{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T08:33:41Z","timestamp":1761294821346,"version":"3.40.3"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T00:00:00Z","timestamp":1740096000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T00:00:00Z","timestamp":1740096000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000943","name":"Commonwealth Scientific and Industrial Research Organisation","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000943","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Inf. Secur."],"published-print":{"date-parts":[[2025,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>The generation of pseudorandom binary sequences is of great importance in numerous applications, ranging from simulation and gambling to cryptography. Pseudorandom bit generators (PRBGs) can be divided into two categories based on their claimed security. The first category includes PRBGs that are provably secure, such as the Blum\u2013Blum\u2013Shub generator. The security of the second category relies on heuristic arguments. Unfortunately, PRBGs from the first category are inherently inefficient, and some are vulnerable to quantum attacks. In contrast, those in the second category are highly efficient, though their security depends on their resistance to known cryptographic attacks. This work presents a construction of a PRBG based on the asymmetric numeral system (ANS) compression algorithm. We define a family of PRBGs for <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$2^R$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mn>2<\/mml:mn>\n                    <mml:mi>R<\/mml:mi>\n                  <\/mml:msup>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> ANS states and prove that it is indistinguishable from a truly random generator for sufficiently large <jats:italic>R<\/jats:italic>. To enhance efficiency, we explore PRBGs with smaller values of <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$R = 7, 8, 9$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>R<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>7<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>8<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>9<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> and demonstrate methods for removing local correlations in the output stream. We permute output bits using rotation and Keccak transformations, showing that the permuted bits pass all NIST tests. Our PRBG design is provably secure for large values of <jats:italic>R<\/jats:italic> and heuristically secure for smaller values. Additionally, we claim that our PRBG is secure against quantum adversaries.<\/jats:p>","DOI":"10.1007\/s10207-025-00995-4","type":"journal-article","created":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:25:45Z","timestamp":1740119145000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Pseudorandom bit generation with asymmetric numeral systems"],"prefix":"10.1007","volume":"24","author":[{"given":"Josef","family":"Pieprzyk","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcin","family":"Paw\u0142owski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pawe\u0142","family":"Morawiecki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arash","family":"Mahboubi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jarek","family":"Duda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seyit","family":"Camtepe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,2,21]]},"reference":[{"issue":"2","key":"995_CR1","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1137\/0217013","volume":"17","author":"W Alexi","year":"1988","unstructured":"Alexi, W., Chor, B., Goldreich, O., Schnorr, C.P.: Rsa and rabin functions: certain parts are as hard as the whole. SIAM J. Comput. 17(2), 194\u2013209 (1988)","journal-title":"SIAM J. Comput."},{"key":"995_CR2","doi-asserted-by":"publisher","first-page":"634","DOI":"10.1007\/11424826_67","volume-title":"Computational Science and Its Applications - ICCSA 2005","author":"A Alkassar","year":"2005","unstructured":"Alkassar, A., Nicolay, T., Rohe, M.: Obtaining true-random binary numbers from a weak radioactive source. In: Gervasi, O., Gavrilova, M.L., Kumar, V., Lagan\u00e0, A., Lee, H.P., Mun, Y., Taniar, D., Tan, C.J.K. (eds.) Computational Science and Its Applications - ICCSA 2005, pp. 634\u2013646. Springer, Berlin (2005)"},{"key":"995_CR3","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/978-3-642-38348-9_19","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2013","author":"G Bertoni","year":"2013","unstructured":"Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: Keccak. In: Johansson, T., Nguyen, P.Q. (eds.) Advances in Cryptology\u2014EUROCRYPT 2013, pp. 313\u2013314. Springer, Berlin (2013)"},{"issue":"2","key":"995_CR4","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1137\/0215025","volume":"15","author":"L Blum","year":"1986","unstructured":"Blum, L., Blum, M., Shub, M.: A simple unpredictable pseudo-random number generator. SIAM J. Comput. 15(2), 364\u2013383 (1986)","journal-title":"SIAM J. Comput."},{"key":"995_CR5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511814068","volume-title":"Random Graphs","author":"B Bollob\u00e1s","year":"2001","unstructured":"Bollob\u00e1s, B.: Random Graphs. Cambridge University Press, Cambridge (2001)"},{"issue":"3\u20134","key":"995_CR6","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","volume":"24","author":"W Bosma","year":"1997","unstructured":"Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symbol. Comput. 