Research On Secret Sharing Based On Newton Interpolation

With the continuous development of information technology and the advent of the age of data,the behavior of information interaction through the Internet has become more and more common,and information has become an important social resource.Due to the sufficient openness and inclusiveness of the Internet and other comprehensive factors,information security time is more and more frequent.Information security plays an important role in the field of information science and it is of great practical significance to study information security.As people’s life is more and more dependent on electronic communication,the use of encryption key is more and more frequent,the key management problem also needs a more suitable solution.Secret sharing is an important subject of key management and a good solution to this problem.In 1979,Shamir and Blakley first designed their own(t,n)threshold secret sharing scheme.The former is constructed according to Lagrange interpolation,while the latter is constructed according to projective geometry theory.The Shamir scheme uses Lagrange interpolation to construct a univariate t-1 degree polynomial to distribute the secret,and the secret recovery stage uses t number pairs to reconstruct the polynomial and restore the secret value.Subsequently,many scholars actively engaged in the secret sharing theory and its scheme design,producing many excellent schemes.A large part of the scheme is based on Lagrange interpolation.This paper proposes two secret sharing schemes based on Newton interpolation theory.The main work contents are as follows:(1)A threshold secret sharing scheme based on Newton interpolation is proposed.The scheme uses Newton interpolation to construct polynomial for secret distribution and reconstruction,and uses RSA cryptography to strengthen the security.The distribution phase can use open channels,and because offsets are used,the secret cannot be recovered even if the polynomial is reconstructed.In the secret recovery stage,the recovery polynomial cannot be completed with less than k participants.After the reconstruction of the polynomial,the secret can be restored by adding back the offset value.The scheme can change the threshold value according to different requirements for confidentiality of secrets.The correctness and security of the scheme are analyzed.Finally,a numerical example is given to illustrate the rapidity of shared secret.(2)Based on the threshold secret sharing scheme,a verifiable multi-secret scheme is constructed.This scheme can share multiple secrets at once.RSA encryption algorithm is used again to achieve verifiability to verify the honesty of the distributor and the validity of the distribution process.The correctness and security of the scheme are analyzed.Numerical examples are given to illustrate the convenience of sharing one set of secrets,the low cost of sharing the next set of secrets and the flexibility of changing thresholds.