The REESSE2+ Public-key Encryption Scheme

TL;DR

This paper introduces the REESSE2+ public-key encryption scheme, analyzing its security, efficiency, and comparing its performance with ECC and NTRU, demonstrating significantly faster encryption speeds.

Contribution

The paper proposes the REESSE2+ encryption scheme with novel algorithms and provides a comprehensive security and performance analysis, including comparisons with existing cryptosystems.

Findings

REESSE2+ encryption is ten thousand times faster than ECC and NTRU at similar security levels.

The scheme's security is analyzed against various cryptanalytic attacks, including lattice reduction and meet-in-the-middle.

Encryption and decryption speeds are comparable to ECC and NTRU, respectively.

Abstract

This paper gives the definitions of an anomalous super-increasing sequence and an anomalous subset sum separately, proves the two properties of an anomalous super-increasing sequence, and proposes the REESSE2+ public-key encryption scheme which includes the three algorithms for key generation, encryption and decryption. The paper discusses the necessity and sufficiency of the lever function for preventing the Shamir extremum attack, analyzes the security of REESSE2+ against extracting a private key from a public key through the exhaustive search, recovering a plaintext from a ciphertext plus a knapsack of high density through the L3 lattice basis reduction method, and heuristically obtaining a plaintext through the meet-in-the-middle attack or the adaptive-chosen-ciphertext attack. The authors evaluate the time complexity of REESSE2+ encryption and decryption algorithms, compare REESSE2+ with ECC and NTRU, and find that the encryption speed of REESSE2+ is ten thousand times faster than ECC and NTRU bearing the equivalent security, and the decryption speed of REESSE2+ is roughly equivalent to ECC and NTRU respectively.