Leon Chernyak

Geometric Cryptosystem

IACR Cryptol. ePrint Arch., 2005

Introduction A. Berenstein, L. Chernyak, Geometric Key Establishment Geometric Key Establishment

We propose a new class of key establishment schemes which are based on geometric generalizations ... more We propose a new class of key establishment schemes which are based on geometric generalizations of the classical Diffie-Hellman. The simplest of our schemes-based on the geometry of the unit circle-uses only multiplication of rational numbers by integers and addition of rational numbers in its key creation. Its first computer implementation works significantly faster than all known implementations of Diffie-Hellman. Preliminary estimations show that our schemes are resistant to attacks. This resistance follows the pattern of the discrete logarithm problem and hardness of multidimensional lattice problems.

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Method and apparatus for geometric key establishment protocols based on topological groups

Geometric Key Establishment

We propose a new class of key establishment schemes which are based on geometric generalizations ... more We propose a new class of key establishment schemes which are based on geometric generalizations of the classical Diffie-Hellman. The simplest of our schemes-based on the geometry of the unit circle-uses only multiplication of rational numbers by integers and addition of rational numbers in its key creation. Its first computer implementation works significantly faster than all known implementations of Diffie-Hellman. Preliminary estimations show that our schemes are resistant to attacks. This resistance follows the pattern of the discrete logarithm problem and hardness of multidimensional lattice problems.

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Method and apparatus for algebro-geometric key establishment protocols based on matrices over topological monoids

Method and apparatus for informational processing based on creation of term-proximity graphs and their embeddings into informational units

Geometry-Based Symmetric Cryptosystem Method

The theme of language in the works of P. A. Florenskii and in the hermeneutics of H.-G. Gadamer

Studies in East European Thought, 1988

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Immunological Reformulations. (Book Reviews: Metchnikoff and the Origins of Immunology. From Metaphor to Theory.)

Science, 1992

Geometric Cryptosystem

In this paper we propose a new class of cryptosystems that utilizes metric continuity. The geomet... more In this paper we propose a new class of cryptosystems that utilizes metric continuity. The geometric cryptosystem considered in this paper as the main example of metric cryptosystems has a number of interesting properties such as resistance to several basic cryptographic attacks, efficiency and detection of transmission errors.

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Kant and the Aesthetic-Expressive Vision of Mathematics

Boston Studies in the Philosophy of Science, 1996

Geometric Cryptosystem

In this paper we propose a new class of cryptosystems that utilizes metric continuity. The geomet... more In this paper we propose a new class of cryptosystems that utilizes metric continuity. The geometric cryptosystem considered in this paper as the main example of metric cryptosystems has a number of interesting properties such as resistance to several basic cryptographic attacks, efficiency and detection of transmission errors.

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Metchnikoff and a theory of medicine

Journal of the Royal Society of Medicine, 1989

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Geometric key establishment

Contemporary Mathematics, 2006

We propose a new class of key establishment schemes which are based on geometric generalizations ... more We propose a new class of key establishment schemes which are based on geometric generalizations of the classical Diffie-Hellman. The simplest of our schemes-based on the geometry of the unit circle-uses only multiplication of rational numbers by integers and addition of rational numbers in its key creation. Its first computer implementation works significantly faster than all known implementations of Diffie-Hellman. Preliminary estimations show that our schemes are resistant to attacks. This resistance follows the pattern of the discrete logarithm problem and hardness of multidimensional lattice problems.

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The theme of language in the works of P. A. Florenskii and in the hermeneutics of H.-G. Gadamer

Studies in Soviet Thought, 1988

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The idea of immunity: Metchnikoff's metaphysics and science

Journal of the History of Biology, 1990

... thought of as another expression of integrity: the &quot;nature&quot; of the organism... more ... thought of as another expression of integrity: the &quot;nature&quot; of the organism, its physis, was the self-sustaining self-hood in a ... For instance, Girolamo Fracastoro, an Italian physician of the sixteenth century, believed that all disease results from small germs (seminaria) that spread ...

Metchnikoff and the Origins of Immunology: From Metaphor to Theory

JAMA: The Journal of the American Medical Association, 1992

... Metchnikoff saw the scientist as savior to the world, and he put his religious faith and ferv... more

The birth of immunology: Metchnikoff, the embryologist

Cellular Immunology, 1988

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The birth of immunology

Cellular Immunology, 1989

The presentation of the phagocytic theory of immunity, proposed by Metchnikoff in 1883, was immed... more The presentation of the phagocytic theory of immunity, proposed by Metchnikoff in 1883, was immediately attacked by German pathologists and microbiologists. Led by Baumgarten and Ziegler, criticism was levied against the hypothesis in three general respects: 1) Can an analogy truly be established between leukocyte phagocytosis and feeding of monocellular organisms? 2) What is compelling about the phagocytic process as a universal defensive activity? 3) General philosophic objections were raised, centered upon the accusation of a teleologic formulation. Underlying the argument was the rejection of the notion that the response of phagocytic leukocytes was truly causal in the successful response to infection. We note that the humoral school of immunity was not established until 1888-1890, and the early debate between Metchnikoff and his detractors was not over an alternative theory of an active immune response. There was none. With the development of the humoralist position, in direct response to Metchnikotf's formulation, a true dialogue about immunity, in the modern context of active host response, was initiated. The debate at this point changed to issues of mechanism (cellular versus humoral effecters), and the relative importance of defining innate versus acquired immune processes. Our study traces the scientific and logical basis ofthe initial rejection ofthe phagocytosis theory. More broadly, the analysis of this debate elucidates the emergence of a new concept of immunity that rested upon the notion of an active host response. The humoralists erected their theory on Metchnikoff's original scaffold, and the ensuing debate of the nascent science relied on the successful establishment of his basic concept. With the studies of Bordet, Metchnikoff's protege, the essential resolution of the acrimonious debate was offered. Metchnikoff continued his research by attempting to apply the phagocytosis theory to mechanisms of senility, while immunology oriented itselftoward the biochemical definition ofimmune recognition. o 1989 Academic Press, Inc. I. THE SETTING Elie Metchnikoff s work must be woven within several threads of prevailing biological attitudes of the 1880s. The first is within the context of inflammation's role in disease and its basic operative mechanisms. As Metchnikoff acknowledged, an important impetus for his own work was Cohnheim's "Lectures on General Pathology," whose conclusions concerning the nature of inflammation were based on experiments performed in the late 1860s and early 1870s (l-3); as opposed to Virchow,

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Concerning individuality

Biology and Philosophy, 1992

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