Prof. Ashay Dharwadker's Courses (2):

Course	Semester	Grade	Add New Course
Information Systems	Fall 2003	View	Update Course
Database Systems	Fall 2003	View	Update Course

Projects (1)

Seminars (3)

• First the web browser sends a public key along with a certificate.
• Then its checked whether the Certificate is genuine and is from a reliable source.
• After this the browser encrypts the random Symmetric encryption using the Keys along with the encrypted URL and the encrypted http Data.
• Now the server decrypts the Symmetric encryption using the private key and further uses it to decrypt the URL and http Data.
• Then the server sends the html document, http data encrypted along with symmetric keys.
• These Symmetric keys are used by the browser to decrypt the http data and html document thus displaying the required information.

• First take a cube (the proof for an arbitrary polyhedron is the same) and cut one face and spread it flat on a plane.
• Now we have same number of V,E and one Face is reduced.
  i.e. If we can prove V-E+F=1 then it is also true for V-E+F=2.
• First "Triangulate" to a Simplicial Complex (as shown in fig-3).
• So now E = E + 1 , F = F + 1 and V = V.
• Now remove the edges of the boundary triangles that do not belong to the inside triangle.(as shown in fig-5)
• E becomes E -1 ,F becomes F-1 and V remains same.
• Further eliminate the edges of the boundary triangle that do not belong to the inside triangle (as shown in fig-6).
• Now count the number of Edges ,Vertices and Faces and Place it in the Equation.
  You will get V- E+F=3-3+1=1 Hence Proved.

• Face is some regular polygon or n-gon with r edges meeting at each vertex. So n>=3 and r>=3.
• Count the Edges: N*F=2E( Because each edges makes 2 faces so each edge is counted twice in n*F).
• Lets take an example of a Cube.
  N*F=2E
  4*6=2*12 (Proved)
  r*V=2E
• By Euler’s Formula V- E + f=2
  (2 E / r) – E + (2 E/n ) =2
  (n*F = 2E => F =2E/n)
  (r*V =2E => V =2E/r)
  
• Placing the values of F and V)in equation .
  After Simplifying we get ((1 / r) +(1/n) =(1/2)+(1/E)).
  Now n>=3 and r>=3 but both n and r cannot be >3.(this you can find out by placing the values of n and r greater than 3 in the equation).
• Case 1:
  N=3 => (1 / r ) = ( 1/6) + (1/E)
  when r =3 E=6 its tetrahedron , r=4 E =12 its octahedron and when r = 5,E=30 its icosahedron.
• Case 2:
  R=3 =>(1/n) = (1/6) + ( 1 / E). When n=3,E=6 its tetrahedron=4, E=12 its cube and When n =5 ,E=30 its dodecahedron).
  There cannot be any other possible values thus it is proved that there are exactly 5 platonic solids.

Research Notes (1)

• Data-String-Expression
  An expression that returns a CHAR or VARCHAR value to be encrypted. The length attribute for the data type of data-string-expression |is limited to 32663
• Password-String-Expression
  An expression that returns a CHAR or VARCHAR value with at least 6 bytes and no more than 127 bytes (SQLSTATE 428FC). The value represents the password used to encrypt the data-string-expression.
  
• Hint-String-Expression An expression that returns a CHAR or VARCHAR value up to 32 bytes that will help data owners remember passwords (for example, 'Student' as a hint to remember 'Dev'). If a hint value is given, the hint is embedded into the result and can be retrieved using the GETHINT function
  

• This example uses the encryption password value to hold the encryption password.
  SET ENCRYPTION PASSWORD = 'Dev54321'; INSERT INTO student(SSN) VALUES ENCRYPT('21');
  
• This example explicitly passes the encryption password. INSERT INTO student(SSN) VALUES ENCRYPT('21,'Dev54321','');
  
• The hint 'Student' is stored to help the user remember the encryption password of 'Dev').
  
• INSERT INTO student(SSN) VALUES ENCRYPT('21','Student','Dev');