# THE APPROACH TO KEY EXCHANGE PROTOCOL BASED ON METACYCLIC GROUP

### Abstract

The goal of this investigation is effective method of key exchange which based on non-commutative group G. The results of Ko K, Lee S, is improved and generalized.

We consider non-commutative generalization of CDH problem [1,2] on base of metacyclic group of Miller’s Moreno type (minimal non-abelian group). We show that conjugacy problem in this group is intractable. Effectivity of computation is provided due to using groups of residues by modulo n. The algorithm of generating (designing) common key in non-commutative group with 2 mutually commuting subgroups is constructed by us.

### References

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8. Ko K, Lee S, Cheon J, Han J, Kang J, Park C 2000 New public-key cryptosystem using braid groups Advances in cryptology — CRYPTO 2000 1880, P. 166–83

9. Anshel I, Anshel M and Goldfeld D 1999 An algebraic method for public-key cryptography Math. Res. Lett. 6, P. 287–91

10. Anshel I, Anshel M, Fisher B and Goldfeld D 2001 New key agreement protocol in braid group cryptography In Topics in Cryptology – CT-RSA2001 2020, P. 13-27

2. Bohli J, Glas B and Steinwandt R 2006 Towards provable secure group key agreement building on group theory Cryptology ePrint Archive: Report 2006/079

3. Gu L and Zheng S 2014 Conjugacy systems based on nonabelian factorization problems and their applications cryptography J. Appl. Math. Article ID 630607

4. Raievska I, Raievska M and Sysak Y 2016 Finite local nearrings with split metacyclic additive group Algebra Discrete Math. 22, P. 129-52

5. Skuratovskii R 2019 Employment of Minimal Generating Sets and Structure of Sylow 2-Subgroups Alternating Groups in Block Ciphers. Springer, Advances in Computer Comm. Comp. Sciences P. 351-64

6. Otmani A, Tillich J and Dallot L 2010 Cryptanalysis of two McEliece cryptosystems based on quasi-cyclic codes Math.Comput.Sci. 3, P. 129–40

7. Vinogradov I 2016 Elements of number theory Courier Dover Publications.

8. Ko K, Lee S, Cheon J, Han J, Kang J, Park C 2000 New public-key cryptosystem using braid groups Advances in cryptology — CRYPTO 2000 1880, P. 166–83

9. Anshel I, Anshel M and Goldfeld D 1999 An algebraic method for public-key cryptography Math. Res. Lett. 6, P. 287–91

10. Anshel I, Anshel M, Fisher B and Goldfeld D 2001 New key agreement protocol in braid group cryptography In Topics in Cryptology – CT-RSA2001 2020, P. 13-27