24(3\u20134), 235\u2013265 (1997)","journal-title":"J. Symbol. Comput."},{"key":"995_CR7","doi-asserted-by":"publisher","first-page":"3859","DOI":"10.1109\/TIFS.2021.3096026","volume":"16","author":"S Camtepe","year":"2021","unstructured":"Camtepe, S., Duda, J., Mahboubi, A., Morawiecki, P., Nepal, S., Paw\u0142owski, M., Pieprzyk, J.: Compcrypt-lightweight ANS-based compression and encryption. IEEE Trans. Inf. Forensics Secur. 16, 3859\u20133873 (2021)","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"995_CR8","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1007\/3-540-39200-9_21","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2003","author":"NT Courtois","year":"2003","unstructured":"Courtois, N.T., Meier, W.: Algebraic attacks on stream ciphers with linear feedback. In: Biham, E. (ed.) Advances in Cryptology\u2014EUROCRYPT 2003, pp. 345\u2013359. Springer, Berlin (2003)"},{"key":"995_CR9","first-page":"244","volume-title":"Trivium","author":"C De Canni\u00e8re","year":"2008","unstructured":"De Canni\u00e8re, C., Preneel, B.: Trivium, pp. 244\u2013266. Springer, Berlin (2008)"},{"key":"995_CR10","doi-asserted-by":"crossref","unstructured":"Dorrendorf, L., Dorrendorf, L., Gutterman, Z., Pinkas, B.: Cryptanalysis of the windows random number generator. In: ACM Conference on Computer and Communications Security, pp. 476\u2013485 (2007)","DOI":"10.1145\/1315245.1315304"},{"key":"995_CR11","unstructured":"Duda, J.: Asymmetric numeral systems. Internet Archive. arxiv-0902.0271:1\u201347 (2009)"},{"issue":"1","key":"995_CR12","first-page":"1","volume":"1","author":"I Goldberg","year":"1996","unstructured":"Goldberg, I., Wagner, D.: Randomness and the netscape browser. Dr. Dobb\u2019s J. 1(1), 1\u20131 (1996)","journal-title":"Dr. Dobb\u2019s J."},{"key":"995_CR13","doi-asserted-by":"crossref","unstructured":"Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing\u2014STOC \u201996, pp. 212\u2013219. ACM Press (1996)","DOI":"10.1145\/237814.237866"},{"key":"995_CR14","doi-asserted-by":"crossref","unstructured":"Haggstrom, O.: Finite Markov Chains and Algorithmic Applications. London Mathematical Society, London (2002)","DOI":"10.1017\/CBO9780511613586"},{"issue":"9","key":"995_CR15","doi-asserted-by":"publisher","first-page":"1098","DOI":"10.1109\/JRPROC.1952.273898","volume":"40","author":"DA Huffman","year":"1952","unstructured":"Huffman, D.A.: A method for the construction of minimum-redundancy codes. Proc. IRE 40(9), 1098\u20131101 (1952)","journal-title":"Proc. IRE"},{"key":"995_CR16","series-title":"Seminumerical Algorithms","volume-title":"The Art of Computer Programming","author":"D Knuth","year":"1973","unstructured":"Knuth, D.: The Art of Computer Programming. Seminumerical Algorithms, vol. 2. Addison-Wesley, Reading (1973)"},{"key":"995_CR17","doi-asserted-by":"crossref","unstructured":"Rukhin, A. Soto, J., Nechvatal, J., Smid, M., Barker, E.: A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. NIST Special Publication 800-22, Gaithersburg (2001)","DOI":"10.6028\/NIST.SP.800-22"},{"key":"995_CR18","doi-asserted-by":"crossref","unstructured":"Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484\u20131509 (1997)","DOI":"10.1137\/S0097539795293172"},{"key":"995_CR19","unstructured":"Shrestha, B.: Multiprime Blum-Blum-Shub pseudorandom number generator. Thesis, Naval Postgraduate School, Monterey, California (2016)"},{"issue":"1","key":"995_CR20","first-page":"2007","volume":"1","author":"D Shumow","year":"2007","unstructured":"Shumow, D., Ferguson, N.: On the possibility of a back door in the NIST SP800-90 dual Ec PRNG. Rump Session Crypto 1(1), 2007 (2007)","journal-title":"Rump Session Crypto"},{"key":"995_CR21","doi-asserted-by":"crossref","unstructured":"vom Dorp, J., von zur Gathen, J., Daniel, L., Jan, L., Simon, S.: Comparative analysis of random generators. In: Algorithmic Combinatorics: Enumerative Combinatorics. Special Functions and Computer Algebra, pp. 181\u2013196. Springer, Berlin (2020)","DOI":"10.1007\/978-3-030-44559-1_10"},{"key":"995_CR22","unstructured":"Wikipedia. RC4. https:\/\/en.wikipedia.org\/wiki\/RC4 (2021). Accessed 27 Nov 2021"},{"key":"995_CR23","doi-asserted-by":"crossref","unstructured":"Yao, A.C.: Theory and application of trapdoor functions. In 23rd Annual Symposium on Foundations of Computer Science (SFCS 1982), pp. 80\u201391. IEEE (1982)","DOI":"10.1109\/SFCS.1982.45"}],"container-title":["International Journal of Information Security"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10207-025-00995-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10207-025-00995-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10207-025-00995-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,30]],"date-time":"2025-03-30T07:58:29Z","timestamp":1743321509000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10207-025-00995-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,21]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,4]]}},"alternative-id":["995"],"URL":"https:\/\/doi.org\/10.1007\/s10207-025-00995-4","relation":{},"ISSN":["1615-5262","1615-5270"],"issn-type":[{"type":"print","value":"1615-5262"},{"type":"electronic","value":"1615-5270"}],"subject":[],"published":{"date-parts":[[2025,2,21]]},"assertion":[{"value":"21 February 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The first author is an Editor for the IJIS journal. The other authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"82"}}