{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:26:01Z","timestamp":1772252761418,"version":"3.50.1"},"reference-count":12,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,11,22]],"date-time":"2018-11-22T00:00:00Z","timestamp":1542844800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University Grants Commision (UGC), Government of India","award":["MRP-2013"],"award-info":[{"award-number":["MRP-2013"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>In this paper, we gave an attack on RSA (Rivest\u2013Shamir\u2013Adleman) Cryptosystem when     \u03c6 ( N )     has small multiplicative inverse modulo e and the prime sum     p + q     is of the form     p + q =  2 n   k 0  +  k 1     , where n is a given positive integer and     k 0     and     k 1     are two suitably small unknown integers using sublattice reduction techniques and Coppersmith\u2019s methods for finding small roots of modular polynomial equations. When we compare this method with an approach using lattice based techniques, this procedure slightly improves the bound and reduces the lattice dimension. Employing the previous tools, we provide a new attack bound for the deciphering exponent when the prime sum     p + q =  2 n   k 0  +  k 1      and performed an analysis with Boneh and Durfee\u2019s deciphering exponent bound for appropriately small     k 0     and     k 1    .<\/jats:p>","DOI":"10.3390\/cryptography2040036","type":"journal-article","created":{"date-parts":[[2018,11,23]],"date-time":"2018-11-23T03:41:31Z","timestamp":1542944491000},"page":"36","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Attack Bound for Small Multiplicative Inverse of \u03c6(N) mod e with a Composed Prime Sum p + q Using Sublattice Based Techniques"],"prefix":"10.3390","volume":"2","author":[{"given":"Pratha Anuradha","family":"Kameswari","sequence":"first","affiliation":[{"name":"Department of Mathematics, Andhra University, Visakhapatnam, Andhra Pradesh 530003, India"}]},{"given":"Lambadi","family":"Jyotsna","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Andhra University, Visakhapatnam, Andhra Pradesh 530003, India"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,22]]},"reference":[{"key":"ref_1","unstructured":"Kobliz, N. (1994). A Course in Number Theory and Cryprography, Springer."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1109\/18.54902","article-title":"Cryptanalysis of Short RSA Secret Exponents","volume":"36","author":"Wiener","year":"1990","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s001459900030","article-title":"Small solutions to polynomial equations, and low exponent RSA vulnerabilities","volume":"10","author":"Coppersmith","year":"1997","journal-title":"J. Cryptol."},{"key":"ref_4","first-page":"111","article-title":"Cryptanalysis of RSA with Private Key D Less than N0.292","volume":"Volume 1592","author":"Boneh","year":"1999","journal-title":"Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques"},{"key":"ref_5","first-page":"419","article-title":"Low Secret Exponent RSA Revisited","volume":"Volume 2146","author":"Blomer","year":"2001","journal-title":"Cryptography and Lattice"},{"key":"ref_6","first-page":"267","article-title":"A Strategy for Finding Roots of Multivariate Polynomials with New Applications in Attacking RSA Variant","volume":"Volume 4284","author":"Jochemsz","year":"2006","journal-title":"Proceedings of the 12th International Conference on the Theory and Application of Cryptology and Information Security"},{"key":"ref_7","first-page":"515","article-title":"Cryptanalysis of RSA with Small Multiplicative Inverse of \u03c6(N) Modulo e and with a Composed Prime Sum p + q","volume":"6","author":"Jyotsna","year":"2018","journal-title":"Int. J. Math. Appl."},{"key":"ref_8","unstructured":"Hoftstein, J., Pipher, J., and Silverman, J.H. (2008). An Introduction to Mathematical Cryptography, Springer."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/BF01457454","article-title":"Factoring polynomials with rational coefficients","volume":"261","author":"Lenstra","year":"1982","journal-title":"Math. Annalen"},{"key":"ref_10","unstructured":"May, A. (2003). New RSA Vulnerabilities Using Lattice Reduction Methods. [Ph.D. Thesis, University of Paderborn]. Available online: http:\/\/wwwcs.upb.de\/cs\/ag-bloemer\/personen\/alex\/publikationen\/."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Howgrave-Graham, N. (1997). Finding small roots of univariate modular equations revisited. Cryptography and Coding, Springer. LNCS 1355.","DOI":"10.1007\/BFb0024458"},{"key":"ref_12","first-page":"174","article-title":"Another Generalization of Wieners Attack on RSA","volume":"Volume 5023","author":"Vaudenay","year":"2008","journal-title":"Proceedings of the First International Conference on Cryptology in Africa"}],"container-title":["Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2410-387X\/2\/4\/36\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:31:27Z","timestamp":1760196687000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2410-387X\/2\/4\/36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,22]]},"references-count":12,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["cryptography2040036"],"URL":"https:\/\/doi.org\/10.3390\/cryptography2040036","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201807.0379.v1","asserted-by":"object"}]},"ISSN":["2410-387X"],"issn-type":[{"value":"2410-387X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,22]]}}}