área tampão de 10km no entorno de seus limites oficiais, no sudeste do Piauí. Para a elaboração do presente trabalho foram selecionados solos considerados frágeis, devido ao alto risco de degradação por erosão, formados de diferentes materiais geológicos representativos do PNSC. Todos os solos estudados são pouco evoluídos, com desenvolvimento pedogenético ainda incipiente, e enquadram-se nas ordens dos Neossolos ou Cambissolos. O bioma representativo da área de estudo é a caatinga, que pela vegetação com pouca biomassa e características decíduas confere pouca cobertura aos solos, aumentando a susceptibilidade dos mesmos à erosão. Foram coletados sete perfis de solos, em diferentes posições na paisagem e formados de materiais de origem. As amostras foram secas ao ar e analisados atributos químicos e granulométricos. Os solos estudados apresentam grandes variações em seus atributos morfológicos, químicos e granulométricos, reflexo dos diferentes materiais de origem. A fragilidade em quase todos os perfis é reflexo da incipiência dos solos, representada pelo baixo grau de agregação e coesão entre as partículas, pequena profundidade e o fator de formação relevo induz na maior erosão de cinco dos sete perfis estudados. Os solos frágeis do PNSC necessitam de cuidados especiais quanto ao manejo, pois alguns deles, principalmente os originários de rochas pelíticas da Formação Pimenteiras, encontram-se em forte processo de degradação, em muitas áreas com as rochas expostas. Palavras-chave: Conservação do solo. Classificação de solos. Degradação ambiental. Semiárido tropical. FRAGILE SOILS OF SERRA DA CAPIVARA NATIONAL PARK, PIAUÍ Abstract: The Serra da Capivara National Park (PNSC) are some of the most important archaeological sites in the Americas. The area where the soils were sampled corresponds to the PNSC and a buffer area of 10km around of its official limits in southeastern of Piauí. For this work were considered fragile soils, due to the high risk of degradation by erosion, formed in different geological materials representative of PNSC. All soils are poorly evolved, with pedogenic development incipient fall in orders of Entisols or Inceptisols. The representative of the study area biome is the caatinga, which vegetation with little biomass and deciduous characteristics, gives little coverage to the soil, increasing susceptibility to erosion. Seven soil profiles were collected at different positions and mother rocks. The soils were classified according to the Brazilian System of Soil Classification (SiBCS). The samples were air dried and analyzed the chemical attributes and texture. The soils vary widely in their morphological, chemical and grain size, reflecting the different source material attributes. The weakness in nearly all profiles reflects the incipient soil, represented by a low degree of aggregation and cohesion between the particles of soil and small depth of relief factor induces the formation of further erosion profiles 5 of the 7 studied. Fragile soils of PNSC require special care in the mangement, because some soils, especially those originating from pelitic rocks by Pimenteiras Formation, are in strong degradation process in many areas with exposed rocks. Keywords: Soil conservation. Soil classification. Environmental degradation. Tropical semiarid. SUELOS FRÁGILES DEL PARQUE NACIONAL DE LA SIERRA DE CAPYBARA, PIAUÍ Resumen: El Parque Nacional de la Sierra de Capybara (PNSC) tiene algunos de los sitios arqueológicos más importantes de las Américas. El área donde los suelos fueron muestreados corresponde al PNSC y un área tampón de 10km en el entorno de sus límites oficiales, en el sureste del Piauí. Para la elaboración del presente trabajo se seleccionaron suelos considerados frágiles, debido al alto riesgo de degradación por erosión, formados de diferentes materiales geológicos representativos del PNSC. Todos los suelos estudiados son poco evolucionados, con desarrollo pedogenético aún incipiente, y se encuadran en las órdenes de los Neossolos o Cambissolos (en portugués). El bioma representativo del área de estudio es la caatinga, que por la vegetación con poca biomasa y características deciduas, confiere poca cobertura a los suelos, aumentando la susceptibilidad de los mismos a la erosión. Se recogieron muestras de siete perfiles de suelos, en diferentes posiciones en el paisaje y formados de materiales geológicos distintos. Las muestras fueron secas al aire y analizados los atributos químicos y granulométricos. Los suelos estudiados presentan grandes variaciones en sus atributos morfológicos, químicos y granulométricos, reflejo de los diferentes materiales de origen. La fragilidad en casi todos los perfiles es reflejo de la incipiente de los suelos, representada por el bajo grado de agregación y cohesión entre las partículas, pequeña profundidad y el factor de formación relieve induce en la mayor erosión de cinco de los siete perfiles estudiados. Los suelos frágiles del PNSC necesitan cuidados especiales en cuanto al manejo, pues algunos de ellos, principalmente los originarios de rocas pelíticas de la Formación Pimenteiras, se encuentran en fuerte proceso de degradación, en muchas áreas con las rocas expuestas. Palabras clave: Conservación del suelo. Clasificación de suelos. Degradación ambiental. Semiárido tropical.


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