Two Generic Constructions of Probabilistic Cryptosystems and their Applications

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Provided by: GREYC
Topic: Security
Format: PDF
In this paper, the authors build, in a generic way, two asymmetric cryptosystems with a careful study of their security. They present first an additively homomorphic scheme which generalizes, among others, the paillier cryptosystem, and then, another scheme, built from a deterministic trapdoor function. Both schemes are proved semantically secure against chosen plaintext attacks in the standard security model and modify versions can be proved secure against adaptive chosen ciphertext attacks. By implementing these constructions with quotients of Z, elliptic curves and quadratic field's quotients they get some cryptosystems yet described in the past few years and provide variants that achieve higher levels of security than the original schemes.
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