Selected publications and preprints
1993-96
N. Gupta, V.
Shpilrain,
Nielsen's commutator test for two-generator groups,
Math. Proc. Cambridge Phil. Soc. 114 (1993), 295-301.
V. Shpilrain,
On generators of L/R^2 Lie algebras, Proc. Amer. Math. Soc.
119 (1993), 1039-1043.
V. Shpilrain,
Recognizing
automorphisms of the free groups, Arch. Math. 62 (1994), 385-392.
V. Shpilrain,
Test elements
for endomorphisms of free groups and algebras, Israel J. Math. 92
(1995), 307-316.
V. Shpilrain,
On monomorphisms of free groups, Arch. Math. 64 (1995), 465-470.
V. Shpilrain, Magnus embeddings
for semigroups, Internat. J. Algebra and Comput. 6 (1996),
155-163.
1997-99
V. Shpilrain,
Non-commutative
determinants and automorphisms of groups, Comm. Algebra 25 (1997),
559-574.
V. Shpilrain and J.-T.
Yu,
Polynomial automorphisms and Groebner reductions, J.
Algebra 197 (1997), 546-558.
A. van den Essen, V.
Shpilrain,
Some combinatorial questions about polynomial mappings,
J. Pure Appl. Algebra 119 (1997), 47-52.
V. Shpilrain and J.-T.
Yu,
On generators of polynomial algebras in two commuting or non-commuting
variables, J. Pure Appl. Algebra 132 (1998), 309-315.
V. Shpilrain,
Fixed
points of endomorphisms of a free metabelian group, Math. Proc.
Cambridge Phil. Soc. 123 (1998), 77-85.
V. Shpilrain,
Generalized
primitive elements of a free group, Arch. Math. 71 (1998),
270-278.
V. Shpilrain,
Combinatorial
methods: from groups to polynomial algebras, Groups '97 Bath/St.
Andrews, Vol. 2 (Bath, 1997), 679-688, London Math. Soc. Lecture
Note Ser. 261, Cambridge Univ. Press, Cambridge, 1999.
V. Shpilrain,
Automorphisms
of one-relator groups, Math. Proc. Cambridge Phil. Soc. 26
(1999), 499--504.
V. Shpilrain and J.-T.
Yu, Embeddings
of curves in the plane, J.Algebra 217 (1999), 668-678.
G.Baumslag, A.G.Myasnikov
and V.Shpilrain,
Open problems in combinatorial group theory,
Contemp. Math., Amer. Math. Soc. 250 (1999), 1-27.
2000
V. Shpilrain and J.-T.
Yu,
Polynomial
retracts and the Jacobian conjecture, Trans. Amer. Math. Soc. 352
(2000), 477-484.
V.Drensky, V.
Shpilrain and J.-T. Yu,
On
the density of the set of generators of a polynomial algebra, Proc.
Amer. Math. Soc. 128 (2000), 3465-3469.
A.A.Mikhalev, V.
Shpilrain and J.-T. Yu,
Combinatorial
problems about free groups and algebras,
in: Lie algebras, rings
and related topics, 80-107. Springer, 2000.
V. Shpilrain and J.-T.
Yu, Peak
reduction technique in commutative algebra: a survey. Contemp. Math.,
Amer. Math. Soc. 264 (2000), 237-247.
2001
V. Shpilrain and J.-T.
Yu, Embeddings
of hypersurfaces in affine spaces, J.Algebra
239 (2001), 161-173.
V. Shpilrain, Representing
braids by automorphisms, Internat. J. Algebra and
Comput. 11 (2001), 773-778.
2002
G.Baumslag,
A.G.Myasnikov
and V.Shpilrain,
Open
problems in combinatorial group theory. Second edition,
Contemp. Math., Amer. Math. Soc. 296 (2002), 1-38.
A.D.Myasnikov,
A.G.Myasnikov and V.Shpilrain,
On
the Andrews-Curtis equivalence, Contemp. Math.,
Amer. Math. Soc. 296 (2002), 183-198.
V. Shpilrain and
J.-T.Yu,
Affine varieties with equivalent cylinders, J.
Algebra 251 (2002), 295-307.
A.Borovik, A.G.Myasnikov,
V. Shpilrain,
Measuring sets in infinite groups,
Contemp. Math., Amer. Math. Soc. 298 (2002), 21-42.
V. Shpilrain and J.-T.Yu,
Non-extendable isomorphisms between affine varieties, J. Pure Appl. Algebra 172 (2002), 285-291.
2003
A.A.Mikhalev, V.
Shpilrain and J.-T. Yu,
Combinatorial Methods: Free Groups, Polynomials, and Free Algebras,
Springer, 2003, 315 pp.
I. Kapovich, A. G. Myasnikov, P.
Schupp,
and V.Shpilrain,
Generic-case complexity, decision problems in group theory and random
walks, J. Algebra 264 (2003), 665-694. pdf
V. Shpilrain and J.-T. Yu,
Factor algebras of free algebras: on a problem of G. Bergman,
Bull. London Math. Soc. 35 (2003), 706-710.
A.G.Myasnikov,
V. Shpilrain,
Automorphic orbits in free groups, J.
