{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T17:12:01Z","timestamp":1775754721657,"version":"3.50.1"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032226945","type":"print"},{"value":"9783032226952","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-22695-2_10","type":"book-chapter","created":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T16:30:05Z","timestamp":1775752205000},"page":"287-318","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Learning with\u00a0Errors with\u00a0Output Dependencies: LWE, LWR, and\u00a0Physical Learning Problems Under the\u00a0Same Umbrella"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9744-1539","authenticated-orcid":false,"given":"Cl\u00e9ment","family":"Hoffmann","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5733-4341","authenticated-orcid":false,"given":"Pierrick","family":"M\u00e9aux","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9268-3034","authenticated-orcid":false,"given":"M\u00e9lissa","family":"Rossi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7444-0285","authenticated-orcid":false,"given":"Fran\u00e7ois-Xavier","family":"Standaert","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,4,10]]},"reference":[{"key":"10_CR1","doi-asserted-by":"publisher","unstructured":"Albrecht, M.R., et al.: Estimate all the LWE, NTRU schemes! In: Catalano, D., De Prisco, R. (eds.) SCN 2018. LNCS, vol. 11035, pp. 351\u2013367. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-98113-0_19","DOI":"10.1007\/978-3-319-98113-0_19"},{"key":"10_CR2","doi-asserted-by":"publisher","unstructured":"Alekhnovich, M.: More on average case vs approximation complexity. In: 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings, pp. 298\u2013307 (2003). https:\/\/doi.org\/10.1109\/SFCS.2003.1238204","DOI":"10.1109\/SFCS.2003.1238204"},{"key":"10_CR3","doi-asserted-by":"publisher","unstructured":"Banerjee, A., Peikert, C., Rosen, A.: Pseudorandom functions and lattices. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT\u00a02012. LNCS, vol.\u00a07237, pp. 719\u2013737. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-29011-4_42","DOI":"10.1007\/978-3-642-29011-4_42"},{"key":"10_CR4","doi-asserted-by":"publisher","unstructured":"Bellizia, D., et al.: Learning parity with physical noise: imperfections, reductions and FPGA prototype. IACR TCHES 2021(3), 390\u2013417 (2021). https:\/\/doi.org\/10.46586\/tches.v2021.i3.390-417. https:\/\/tches.iacr.org\/index.php\/TCHES\/article\/view\/8979","DOI":"10.46586\/tches.v2021.i3.390-417"},{"key":"10_CR5","doi-asserted-by":"publisher","unstructured":"Bellizia, D., Hoffmann, C., Kamel, D., M\u00e9aux, P., Standaert, F.X.: When bad news become good news towards usable instances of learning with physical errors. IACR TCHES 2022(4), 1\u201324 (2022). https:\/\/doi.org\/10.46586\/tches.v2022.i4.1-24","DOI":"10.46586\/tches.v2022.i4.1-24"},{"key":"10_CR6","doi-asserted-by":"publisher","unstructured":"Blum, A., Furst, M.L., Kearns, M.J., Lipton, R.J.: Cryptographic primitives based on hard learning problems. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol.\u00a0773, pp. 278\u2013291. Springer, Heidelberg (1994). https:\/\/doi.org\/10.1007\/3-540-48329-2_24","DOI":"10.1007\/3-540-48329-2_24"},{"key":"10_CR7","doi-asserted-by":"publisher","unstructured":"Blum, A., Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. In: 32nd ACM STOC, pp. 435\u2013440. ACM Press (2000). https:\/\/doi.org\/10.1145\/335305.335355","DOI":"10.1145\/335305.335355"},{"key":"10_CR8","doi-asserted-by":"publisher","unstructured":"Bogdanov, A., Guo, S., Masny, D., Richelson, S., Rosen, A.: On the hardness of learning with rounding over small modulus. In: Kushilevitz, E., Malkin, T. (eds.) TCC\u00a02016-A, Part\u00a0I. LNCS, vol.\u00a09562, pp. 209\u2013224. