RSA DECRYPTION USING MULTIPLICATIVE SECRET SHARING

摘要

An embodiment features an RSA process in which the private key is separated into shares. Decryption (and authentication and other RSA objectives) may be accomplished by successive modular exponentiation of, for example, a ciphertext or a signature.

主权项

1. Performing, in a processor, a cryptographic process comprising:
in an RSA process having a private key, d, splitting d into k shares, such that
d=Πd*imodφ(N), 1≦i≦k, where N is the RSA modulus and φ(N) is the Euler totient function, and being provided a text, C, determining a text, M, such that
M=CΠd*i mod φ(N)≡Cd≡M (mod N) for 1≦i≦k such that M is computed with k modular exponentiations performed in a sequence such that
Mi+1=Mid*imod N for 1≦i≦k and where
M1=M and C=Mk+1.