Refine
Year of publication
- 1996 (2) (remove)
Language
- English (2)
Has Fulltext
- yes (2)
Is part of the Bibliography
- no (2)
Keywords
Institute
- Informatik (2)
- Mathematik (2)
Korrektur zu: C.P. Schnorr: Security of 2t-Root Identification and Signatures, Proceedings CRYPTO'96, Springer LNCS 1109, (1996), pp. 143-156 page 148, section 3, line 5 of the proof of Theorem 3. Die Korrektur wurde präsentiert als: "Factoring N via proper 2 t-Roots of 1 mod N" at Eurocrypt '97 rump session.
We analyse a continued fraction algorithm (abbreviated CFA) for arbitrary dimension n showing that it produces simultaneous diophantine approximations which are up to the factor 2^((n+2)/4) best possible. Given a real vector x=(x_1,...,x_{n-1},1) in R^n this CFA generates a sequence of vectors (p_1^(k),...,p_{n-1}^(k),q^(k)) in Z^n, k=1,2,... with increasing integers |q^{(k)}| satisfying for i=1,...,n-1 | x_i - p_i^(k)/q^(k) | <= 2^((n+2)/4) sqrt(1+x_i^2) |q^(k)|^(1+1/(n-1)) By a theorem of Dirichlet this bound is best possible in that the exponent 1+1/(n-1) can in general not be increased.