## Cryptology ePrint Archive: Report 2009/208

**PUBLIC KEY CRYPTOGRAPHY USING PERMUTATION P-POLYNOMIALS OVER FINITE FIELDS**

*Rajesh P Singh and B.K.Sarma and A.Saikia*

**Abstract: **In this paper we propose an efficient multivariate
public key cryptosystem based on permutation p-polynomials over
finite fields. We first characterize a class of permutation
p-polynomials over finite fields $F_{q^{m}}$ and then construct a
trapdoor function using this class of permutation p-polynomials.
The complexity of encryption in our public key cryptosystem is
$O(m^{3})$ multiplication which is equivalent to other
multivariate public key cryptosystems. However the decryption is
much faster than other multivariate public key cryptosystems. In
decryption we need $O(m^{2})$ left cyclic shifts and $O(m^{2})$
xor operations.

**Category / Keywords: **Public Key Cryptography, Multivariate Cryptography, Permutation Polynomials, Linearized Polynomials

**Publication Info: **Unpublished

**Date: **received 13 May 2009, last revised 24 Jun 2009

**Contact author: **r pratap at iitg ernet in

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

**Note: **Some modifications related to Latex formatting has been done.

**Version: **20090624:084547 (All versions of this report)

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