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US 2017/0012948 A1Published application
Rsa decryption using multiplicative secret sharing
AssigneeNXP B.V.
InventorsMichael Michel Patrick Peeters, Ventzislav Nikov
Life of this patent
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Abstract
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.
Claims20
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.
5 more elements
A device for transmitting a message, M, comprising:
- a memory;
- a processor in communication with the memory, the processor being configured to:
- perform a cryptographic process including an RSA process having a private key, d, being split 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
- determining said message M after being provided a text, C, being capable of, by calculating
- 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.
9 more elements
Dependencies are inferred from the claim text.