I study some problems concerning pseudo-freeness of families of computational universal algebras. Several types of decidability for classes of algebraic systems in polynomial time using an oracle that performs basic operations and predicates were studied. I obtained some results concerning both decidability and undecidability in polynomial time for some finitely based varieties of universal algebras. A number of problems from the Kourovka Notebook was solved. Most part of the Cand. Sci. thesis was concerned with algorithmic problems for groups presented by finitely many generators and identical relations as well as for finitely based varieties of groups.
Biography
I graduated from Faculty of Mathematics and Mechanics of Lomonosov Moscow State University (department of higher algebra) in 1990. After the postgraduate course of the above-mentioned faculty, I earned the degree of Cand. Sci. (PhD) in 1993.
In 1993–2004 I worked at the Laboratory of Mathematical
Problems in Cryptography of Lomonosov Moscow State University. Since 2004 I am a Senior Researcher at the Information Security Institute of Lomonosov Moscow State University.
Main publications:
M. Anokhin, “A certain family of subgroups of $\mathbb Z_n^\star$ is weakly pseudo-free under the general integer factoring intractability assumption”, Groups Complex. Cryptol., 10:2 (2018), 99–110
M. Anokhin, “Pseudo-free families of finite computational elementary abelian $p$-groups”, Groups Complex. Cryptol., 9:1 (2017), 1–18
M. Anokhin, “Constructing a pseudo-free family of finite computational groups under the general integer factoring intractability assumption”, Groups Complex. Cryptol., 5:1 (2013), 53 –74
M. I. Anokhin, “Decidability of classes of algebraic systems in polynomial time”, Sb. Math., 193:2 (2002), 157–186
M. I. Anokhin, “Embedding lattices in lattices of varieties of groups”, Izv. Math., 63:4 (1999), 649–665
M. I. Anokhin, “Decidability of classes of algebraic systems in polynomial time”, Mat. Sb., 193:2 (2002), 3–34; Sb. Math., 193:2 (2002), 157–186
2000
8.
M. I. Anokhin, “On the reducibility of the integer factorization problem to the Diffie–Hellman problem”, Tr. Diskr. Mat., 3 (2000), 7–20
1999
9.
M. I. Anokhin, “Embedding lattices in lattices of varieties of groups”, Izv. RAN. Ser. Mat., 63:4 (1999), 19–36; Izv. Math., 63:4 (1999), 649–665
1998
10.
M. I. Anokhin, “A basis of identities of a variety generated by a finitely-based quasi-variety of groups”, Mat. Sb., 189:8 (1998), 3–12; Sb. Math., 189:8 (1998), 1115–1124
1997
11.
M. I. Anokhin, “On the word problem and the conjugacy problem for groups of the form $F/V(R)$”, Mat. Zametki, 61:1 (1997), 3–9; Math. Notes, 61:1 (1997), 3–8
M. I. Anokhin, “Remark on lattices and existence of impassable varieties of groups”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1996, no. 1, 88–89
1992
13.
M. I. Anokhin, “Unrecognizability of some residual properties of relatively free groups”, Sibirsk. Mat. Zh., 33:5 (1992), 3–14; Siberian Math. J., 33:5 (1992), 743–753
Contact us: