Construction of an elliptic curve over finite fields to combine with convolutional code for cryptography

“…Further, we have simulated the performance curves of different codes using algebraic curves; such as Elliptic [27] and Hyperelliptic curves [19,35]. Also, in previous papers we have explored the use of reduced divisors for compression, but with other cryptographic schemes, for example, Diffie Hellman and ElGamal, which are based on DLP [19].…”

Section: Introductionmentioning

confidence: 98%

A new DNA cryptosystem based on AG codes evaluated in gaussian channels

et al. 2016

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This paper proposes a new cryptosystem system that combines DNA cryptography and algebraic curves defined over different Galois fields. The security of the proposed cryptosystem is based on the combination of DNA encoding, a compression process using a hyperelliptic curve over a Galois field G F (2 p ), and coding via an algebraic geometric code built using a Hermitian curve on a Galois field G F 2 2q , where p > 2q. The proposed cryptosystem resists the newest attacks found in the literature because there is no linear relationship between the original data and the information encoded with the Hermitian code. Further, the work factor for such attacks increases proportionally to the number of possible choices for the generator matrix of the Hermitian code. Simulations in terms of BER and signal-to-noise ratio (SNR) are included, which evaluate the gain of the transmitted data in an AWGN channel. The performance of the Electronic supplementary material The online version of this article (4 University of Newcastle upon Tyne, Tyne and Wear, UK DNA/AG cryptosystem scheme is compared with un-coded QPSK, and the McEliece code in terms of BER. Further, the proposed DNA/AG system outperforms the security level of the McEliece algorithm.

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“…In [6] show a combination of a nonlinear elliptic curve with convolutional codes to provide secure transmission and error correction over a Galois field at the channel level. That paper presents algorithms to construct efficient elliptic curves to combine with convolutional codes.…”

Section: Introductionmentioning

confidence: 99%

“…Based in [6] we introduce a public key encryption scheme for wireless sensor networks. This scheme is based on elliptic curves [7] defined over binary finite field combined with Low Density Parity Check codes (LDPC) [8].…”

Section: Introductionmentioning

confidence: 99%