Algebra 269 (2003), 18-27.
2004
V. Shpilrain and J.-T.Yu, Birational morphisms of the plane,
Proc. Amer. Math. Soc. 132 (2004), 2511-2515.
L. Makar-Limanov, P. van Rossum,
V. Shpilrain and J.-T.Yu,
The stable equivalence and cancellation
problems, Comment. Math. Helv. 79 (2004), 341-349.
A.A.Mikhalev, V.
Shpilrain, and U.U.Umirbaev,
On isomorphism of Lie algebras
with one defining relation, Internat. J. Algebra and
Comput. 14 (2004), 389-393.
V. Shpilrain,
Assessing security of some
group based cryptosystems, Contemp. Math., Amer. Math. Soc.
360 (2004), 167-177.
2005
I. Kapovich, A. G. Myasnikov, P.
Schupp,
and V.Shpilrain,
Average-case complexity and decision problems in group theory,
Advances in Math. 190 (2005), 343-359.
V. Shpilrain and J.-T.Yu, Test polynomials, retracts, and the
Jacobian conjecture, Contemp. Math., Amer. Math. Soc. 369 (2005), 253-259.
V. Bardakov,
V. Shpilrain, V. Tolstykh,
On the palindromic and primitive widths of a free
group, J. Algebra 285 (2005), 574-585.
V. Shpilrain,
Counting primitive elements of a free group,
Contemp. Math., Amer. Math. Soc. 372 (2005), 91-97.
V. Shpilrain and A.Ushakov,
Thompson's group
and public key cryptography, Lecture Notes Comp. Sc.
3531 (2005), 151-164.
A. G. Myasnikov,
V. Shpilrain and A.Ushakov,
A practical attack on some braid group based cryptographic
protocols, in CRYPTO 2005, Lecture Notes Comp. Sc. 3621 (2005), 86-96.
2006
I. Kapovich, P.
Schupp,
and V.Shpilrain,
Generic properties of Whitehead's algorithm
and isomorphism rigidity of random one-relator groups, Pacific J. Math.
223 (2006), 113-140.
A. G. Myasnikov,
V. Shpilrain and A.Ushakov,
Random subgroups of braid groups:
an approach to cryptanalysis of a braid group based cryptographic
protocol, in PKC 2006, Lecture Notes Comp. Sc. 3958 (2006), 302-314.
V. Shpilrain and A.Ushakov,
The conjugacy search problem in
public key cryptography: unnecessary and insufficient, Applicable Algebra in Engineering, Communication
and Computing 17 (2006), 285-289.
V. Shpilrain and G.Zapata, Combinatorial group theory and public key
cryptography, Applicable Algebra in Engineering,
Communication and Computing 17 (2006), 291-302.
A.G.Myasnikov,
V. Shpilrain,
Some metric properties of automorphisms of groups, J. Algebra 304
(2006), 782-792.
V. Shpilrain,
Hashing with polynomials, in: ICISC 2006, Lecture Notes Comp. Sc., 4296 (2006),
22-28.
V. Shpilrain and G. Zapata, Using the
subgroup membership search problem in public key cryptography, Contemp. Math., Amer. Math. Soc.
418 (2006), 169-179.
V. Shpilrain and A.Ushakov,
A new key exchange protocol based on the decomposition problem, Contemp.
Math., Amer. Math. Soc. 418 (2006), 161-167.
2007
L. Makar-Limanov,
V. Shpilrain and J.-T.Yu,
Equivalence of polynomials under automorphisms of K[x,y], J. Pure Appl.
Algebra 209 (2007), 71-78.
I. Kapovich, G. Levitt, P. Schupp,
and V.Shpilrain,
Translation equivalence in free groups, Trans. Amer. Math. Soc.
359 (2007), 1527-1546.
I. Kapovich, I. Rivin, P. Schupp,
and V.Shpilrain,
Densities in free groups and Z^k, visible points and
test elements, Math. Res. Lett. 14 (2007), 263-284.
C. M. Lam,
V. Shpilrain, and J.-T.Yu,
Recognizing and parametrizing curves isomorphic to a line, J. Symb. Comput.
42 (2007), 751-756.
2008
V. Shpilrain and A.Ushakov,
An authentication scheme based on the twisted conjugacy problem, in:
ACNS 2008, Lecture Notes Comp. Sc. 5037 (2008), 366-372.
Preprints
A.G.Myasnikov, V.
Shpilrain and A.Ushakov,
Group-based cryptography, to appear.
D. Osin and
V. Shpilrain,
Public key encryption and encryption emulation attacks, version for group
theorists
version for cryptographers, in: Computer Science
in Russia 2008, Lecture Notes Comp. Sc., to appear.
V. Shpilrain, Cryptanalysis of
Stickel's key exchange scheme, in: Computer Science
in Russia 2008, Lecture Notes Comp. Sc., to appear.
V. Shpilrain and G. Zapata, Using decision
problems in public key cryptography, preprint.
D. Grigoriev and
V. Shpilrain, Zero-knowledge authentication schemes
from actions on graphs, groups, or rings, preprint.