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Codes Cryptogr."],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We construct an efficient dynamic group signature (or more generally an accountable ring signature) from isogeny and lattice assumptions. Our group signature is based on a simple generic construction that can be instantiated by cryptographically hard group actions such as the CSIDH group action or an MLWE-based group action. The signature is of size <jats:inline-formula><jats:alternatives><jats:tex-math>$$O(\\log N)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mo>log<\/mml:mo>\n                    <mml:mi>N<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, where <jats:italic>N<\/jats:italic> is the number of users in the group. Our idea builds on the recent efficient OR-proof by Beullens, Katsumata, and Pintore (Asiacrypt\u201920), where we efficiently add a proof of valid ciphertext to their OR-proof and further show that the resulting non-interactive zero-knowledge proof system is <jats:italic>online extractable<\/jats:italic>. Our group signatures satisfy more ideal security properties compared to previously known constructions, while simultaneously having an attractive signature size. The signature size of our isogeny-based construction is an order of magnitude smaller than all previously known post-quantum group signatures (e.g., 6.6 KB for 64 members). In comparison, our lattice-based construction has a larger signature size (e.g., either 126 KB or 89 KB for 64 members depending on the satisfied security property). However, since the <jats:inline-formula><jats:alternatives><jats:tex-math>$$O(\\cdot )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mo>\u00b7<\/mml:mo>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-notation hides a very small constant factor, it remains small even for very large group sizes, say <jats:inline-formula><jats:alternatives><jats:tex-math>$$2^{20}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mn>2<\/mml:mn>\n                    <mml:mn>20<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s10623-023-01192-x","type":"journal-article","created":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T17:03:20Z","timestamp":1677517400000},"page":"2141-2200","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Group signatures and more from isogenies and lattices: generic, simple, and efficient"],"prefix":"10.1007","volume":"91","author":[{"given":"Ward","family":"Beullens","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Samuel","family":"Dobson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuichi","family":"Katsumata","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi-Fu","family":"Lai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Federico","family":"Pintore","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,2,27]]},"reference":[{"key":"1192_CR1","doi-asserted-by":"publisher","unstructured":"Abe M., Ohkubo M., Suzuki K.: 1-out-of-n signatures from a variety of keys. 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