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-49096-9_9","DOI":"10.1007\/978-3-662-49096-9_9"},{"key":"10_CR9","doi-asserted-by":"publisher","unstructured":"Brakerski, Z., Lyubashevsky, V., Vaikuntanathan, V., Wichs, D.: Worst-case hardness for LPN and cryptographic hashing via code smoothing. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT\u00a02019, Part\u00a0III. LNCS, vol. 11478, pp. 619\u2013635. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17659-4_21","DOI":"10.1007\/978-3-030-17659-4_21"},{"key":"10_CR10","doi-asserted-by":"publisher","unstructured":"Cheon, J.H., Kim, A., Kim, M., Song, Y.S.: Homomorphic encryption for arithmetic of approximate numbers. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT\u00a02017, Part\u00a0I. LNCS, vol. 10624, pp. 409\u2013437. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-70694-8_15","DOI":"10.1007\/978-3-319-70694-8_15"},{"issue":"1","key":"10_CR11","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1007\/s00145-019-09319-x","volume":"33","author":"I Chillotti","year":"2020","unstructured":"Chillotti, I., Gama, N., Georgieva, M., Izabach\u00e8ne, M.: TFHE: fast fully homomorphic encryption over the torus. J. Cryptol. 33(1), 34\u201391 (2020). https:\/\/doi.org\/10.1007\/s00145-019-09319-x","journal-title":"J. Cryptol."},{"key":"10_CR12","doi-asserted-by":"publisher","unstructured":"Dachman-Soled, D., Ducas, L., Gong, H., Rossi, M.: LWE with side information: attacks and concrete security estimation. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO\u00a02020, Part\u00a0II. LNCS, vol. 12171, pp. 329\u2013358. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-56880-1_12","DOI":"10.1007\/978-3-030-56880-1_12"},{"key":"10_CR13","doi-asserted-by":"publisher","unstructured":"D\u2019Anvers, J.P., Karmakar, A., Roy, S.S., Vercauteren, F.: Saber: module-LWR based key exchange, CPA-secure encryption and CCA-secure KEM. In: Joux, A., Nitaj, A., Rachidi, T. (eds.) AFRICACRYPT 2018. LNCS, vol. 10831, pp. 282\u2013305. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-89339-6_16","DOI":"10.1007\/978-3-319-89339-6_16"},{"key":"10_CR14","doi-asserted-by":"publisher","unstructured":"Duc, A., Vaudenay, S.: HELEN: a public-key cryptosystem based on the LPN and the decisional minimal distance problems. In: Youssef, A., Nitaj, A., Hassanien, A.E. (eds.) AFRICACRYPT 2013. LNCS, vol.\u00a07918, pp. 107\u2013126. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-38553-7_6","DOI":"10.1007\/978-3-642-38553-7_6"},{"key":"10_CR15","doi-asserted-by":"publisher","unstructured":"Ducas, L., et al.: CRYSTALS-Dilithium: a lattice-based digital signature scheme. IACR TCHES 2018(1), 238\u2013268 (2018). https:\/\/doi.org\/10.13154\/tches.v2018.i1.238-268. https:\/\/tches.iacr.org\/index.php\/TCHES\/article\/view\/839","DOI":"10.13154\/tches.v2018.i1.238-268"},{"key":"10_CR16","doi-asserted-by":"publisher","unstructured":"Duval, S., M\u00e9aux, P., Momin, C., Standaert, F.X.: Exploring crypto-physical dark matter and learning with physical rounding. IACR TCHES 2021(1), 373\u2013401 (2021). https:\/\/doi.org\/10.46586\/tches.v2021.i1.373-401. https:\/\/tches.iacr.org\/index.php\/TCHES\/article\/view\/8738","DOI":"10.46586\/tches.v2021.i1.373-401"},{"key":"10_CR17","doi-asserted-by":"publisher","unstructured":"Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. (ed.) 41st ACM STOC, pp. 169\u2013178. ACM Press (2009). https:\/\/doi.org\/10.1145\/1536414.1536440","DOI":"10.1145\/1536414.1536440"},{"key":"10_CR18","doi-asserted-by":"publisher","unstructured":"Gilbert, H., Robshaw, M.J.B., Seurin, Y.: How to encrypt with the LPN problem. In: Aceto, L., Damg\u00e5rd, I., Goldberg, L.A., Halld\u00f3rsson, M.M., Ing\u00f3lfsd\u00f3ttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part\u00a0II. LNCS, vol.\u00a05126, pp. 679\u2013690. