Die Suche nach dem Mathe Magier

To retrieve this cache's coordinates you will have to solve two exercises in geodesy and mathematics. A calculator, paper & pencil will help you on your way.

The coordinates of the final cache were partially encrypted using the RSA algorithm.
From a table with three years and a number in words you can derive the public key (e, n) used for encryption. (you will have to calculate the decryption key)

Position of the table:

Position of the final cache: (WGS84)
N 49° 0,(1131)'
O 8° 23,(229)'

Please log the tools used (calculator, notebook, books not listed, no websites please) and how long the whole search took you.

Hints:

• All points are within 2000 meters of the 'Karlsruher Schloss'
• You should seek the final Cache during daytime. Terrain rating increases after 8pm.
• The final cache's position may be off a few meters because of lousy GPS reception at the cache site.
• The table's position is given in the earth centered, earth fixed (ECEF) cartesian coordinate system.
  I used the WGS84 ellipsoid and set the height (above the ellipsoid) to zero to allow for an accurate analytic solution. Your results may be off if you choose another ellipsoid.
• Earth centered, earth Fixed X, Y, and Z
  Earth centered, earth-fixed, X, Y, and Z, Cartesian coordinates (XYZ) define three dimensional positions with respect to the center of mass of the reference ellipsoid.
  

  The Z-axis	points toward the North Pole.
  The X-axis	is defined by the intersection of the plane defined by the prime meridian and the equatorial plane.
  The Y-axis	completes a right handed orthogonal system by a plane 90° east of the X-axis and its intersection with the equator.

• Geodetic latitude, longitude, and height
  

  The Prime Meridian and the Equator are the reference planes used to define latitude and longitude.
  The geodetic latitude	of a point is the angle from the equatorial plane to the vertical direction of a line normal to the reference ellipsoid.
  The geodetic longitude	of a point is the angle between a reference plane and a plane passing through the point, both planes being perpendicular to the equatorial plane.
  The geodetic height	at a point is the distance from the reference ellipsoid to the point in a direction normal to the ellipsoid.

• WGS84-ellipsoid:
  

  semi-major axis	a = 6378137m (equatorial radius)
  semi-minor axis	b = 6356752.3142m (polar radius)

• The RSA algorithm is discussed in many standard textbooks, eg.
  Cormen/Leiserson/Rivest/Stein: Introduction To Algorithms (second edition)
  and some more recent books about linear algebra.
• There are some tricks to simplify RSA calculation. (residue class ring)
• You can find the literature you need at
  N49°0,671' O8°24,971' (WGS84) (University of Karlsruhe University Library)
  N49°0,464' O8°23,939' (WGS84) (Badische Landesbibliothek)
• Non-local cachers may request a photograph of the first stage via eMail. (with coordinates attached)