Cryptanalysis of Multi-Prime \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varPhi $$\end{document}-Hiding Assumption

• Published in: Information Security pp. 440 - 453
• Main Authors: Xu, Jun, Hu, Lei, Sarkar, Santanu, Zhang, Xiaona, Huang, Zhangjie, Peng, Liqiang
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing 2016
• Series: Lecture Notes in Computer Science
• Subjects: Coppersmith’s technique; Gauss algorithm; Hiding Assumption; Hiding Problem; Lattice; LLL algorithm; Multi-Prime
• ISBN: 3319458701; 9783319458700
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-45871-7_26

In Crypto 2010, Kiltz, O’Neill and Smith used m-prime RSA modulus N with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m\ge 3$$\end{document} for constructing lossy RSA. The security of the proposal is based on the Multi-Prime \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varPhi $$\end{document}-Hiding Assumption. In this paper, we propose a heuristic algorithm based on the Herrmann-May lattice method (Asiacrypt 2008) to solve the Multi-Prime \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varPhi $$\end{document}-Hiding Problem when prime \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e>N^{\frac{2}{3m}}$$\end{document}. Further, by combining with mixed lattice techniques, we give an improved heuristic algorithm to solve this problem when prime \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e>N^{\frac{2}{3m}-\frac{1}{4m^2}}$$\end{document}. These two results are verified by our experiments. Our bounds are better than the existing works.