Editing Paillier cryptosystem (section)

===Applications===
====Electronic voting====
Semantic security is not the only consideration. There are situations under which malleability may be  desirable. Secure [[electronic voting]] systems can utilize the above homomorphic properties. Consider a simple binary ("for" or "against") vote. Let ''m'' voters cast a vote of either ''1'' (for) or ''0'' (against). Each voter encrypts their choice before casting their vote. The election official takes the product of the ''m'' encrypted votes and then decrypts the result and obtains the value ''n'', which is the sum of all the votes. The election official then knows that ''n'' people voted ''for'' and ''m-n'' people voted ''against''. The role of the random ''r'' ensures that two equivalent votes will encrypt to the same value only with negligible likelihood, hence ensuring voter privacy.

====Electronic cash====
Another feature named in paper is the notion of self-[[Blinding (cryptography)|blinding]]. This is the ability to change one ciphertext into another without changing the content of its decryption. This has application to the development of [[ecash]], an effort originally spearheaded by [[David Chaum]]. Imagine paying for an item online without the vendor needing to know your credit card number, and hence your identity. The goal in both electronic cash and electronic voting, is to ensure the e-coin (likewise e-vote) is valid, while at the same time not disclosing the identity of the person with whom it is currently associated.

====Electronic auction====
The Paillier cryptosystem plays a crucial role in enhancing the security of [[Electronic auction|electronic auctions]]. It prevents fraudulent activities such as dishonest auctioneers and collusion between bidders and auctioneers who manipulate bids. By ensuring the confidentiality of actual bidding values while revealing auction results, the Pailler cryptosystem successfully promotes fair practices. <ref>Pan, M., Sun, J., & Fang, Y. (2011). Purging the Back-Room Dealing: Secure Spectrum Auction Leveraging Paillier Cryptosystem. IEEE Journal on Selected Areas in Communications, 29(4), 866–876. https://doi.org/10.1109/JSAC.2011.110417</ref>

====Threshold cryptosystem====
The homomorphic property of Paillier cryptosystem is sometimes used to build [[Threshold cryptosystem|Threshold]] ECDSA signature.<ref>{{cite book |last1=Canetti |first1=Ran |last2=Gennaro |first2=Rosario |last3=Goldfeder |first3=Steven |last4=Makriyannis |first4=Nikolaos |last5=Peled |first5=Udi |title=Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security |chapter=UC Non-Interactive, Proactive, Threshold ECDSA with Identifiable Aborts |date=30 October 2020 |pages=1769–1787 |doi=10.1145/3372297.3423367 |chapter-url=https://dl.acm.org/doi/10.1145/3372297.3423367 |publisher=Association for Computing Machinery|isbn=9781450370899 |s2cid=226228099 }}</ref>