1.

M. Ajtai and C. Dwork, “A public-key cryptosystem with worst-case/average case equivalence,” *Proceedings of the* 29*th Annual ACM Symposium on Theory of Computing*(1997), ACM, New York (1999), pp. 284–293.

2.

I. Anshel and M. Anshel, “From the post-Markov theorem through decision problems to public-key cryptography,” *Amer. Math. Monthly*, **100**, 835–844 (1993).

3.

I. Anshel, M. Anshel, and D. Goldfeld, “An algebraic method for public-key cryptography,” *Math. Res. Lett.*, **6**, 287–291 (1999).

4.

J. Benaloh, “Dense probabilistic encryption,” *First Annual Workshop on Selected Areas in Cryptology*(1994), pp. 120–128.

5.

A. Blass and Y. Gurevich, “Matrix transformation is complete for the average case,” *SIAM J. Comput.*, **24**, 3–29 (1995).

6.

D. Coppersmith and I. Shparlinski, “On polynomial approximation of the discrete logarithm and the Diffie-Hellman mapping,” *J. Cryptology*, **13**, 339–360 (2000).

7.

J. Dieudonn’e and J. Carrell, *Invariant Theory, Old and New*, Academic Press (1971).

8.

Do Long Van, A. Jeyanthi, R. Siromony, and K. Subramanian, “Public key cryptosystems based on word problems,” *ICOMIDC Symp. Math. of Computation*, Ho Chi Minh City (1988).

9.

J. Feigenbaum and M. Merritt, “Open questions, talk abstracts, and summary of discussions,” *DIMACS Ser. Discrete Math. Theoret. Comput. Sci.*, **2**, 1–45 (1991).

10.

M. Garzon and Y. Zalcstein, “The complexity of Grigorchuk groups with application to cryptography,” *Theoret. Comput. Sci.*, **88**, 83–98 (1991).

11.

O. Goldreich, *Modern Cryptography, Probabilistic Proofs, and Pseudorandomness*, Springer (1998).

12.

O. Goldreich, S. Goldwasser, and S. Halevi, “Public-key cryptosystems from lattice reduction problems,” *Lect. Notes Comput. Sci.*, **1294**, 112–131 (1997).

13.

S. Goldwasser and M. Bellare, *Lecture Notes on Cryptography*, http://www-cse.ucsd.edu/users/mihir/papers/gb.html (2001).

14.

S. Goldwasser and S. Micali, “Probabilistic encryption,” *J. Comput. System Sci.*, **28**, 270–299 (1984).

15.

D. Grigoriev and I. Ponomarenko, “On non-Abelian homomorphic public-key cryptosystems,” *Zap. Nauchn. Semin. POMI*, **293**, 39–58 (2002).

16.

K. H. Ko, S. J. Lee, J. H. Cheon, J. W. Han, J. Kang, and C. Park, “New public-key cryptosystem using braid groups,” *Lect. Notes Comput. Sci.*, **1880**, 166–183 (2000).

17.

N. Koblitz, *Algebraic Aspects of Cryptography*, Springer-Verlag, Berlin (1998).

18.

K. Koyama, U. Maurer, T. Okamoto, and S. Vanstone, “New public-key schemes based on elliptic curves over the ring ℤ_{n},” *Lect. Notes Comput. Sci.*, **576**, 252–266 (1991).

19.

L. Levin, “Average case complete problems,” *SIAM J. Comput.*, **15**, 285–286 (1986).

20.

E. Luks, “Permutation groups and polynomial-time computations,” *DIMACS Ser. Discrete Math. Theoret. Comput. Sci.*, **11**, 139–175 (1993).

21.

E. Luks, *Personal communication*(2002).

22.

U. Maurer and S. Wolf, “Lower bounds on generic algorithms in groups,” *Lect. Notes Comput. Sci.*, **1403**, 72–84 (1998).

23.

D. Naccache and J. Stern, “A new public-key cryptosystem,” *Lect. Notes Comput. Sci.*, **1233**, 27–36 (1997).

24.

D. Naccache and J. Stern, “A new public-key cryptosystem based on higher residues,” *Proceedings of the* 5*th ACM Conference on Computer and Communication Security*(1998), pp. 59–66.

25.

T. Okamoto and S. Uchiyama, “A new public-key cryptosystem as secure as factoring,” *Lect. Notes Comput. Sci.*, **1403**, 308–317 (1998).

26.

S.-H. Paeng, D. Kwon, K.-C. Ha, and J. H. Kim, “Improved public key cryptosystem using finite non-Abelian groups,” Preprint NSRI Korea.

27.

P. Paillier, “Public-key cryptosystem based on composite degree residuosity classes,” *Lect. Notes Comput. Sci.*, **1592**, 223–238 (1999).

28.

D. Rappe, *Algebraisch Homomorphe Kryptosysteme*, Diplomarbeit, Universit¨at Dortmund (2000).

29.

L. Ronyai, “Computations in associative algebras,” *DIMACS Ser. Discrete Math. Theoret. Comput. Sci.*, **11**, 221–243 (1993).

30.

T. Springer, “Invariant theory,” *Lect. Notes Math.*, **585**, Springer (1977).

31.

B. Sturmfels, *Algorithms in Invariant Theory*, Springer-Verlag, Vienna (1993).

32.

N. Wagner and M. Magyarik, “A public-key cryptosystem based on the word-problem,” *Lect. Notes Comput. Sci.*, **196**, 19–36 (1985).

33.

A. Yao, “How to generate and exchange secrets,” *Proceedings of the* 27*th Annual IEEE Symposium on Foundations of Computer Sciences*(1986), pp. 162–167.