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-70583-3_55","DOI":"10.1007\/978-3-540-70583-3_55"},{"key":"10_CR19","doi-asserted-by":"publisher","unstructured":"Hoffmann, C., Libert, B., Momin, C., Peters, T., Standaert, F.X.: POLKA: towards leakage-resistant post-quantum CCA-secure public key encryption. In: Boldyreva, A., Kolesnikov, V. (eds.) PKC\u00a02023, Part\u00a0I. LNCS, vol. 13940, pp. 114\u2013144. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-31368-4_5","DOI":"10.1007\/978-3-031-31368-4_5"},{"key":"10_CR20","doi-asserted-by":"publisher","unstructured":"Hoffmann, C., M\u00e9aux, P., Momin, C., Rotella, Y., Standaert, F.X., Udvarhelyi, B.: Learning with physical rounding for linear and quadratic leakage functions. In: Handschuh, H., Lysyanskaya, A. (eds.) CRYPTO\u00a02023, Part\u00a0III. LNCS, vol. 14083, pp. 410\u2013439. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-38548-3_14","DOI":"10.1007\/978-3-031-38548-3_14"},{"key":"10_CR21","doi-asserted-by":"publisher","unstructured":"Hopper, N.J., Blum, M.: Secure human identification protocols. In: Boyd, C. (ed.) ASIACRYPT\u00a02001. LNCS, vol.\u00a02248, pp. 52\u201366. Springer, Heidelberg (2001). https:\/\/doi.org\/10.1007\/3-540-45682-1_4","DOI":"10.1007\/3-540-45682-1_4"},{"issue":"5","key":"10_CR22","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1109\/TDSC.2018.2830763","volume":"17","author":"D Kamel","year":"2020","unstructured":"Kamel, D., Standaert, F.X., Duc, A., Flandre, D., Berti, F.: Learning with physical noise or errors. IEEE Trans. Dependable Secure Comput. 17(5), 957\u2013971 (2020). https:\/\/doi.org\/10.1109\/TDSC.2018.2830763","journal-title":"IEEE Trans. Dependable Secure Comput."},{"key":"10_CR23","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/978-3-642-27660-6_9","volume-title":"SOFSEM 2012","author":"K Pietrzak","year":"2012","unstructured":"Pietrzak, K.: Cryptography from learning parity with noise. In: Bielikov\u00e1, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Tur\u00e1n, G. (eds.) SOFSEM 2012. LNCS, vol. 7147, pp. 99\u2013114. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-27660-6_9"},{"key":"10_CR24","doi-asserted-by":"publisher","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Gabow, H.N., Fagin, R. (eds.) 37th ACM STOC, pp. 84\u201393. ACM Press (2005). https:\/\/doi.org\/10.1145\/1060590.1060603","DOI":"10.1145\/1060590.1060603"},{"key":"10_CR25","doi-asserted-by":"publisher","unstructured":"Yu, Y., Steinberger, J.P.: Pseudorandom functions in almost constant depth from low-noise LPN. In: Fischlin, M., Coron, J.S. (eds.) EUROCRYPT\u00a02016, Part\u00a0II. LNCS, vol.\u00a09666, pp. 154\u2013183. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-49896-5_6","DOI":"10.1007\/978-3-662-49896-5_6"},{"key":"10_CR26","doi-asserted-by":"publisher","unstructured":"Yu, Y., Zhang, J., Weng, J., Guo, C., Li, X.: Collision resistant hashing from sub-exponential learning parity with noise. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT\u00a02019, Part\u00a0II. LNCS, vol. 11922, pp. 3\u201324. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-34621-8_1","DOI":"10.1007\/978-3-030-34621-8_1"}],"container-title":["Lecture Notes in Computer Science","Post-Quantum Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-22695-2_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T16:30:05Z","timestamp":1775752205000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-22695-2_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032226945","9783032226952"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-22695-2_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"10 April 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"PQCrypto","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Post-Quantum Cryptography","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Saint-Malo","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 April 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 April 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"pqcrypto2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}