Suggestions for RSA assignment

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Suggestions for RSA assignment
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Generation of random primes

• Use a value of n that is close to the size of the
  Java data type long. The largest signed long
  integer is ____________________.
• Question. Does Java support unsigned data types?
• Though there are interesting methods that can be
  used to generate random primes p and q, just pick
  a p and q from a table of primes.
• Search the internet for p and q.
• http//www.utm.edu/research/primes/lists/

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more on n, p, and q

• Since pq n choose p and q so that n will not
  be larger than the longest signed long integer.
• Calculate (p-1)(q-1) and call this phi.

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Choosing e

• Choose e such that 1lte lt phi and gcd (e, phi)
  1.
• In practice e 3, 7 or 65537 (216 1), called
  the Fermat primes. In the binary representation
  nearly all the bit are zero.

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Choosing d

• The public key is (n,e)
• Choose d such that 1ltdltphi and
  ed 1 mod (phi).

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Encoding

• Let m be the numeric block number. The
  cipherText c me mod (n)
• Method for the calculation of me mod (n).
• In general y xe mod (n)
• Express e in binary
• Let bit j be an array contains zeros or 1 that
  is the binary representation of e. bit 0 is the
  least significant bit and bit j 1 is the first
  non zero bit.
• Continued on next slide.

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Modular exponentiation

• y x
• for k j 2 j gt0 j - -
• y yy mod (n)
• if ( bit k 1)
• y y x mod n
• return y

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Decoding

• Decoding, m cd mod (n), is not nearly as
  efficient since d does not have most of its bits
  as 1. For large message decoding can be quite
  lengthy

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Project Summary

• Create your own public and private key. Note n
  should be near the maximum size of long.
• Send lackey your public key to be placed on the
  web at www3.ltu.edu/lackey.
• Get the message intended for you and decode it.
• Use A-1, B-2, ,Z-27,?-28 ,. -29, blank-30.
• Block the message by 4s. Pad with blanks if
  short. Replace unknown characters with .

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Methods

• Convert a long to binary
• Modular exponentiation
• Encode
• Decode
• Convert one 8 digit number to 4 letters
• Convert 4 letters to on 8 digit number
• Note get p,q, n and phi by hand

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The Project

• E-mail the instructor (lackey_at_ltu.edu) your
  private key. This will be posted to the web.
• An encoded message will be posted to the web (
  blocked 4) for you.
• Decode the message.
• E-mail the decoded message to the instructor.
• Turn in a listing of all programs used and the
  lab handout.