
Main / Andrei Mikhailovich Ivantsov
Author: "Andrei Mikhailovich Ivantsov"
Sergei Mikhailovich Ratseev, Ulyanovsk State University, Doctor of Sciences in Physics and Mathematics, Associate Professor; graduated from the Faculty of Mechanics and Mathematics of Ulyanovsk State University; Professor of the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks in the field of cryptographic methods of information protection, PIalgebras. [email: ratseevsm@mail.ru]S. Ratseev,
Andrei Mikhailovich Ivantsov, Ulyanovsk State University, Candidate of Science in Engineering; graduated from the Leningrad Higher Military Engineering School of Communications; graduated from the Military Academy of Communications; a postgraduate from the Military Academy of Communications; Associate Professor of the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks in the field of information security. [email: iwanzow@mail.ru]A. Ivantsov


On Some Properties of Cryptographic Hash Functions
The article deals with hash functions with and without secret key. For the hash functions without a secret key, a condition of uniform distribution of hash functions values with a random equiprobable choice of argument values is one of the additional requirements. The rationale of this requirement is given on the example of a finite set of messages using the concept of the balanced functions. Authors demonstrate that the probability of the fact of nondetection of the message (or file) change does not exceed the reciprocal power value of hash function images. For modern hash functions with length of hash values of 256‒512 bits, it means that such probability is slim to none. The paper is also survey of recent results of investigations on authentication codes resistant to imitation and substitution messages. The case when the probabilities of imitation and substitution reach the lower limits has been highlighted. Such authentication codes are called optimal. We study constructions of optimal authentication codes based on orthogonal tables. The case of optimal authentication codes with optional uniform distribution on the set of keys is studied. Hash function, authentication code, message simulation.



Sections: Information systems
Subjects: Information systems. 
Andrei Mikhailovich Ivantsov, Ulyanovsk State University, Candidate of Engineering; graduated from Leningrad Higher Military Engineering School of Communications, Military Academy of Communications; finished his postgraduate studies in Military Academy of Communications; Associate Professor at the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles and textbooks in the field of information security. [email: iwanzow@mail.ru]A. Ivantsov, Sergei Mikhailovich Ratseev, Ulyanovsk State University, Doctor of Physics and Mathematics; Associate Professor; graduated from the Faculty of Mechanics and Mathematics of Ulyanovsk State University; Professor at the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles and textbooks in the field of cryptographic methods of information protection, PIalgebras. [email: ratseevsm@mail.ru]S. Ratseev


On Application of Elliptic Curves in Some Verifiable Protocols of Secret Sharing
The threshold secret sharing is the secret sharing with n participants for the structure of access in which all coalitions supporting at least t participants for some t are authorized, and all coalitions with smaller number of participants are unauthorized. The special role is given to perfect secret sharing schemes in which shares of a secret of any unauthorized coalition don't allow to obtain any information on value of a secret. One of wellknown perfect secret sharing schemes is the Shamir's one. In the Shamir's scheme, the dishonest dealer can distribute incompatible shares from which they will never recover the initial secret to participants. In this case, the checked secret sharing schemes are applied. Such schemes allow each participant to check compatibility of the share with shares of a secret of other participants. For this purpose, complementary to a secret share, some additional information allowing to check the given secret share is transferred to each participant. The wellknown checked schemes are FeldmanShamir's one and PedersenShamir's one. PedersenShamir's one is perfect. Modifications of FeldmanShamir and PedersenShamir schemes on elliptic curves which application allows to reduce considerably the sizes of parameters of protocols and to increase their cryptography firmness are considered. Secret sharing, shamir’s scheme, elliptic curve.



Sections: Mathematical modeling
Subjects: Mathematical modeling, Automated control systems. 
Andrei Mikhailovich Ivantsov, Ulyanovsk State University, Candidate of Engineering; graduated from the Leningrad higher military engineering school of communications, the Military Academy of Communications; finished his postgraduate studies at the Military Academy of Communications; Associate Professor at the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles and textbooks in the field of information security. [email: iwanzow@mail.ru]A. Ivantsov, Sergei Mikhailovich Ratseev, Ulyanovsk State University, Doctor of Physics and Mathematics, Associate Professor; graduated from the Faculty of Mechanics and Mathematics of Ulyanovsk State University; Professor at the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles and textbooks in the field of cryptographic methods of information security, PIalgebras. [email: ratseevsm@mail.ru]S. Ratseev


On Application of Elliptic Curves in Some Authentication and Key Distribution Protocols
Cryptographic authentication protocols with zero disclosure of knowledge and key exchange protocols are considered in the article. The cryptographic authentication protocols based on the proof of knowledge with zero disclosure allow to verify authenticity of the sides without leakage of the classified information during information exchange. Key exchange protocols allow to create the general secret keys of participants of cryptosystems. Modifications of some cryptographic protocols of open distribution of keys and such cryptographic authentication protocols with zero disclosure of knowledge as families of the MTI protocols, Shnor’s triplepass authentication protocol and authentication protocol on the basis of the DiffieHellman algorithm are offered. These protocols are provided on the basis of elliptic curves, which application allows to reduce considerably the sizes of protocols parameters and to increase their cryptography firmness. Firmness of the provided protocols is based on the difficult task of the discrete logarithmation in group of points of an elliptic curve. Cryptographic protocol, authentication protocol, key exchange protocol, shnor's protocol, elliptic curve.



Sections: Information systems
Subjects: Information systems, Automated control systems. 
