de Weger, Benne Cryptanalysis of RSA with small prime difference. (English) Zbl 1010.94007 Appl. Algebra Eng. Commun. Comput. 13, No. 1, 17-28 (2002). The author proves that choosing an RSA modulus with a small difference between its prime factors yields improvements on the small private exponent attacks of Wiener and Boneh-Durfee. The following theorem is the main result of this paper. Theorem. Let \(p,q\) be large primes of about the same size, \(n=pq\) and \(\Delta=|p-q|\). Let \(e,d\) be integers \(>1\) and \(<\varphi (n)\), satisfying \(ed\equiv 1\pmod{\varphi (n)}\). Put \(\Delta=n^{\beta}\) and \(d=n^{\delta}\). Given only \(n\) and \(e\), the factors \(p,q\) of \(n\) and the number \(d\) can be recovered efficiently whenever \(2-4\beta<\delta<1-\sqrt{2\beta -\frac 12}\) or \(\delta<\frac 16(4\beta +5)-\frac 13\sqrt{(4\beta +5)(4\beta -1)}\). Reviewer: Zhenfu Cao (Shanghai) Cited in 3 ReviewsCited in 29 Documents MSC: 94A60 Cryptography 11Y05 Factorization Keywords:cryptanalysis; RSA; factoring large integers Software:PARI/GP PDFBibTeX XMLCite \textit{B. de Weger}, Appl. Algebra Eng. Commun. Comput. 13, No. 1, 17--28 (2002; Zbl 1010.94007) Full Text: DOI