Public Key Encryption and Signature Schemes Based on Polynomials over ℤn
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The problem of computing roots of a polynomial over the ring ℤn is equivalent to factoring n. Starting from this intractable pro- blem we construct a public key encryption scheme where the message blocks are encrypted as roots of a polynomial over ℤn and a signature scheme where the signature belonging to a message is a (set of) root(s) of a polynomial having the message blocks as coefficients. These sche- mes can be considered as extensions of Rabin’s encryption and signature scheme. However, our signature scheme has some new properties: a short signature can be generated for a long message without using a hash func- tion, and the security features of the scheme can be chosen either to be similar to those of the RSA scheme or to be equivalent to those of Rabin’s scheme.
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