Acceleration of Computations in Jacobian Hyperelliptic Curve
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Aleshnikova M. V., Aleshnikov S. I., Gorbachev A. A., Olefirenko D. O.
hyperelliptic curve, Jacobian, addition and doubling of divisors, Miller‘s algorithm, projective coordinates
13-20
Development and Research of Properties of Mail Exchange Protocols Inside a Hybrid Cloud with Two Re-Encryption Based on Hess Pairing
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ACM Symposium on Information, Computer and Communications Security. 2012.
Olefirenko D. O., Aleshnikov S. I., Aleshnikova M. V., Vetrov I. A.
elliptic curve, Hess pairing, cloud storage, authentification, protocol
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Investigation of the conditions of applicability of Wiener's attack on the RSA cryptosystem
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Boltnev Y. F., Aleshnikova M. V., Kozminykh E. V.
RSA cryptosystem, Wiener’s attack, Wiener’s bound, continued fraction, convergents
42-48
An elementary solving of cubic Diophantine equations
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Aleshnikov S., Aleshnikova M., Gorbachev A.
Diophantine equation, quadratic field, class number, Pell equation, divisibility, Gaussian integers, fundamental unit
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About one algorithm of calculation of inverses in finite fields
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Aleshnikov S., Aleshnikova M., Gorbachev A.
finite field, multiplication, inversion, normal basis, cyclic shift, algorithm, fast algorithm
34-40
About pairing on abelian varieties p-rank one and their cryptographic applications
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Aleshnikov S., Aleshnikova M.
algebraic curves, hyperelliptic curves, Jacobians of curves, abelian varieties, p-rank, embedding degree, bilinear pairings, Tate-Lichtenbaum pairing, Ate pairing, twisted Ate pairing, Weil pairing
155-161