2. 1 2
Dead
Information
Outline
or
Theft Alive
3 4
secret sharing schemes Secret
What to do? Sharing
what, when why
secret sharing 5 6
schemes
Phases Applications
3. Information Theft
~Secret and confidential information
theft is a major computer crime.
~In 2002, more than
$70 million loss was
reported due to
information theft
in US only.
4. Dead or Alive
~Some criminals’ tools (like viruses)
tend to destroy information.
~ More than 80% of
organizations
reported virus’s attacks.
5. What to do?
~Having only one copy of this information means that if
this copy is destroyed there is no way to retrieve it.
What to do??
Replicate!!!
~ Replicating the important information will give more
chance to intruders to gain access to it.
~ Thus, there is a grate need to keep informat ion in a
secure and reliable way.
What to do??
Secret Sharing
6. Secret Sharing
~The basic idea of secret sharing is to divide
information into several pieces such that certain
subsets of these pieces (shares) can
be used to recover the information.
~ Intruders wants to
•GET the info. several shares need to be theft
•Destroy. several shares need to be destroyed
7. (t, n)- • in a secret sharing scheme there
is one dealer and n players.
threshold • The dealer gives each player a
scheme share in such a way that any
group of t (for threshold) or
more players can together
reconstruct the secret but no
group of fewer than t players
can.
• Such a system is called a (t, n)-
threshold scheme
8. PROPOSED SECRET SHARING SCHEME
•We assume that the set of participants is
P = {P1 , P2 , ... , Pn}
•the access structure is Г ={Г1, Г2,… Гm }
•S is a secret integer of arbitrary precision, p is a prime number
larger than S , and all arithmetic operations are performed mod
p.
•Assume that there are “t” shareholders in the access
instance Гj Є Г.
That is if all “t” qualified participants in Гj release shares
honestly then the secret can be reconstructed
•Also assume the presence of a trusted party (dealer) or a
piece of trusted software that can construct and
reconstruct the secret
9. Secret Sharing Phases
~ Shares building phase.
~ Shares distribution phase.
~Secret reconstruction phase.
~Shares update phase.
14. Applications
secure implementation of an encrypted backup system
encrypted Assuming that data recoveries are needed rarely, backup
backup data can be public key encrypted -- this can be done
system automatically and without user interaction -- while the
private recovery key is protected via secret sharing.
The director of a bank generates shares for the bank's
shares for the vault unlocking code and hands them out to his
bank's vault employees.
unlocking Even if the director is not available, the vault can be
code opened, but only, when a certain number of employees
do it together.
Good passwords are hard to memorize. A clever user
could use a secret sharing scheme to generate a set of
Sharing shares for a given password and store one share in his
password address book, one in his bank deposit safe, leave one
share with a friend, etc. If one day he forgets his
password, he can reconstruct it easily.
15. Thank You
Made By :
Sandeep Kumar
Anuj Singh
Navdeep Garg
