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One main goal for designing actively secure 2PC protocols is to reduce the communication overhead, compared to semi-honest 2PC protocols. In this paper, we make significant progress in closing this gap by proposing two new actively secure constant-round 2PC protocols, one with one-way communication of \n \n $$2\\kappa +5$$<\/jats:tex-math>\n \n \n 2<\/mml:mn>\n \u03ba<\/mml:mi>\n +<\/mml:mo>\n 5<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> bits per AND gate (for \n \n $$\\kappa $$<\/jats:tex-math>\n \n \u03ba<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-bit computational security and any statistical security) and one with total communication of \n \n $$2\\kappa +\\rho +5$$<\/jats:tex-math>\n \n \n 2<\/mml:mn>\n \u03ba<\/mml:mi>\n +<\/mml:mo>\n \u03c1<\/mml:mi>\n +<\/mml:mo>\n 5<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> bits per AND gate (for \n \n $$\\rho $$<\/jats:tex-math>\n \n \u03c1<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-bit statistical security). In particular, our first protocol essentially matches the one-way communication of semi-honest half-gates protocol. Our optimization is achieved by three new techniques: \n \n The recent compression technique by Dittmer et al. (Crypto 13510:57\u201387, 2022) shows that a relaxed preprocessing is sufficient for authenticated garbling that does not reveal masked wire values to the garbler. We introduce a new form of authenticated bits and propose a new technique of generating authenticated AND triples to reduce the one-way communication of preprocessing from \n \n $$5\\rho +1$$<\/jats:tex-math>\n \n \n 5<\/mml:mn>\n \u03c1<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> bits to 2 bits per AND gate for \n \n $$\\rho $$<\/jats:tex-math>\n \n \u03c1<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-bit statistical security.<\/jats:p>\n <\/jats:list-item>\n \n Unfortunately, the above compressing technique is only compatible with a less compact authenticated garbled circuit of size \n \n $$2\\kappa +3\\rho $$<\/jats:tex-math>\n \n \n 2<\/mml:mn>\n \u03ba<\/mml:mi>\n +<\/mml:mo>\n 3<\/mml:mn>\n \u03c1<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> bits per AND gate. We designed a new authenticated garbling that does not use information-theoretic MACs but rather dual execution without leakage to authenticate wire values in the circuit. This allows us to use a more compact half-gates based authenticated garbled circuit of size \n \n $$2\\kappa +1$$<\/jats:tex-math>\n \n \n 2<\/mml:mn>\n \u03ba<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> bits per AND gate, and meanwhile keep compatible with the compression technique. Our new technique can achieve one-way communication of \n \n $$2\\kappa +5$$<\/jats:tex-math>\n \n \n 2<\/mml:mn>\n \u03ba<\/mml:mi>\n +<\/mml:mo>\n 5<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> bits per AND gate.<\/jats:p>\n <\/jats:list-item>\n \n In terms of total communication, we notice that the communication overhead of the consistency checking method by Dittmer et al.\u00a0(Crypto 13510:57\u201387, 2022) can be optimized by adding one-round of interaction and utilizing the Free-XOR property. This reduces the online communication from \n \n $$2\\kappa +3\\rho $$<\/jats:tex-math>\n \n \n 2<\/mml:mn>\n \u03ba<\/mml:mi>\n +<\/mml:mo>\n 3<\/mml:mn>\n \u03c1<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> bits down to \n \n $$2\\kappa +\\rho +1$$<\/jats:tex-math>\n \n \n 2<\/mml:mn>\n \u03ba<\/mml:mi>\n +<\/mml:mo>\n \u03c1<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> bits per AND gate. Combined with our first contribution, this yields total amortized communication of \n \n $$2\\kappa +\\rho +5$$<\/jats:tex-math>\n \n \n 2<\/mml:mn>\n \u03ba<\/mml:mi>\n +<\/mml:mo>\n \u03c1<\/mml:mi>\n +<\/mml:mo>\n 5<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> bits.<\/jats:p>\n <\/jats:list-item>\n <\/jats:list>\n <\/jats:p>","DOI":"10.1007\/s00145-025-09539-4","type":"journal-article","created":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T23:10:11Z","timestamp":1740611411000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Actively Secure Half-Gates with Minimum Overhead under Duplex Networks"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6203-413X","authenticated-orcid":false,"given":"Hongrui","family":"Cui","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5991-7417","authenticated-orcid":false,"given":"Xiao","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7453-4043","authenticated-orcid":false,"given":"Kang","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9278-4521","authenticated-orcid":false,"given":"Yu","family":"Yu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,2,26]]},"reference":[{"key":"9539_CR1","doi-asserted-by":"publisher","unstructured":"J. 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