Evaluation of Cryptographic Strength and Energy Intensity of Design of Modified Crypto-Code Structure of McEliece with Modified Elliptic Codes

Abstract

The computing development in the post-quantum cryptography era puts forward new requirements for cryptographic mechanisms for providing basic security services. The advent of a full-scale quantum computer casts doubt on the cryptographic strength of cryptosystems based on symmetric cryptography and public-key cryptography. One of the promising areas in the opinion of US NIST experts is the use of crypto-code constructions (crypto-code schemes or code-theoretic schemes) by McEliece or Niederreiter. The construction allows one integrated mechanism to provide the basic requirements for cryptosystems - cryptographic stability, speed of cryptoconversion and besides - reliability based on the use of noise-resistant coding. However, their use is difficult due to the large volume of power of the alphabet, and the possibility of hacking based on Sidelnikov’s attack. The paper proposes to use non-cyclic noise-resistant codes on elliptic curves in a modified McEliece cryptosystem that are not susceptible to Sidelnikov’s attack. The main criteria for constructing a modified crypto code based on the McEliece scheme on elongated elliptic codes are investigated. It is proposed to reduce the energy intensity in the proposed crypto-code design by reducing the power of the Galois field while ensuring the level of cryptographic stability of the modified cryptosystem as a whole with its software implementation. To reduce the field power, it is proposed to use modified elliptic codes, which allows to reduce the field power by 2 times. A comparative assessment of the performance of cryptosystems is carried out. The results of statistical stability studies based on the NIST STS 822 package confirm the cryptographic strength of the proposed cryptosystem on modified elongated elliptic codes. It is proposed to use the method of evaluating the cryptographic strength of various cryptosystems based on the entropy approach.