Selected publications and preprints

Preprints

G. Di Crescenzo, D. Kahrobaei, M. Khodjaeva, V. Shpilrain, Computing Multiple Exponentiations in Discrete Log and RSA Groups: From Batch Verification to Batch Delegation, in: IEEE CNS 2017, 3rd Workshop on Security and Privacy in the Cloud (SPC), to appear.
G. Di Crescenzo, D. Kahrobaei, M. Khodjaeva, V. Shpilrain, Practical and Secure Outsourcing of Discrete Log Group Exponentiation to a Single Malicious Server, in: CCSW 2017, 9th ACM Cloud Computing Security Workshop, to appear.
V. Shpilrain, Randomness and complexity in matrix groups, preprint.
D. Kahrobaei, H. Lam, V. Shpilrain, Public key exchange using extensions by endomorphisms and matrices over a Galois field.

2017

A. Chorna, K. Geller, and V. Shpilrain, On two-generator subgroups of SL_2(Z), SL_2(Q), and SL_2(R), J. Algebra 478 (2017), 367-381.
L. Bromberg, V. Shpilrain, A. Vdovina, Navigating in the Cayley graph of SL_2(F_p) and applications to hashing, Semigroup Forum 94 (2017), 314-324.
D. Grigoriev and V. Shpilrain, Secure multiparty computation without one-way functions, Journal of Logics and their Applications 4 (2017), 993--1010.
D. Grigoriev, L. Kish, V. Shpilrain, Yao's millionaires' problem and public-key encryption without computational assumptions, Int. J. Foundations Comp. Sci. 28 (2017), 379--389.

2016

D. Kahrobaei and V. Shpilrain, Using semidirect product of (semi)groups in public key cryptography, in: CiE 2016, Lecture Notes Comp. Sc. 9709 (2016), 132-141.
V. Shpilrain, B.Sosnovski, Compositions of linear functions and applications to hashing, Groups, Complexity, and Cryptology 8 (2016), 155-161.

2015

D. Kahrobaei, C. Koupparis, and V. Shpilrain, A CCA secure cryptosystem using matrices over group rings, Contemp. Math., Amer. Math. Soc. 633 (2015), 73-80.
B. Cavallo, G. Di Crescenzo, D. Kahrobaei, V. Shpilrain, Efficient and secure delegation of group exponentiation to a single server, in: RFIDsec 2015, Lecture Notes Comp. Sc. 9440 (2015), 156-173.

2014

D. Grigoriev and V. Shpilrain, Yao's millionaires' problem and decoy-based public key encryption by classical physics, Int. J. Foundations Comp. Sci. 25 (2014), 409417.
D. Grigoriev and V. Shpilrain, Tropical cryptography, Comm. Algebra 42 (2014), 2624-2632.
V. Shpilrain, Decoy-based information security, Groups, Complexity, and Cryptology 6 (2014), 149-155.

2013

D. Grigoriev and V. Shpilrain, Secure information transmission based on physical principles, in: UCNC 2013, Lecture Notes Comp. Sc. 7956 (2013), 113-124.
M. Habeeb, D. Kahrobaei, C. Koupparis, and V. Shpilrain, Public key exchange using semidirect product of (semi)groups, in: ACNS 2013, Lecture Notes Comp. Sc. 7954 (2013), 475-486.
D. Grigoriev and V. Shpilrain, Secrecy without one-way functions, Groups, Complexity, and Cryptology 5 (2013), 31-52.
D. Kahrobaei, C. Koupparis, and V. Shpilrain, Public key exchange using matrices over group rings, Groups, Complexity, and Cryptology 5 (2013), 97-115.

2012

D. Grigoriev and V. Shpilrain, No-leak authentication by the Sherlock Holmes method, Groups, Complexity, and Cryptology 4 (2012), 177-189.
M. Habeeb, D. Kahrobaei, and V. Shpilrain, A secret sharing scheme based on group presentations and the word problem, Contemp. Math., Amer. Math. Soc. 582 (2012), 143-150.

2011

book:  A.G.Myasnikov, V. Shpilrain and A.Ushakov, Non-commutative Cryptography and Complexity of Group-theoretic Problems, Amer. Math. Soc. Surveys and Monographs, 2011.
V. Shpilrain, Sublinear time algorithms in the theory of groups and semigroups, Illinois J. Math. 54 (2011), 187-197.
G. Baumslag, N. Fazio, A. Nicolosi, V. Shpilrain, W. E. Skeith III, Generalized learning problems and applications to non-commutative cryptography, in: ProvSec 2011, Lecture Notes Comp. Sc. 6980 (2011), 324-339.

2010

D. Grigoriev and V. Shpilrain, Zero-knowledge authentication schemes from actions on graphs, groups, or rings, Ann. Pure Appl. Logic 162 (2010), 194200.
V. Shpilrain, Search and witness problems in group theory, Groups, Complexity, and Cryptology 2 (2010), 231246.

2009

V. Shpilrain and G. Zapata, Using decision problems in public key cryptography, Groups, Complexity, and Cryptology 1 (2009), 33-49.
D. Grigoriev and V. Shpilrain, Authentication from matrix conjugation, Groups, Complexity, and Cryptology 1 (2009), 199-206.

2008

book:  A.G.Myasnikov, V. Shpilrain and A.Ushakov, Group-based cryptography, Birkhauser, 2008.
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. 5010 (2008), 252260.
V. Shpilrain, Cryptanalysis of Stickel's key exchange scheme, in: Computer Science in Russia 2008, Lecture Notes Comp. Sc. 5010 (2008), 283288.
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.

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.

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.

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.

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.

2003

book:  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.
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.

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.  

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.

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.

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.

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.