AWhat changed
Composite-residuosity classes provide a factorization trapdoor for probabilistic public-key encryption whose ciphertext multiplication implements plaintext addition modulo n, with explicit computational and decisional security assumptions.
Scientific scope
Composite-residuosity classes provide a factorization trapdoor for probabilistic public-key encryption whose ciphertext multiplication implements plaintext addition modulo n, with explicit computational and decisional security assumptions. The basic scheme encrypts messages in Z_n using an admissible base, fresh random units and the stated RSA-like modulus conditions. Its additive homomorphism acts modulo n; it is not fully homomorphic encryption. One-wayness and semantic security use different composite-residuosity assumptions; the paper does not supply general chosen-ciphertext security. Fast variants, indicative timing tables and the trapdoor-permutation construction are separate subclaims. WRS has not independently reconstructed every reduction or measured the implementation.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Pascal Paillier · SCIENCE: Sole original byline author of the scoped composite-residuosity and additive-encryption contribution.
- Goldwasser–Micali; Benaloh; Naccache–Stern; Okamoto–Uchiyama · SCIENCE: Explicitly credited prior residuosity and encryption contributions, distinct from this paper's coauthors.
- Jacques Stern; anonymous referee · SCIENCE: Acknowledged in the original paper for independently proving the Class-to-RSA reduction; this specific scientific credit is retained.
- David Pointcheval; other acknowledged discussants · PARTICIPATION: Acknowledged comments, contributions and discussions; additional byline credit or effort percentages are not inferred.
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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