# A new approach to the ElGamal encryption scheme

International Journal of Applied Mathematics and Computer Science (2004)

- Volume: 14, Issue: 2, page 265-267
- ISSN: 1641-876X

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topKościelny, Czesław. "A new approach to the ElGamal encryption scheme." International Journal of Applied Mathematics and Computer Science 14.2 (2004): 265-267. <http://eudml.org/doc/207697>.

@article{Kościelny2004,

abstract = {The ElGamal encryption scheme can be used for both digital signatures and encryption, and its security results from the difficulty of calculating discrete logarithms in a finite field. This algorithm usually works in a multiplicative group of GF(p) and in this case the progress in the discrete logarithm problem forces the users of such a basic ElGamal public key cryptosystem to permanently increase a prime modulus p in order to ensure the desired security. But the task of finding a multiplicative group of GF(p) is unfeasible for an ordinary user. It is possible to overcome this inconvenience by forming an ElGamal encryption scheme which works in a multiplicative group of GF(p^m). Therefore, it is shown in the paper how to implement this cryptosystem for work in the multiplicative group of GF(pm), in its subgroup, and in an algebraic system named the spurious multiplicative group of GF(p^m).},

author = {Kościelny, Czesław},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {public-key encryption; ElGamal cipher; block ciphers},

language = {eng},

number = {2},

pages = {265-267},

title = {A new approach to the ElGamal encryption scheme},

url = {http://eudml.org/doc/207697},

volume = {14},

year = {2004},

}

TY - JOUR

AU - Kościelny, Czesław

TI - A new approach to the ElGamal encryption scheme

JO - International Journal of Applied Mathematics and Computer Science

PY - 2004

VL - 14

IS - 2

SP - 265

EP - 267

AB - The ElGamal encryption scheme can be used for both digital signatures and encryption, and its security results from the difficulty of calculating discrete logarithms in a finite field. This algorithm usually works in a multiplicative group of GF(p) and in this case the progress in the discrete logarithm problem forces the users of such a basic ElGamal public key cryptosystem to permanently increase a prime modulus p in order to ensure the desired security. But the task of finding a multiplicative group of GF(p) is unfeasible for an ordinary user. It is possible to overcome this inconvenience by forming an ElGamal encryption scheme which works in a multiplicative group of GF(p^m). Therefore, it is shown in the paper how to implement this cryptosystem for work in the multiplicative group of GF(pm), in its subgroup, and in an algebraic system named the spurious multiplicative group of GF(p^m).

LA - eng

KW - public-key encryption; ElGamal cipher; block ciphers

UR - http://eudml.org/doc/207697

ER -

## References

top- Kościelny C. (2003): User-friendly ElGamal public-key encrypt-letter scheme. - http://www.mapleapps.com/List.asp?CategoryID=6&Category=Cryptography
- Menezes A.J., van Oorschot P.C. and Vanstone S.A. (1998): Handbook of Applied Cryptography. - Boca Raton: CRC Press.
- Stinson D.R. (1995): Cryptography - Theory and Practice. - Boca Raton: CRC Press. Zbl0855.94001
- Živković M. (1994): Table of primitive binary polynomials, Part II. - Math. Comput., Vol. 63, No. 207, pp. 301-306. Zbl0807.11055

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