Welcome to the resource topic for 2023/504
Title:
Fully Homomorphic Encryption Based On Polynomial Operation
Authors: Shuailiang Hu
Abstract:Homomorphic encryption requires the homomorphism of encrypted ciphertext, and the operation between ciphertexts can be reflected in plaintexts. Fully homomorphic encryption requires that the encryption algorithm can satisfy additive homomorphism and multiplicative homomorphism at the same time. At present, there are many fully homomorphic encryption schemes, such as fully homomorphic encryption based on ideal lattices, AGCD problem, LWE problem, RLWE problem, and so on. But the improvement of efficiency, length of ciphertext, and calculation limit of the fully homomorphic encryption scheme are still problems that need further study.
Based on Lagrangian interpolation polynomials, we propose a fully homomorphic encryption scheme according to the difficulty of finding roots of a polynomial with the degree of at least two(mod n=p*q, p, q are both private large primes). We reasonably construct polynomials trap_1 and trap_0 to generate the ciphertext of message m, so that calculation between ciphertexts can directly act on plaintexts. Our scheme is safe as long as the Rabin encryption algorithm cannot be cracked.
ePrint: https://eprint.iacr.org/2023/504
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