Pur'''[https://tools.ie: tf.org/html/rfc3447%|%RSA]''' disc a public-key cryptography
system wthat RSA stcands for,be whusered iboth is dtocum encrypted, and itso simplicgn dationsa.
---
RSA is
* a public-key cryptosystem, which can also be used for digital signatures.
* an acronym for: Rivest Shamir Adleman, the names of the three inventors of this cryptosystem.
** See Also **
Is t [http://ern.wikipe dia .org/wiki/RSA%|%Wikipebdia]: ''home'' for the topic?
*[RSA httpin Tcl]:// A moren.w complete ikimpledmentation tha.n the one prg/esented belowiki/RSA.
---- [Tcllib]: Provides a pure Tcl math::bignum package.
** Description **
The name "RSA" is derived from the first characters of the surnames of its
inventors: Ron Rivest, Adi Shamir, and Leonard Adleman. It is based on a
The underlying mechanism for this cryptosystem is a generalization of
Fermat's Little Theorem, which says that if ''p'' is a prime then for
all integers ''a'' between 0 and ''p''-1 inclusive, it holds that
a^p = a (mod p)
(where ^ means exponentiation). For an integer ''N'' that is the product
of two primes, it similarly holds that there is an exponent ''m''>1 such that
a^m = a (mod N) for all 0 <= a < N.
However in this case (i) ''m'' is usually not a prime and (ii) it is rather
hard to determine ''m'' from ''N'' (but rather easy to determine ''m'' from
the two primes whose product is ''N'').
As is evident from e.g. the fact that 2''m''-1 is an exponent returning
''a'' to itself whenever ''m'' is such an exponent, there are for every
''N'' infinitely many possible choices of ''m''.
Suppose ''m'' is composite (i.e., not a prime) and the product of two integers
''k'' and ''l'' . Then one can use the above to encrypt a number ''a'' by
computing
b = a^k (mod N)
since the decryption procedure consists of computing
a = b^l (mod N)
A very useful feature of this cryptosystem is that the information needed
to decrypt messages (numbers ''l'' and ''N'') is not the same as that
needed to encrypt messages (numbers ''k'' and ''N''). This means you can
make one half of the key public, but keep the other secret, thus allowing
anyone to make encrypted messages that only you can read, or conversely
produce encrypted messages that anyone can read but which could only have
been encrypted by you. The latter can be used to make digital signatures.
The security of the cryptosystem relies on the fact that it is hard to
factorize the number ''N''. Should anyone make a major improvement in
integer factorization techniques (e.g. so that factorization and primality
checking would be of comparable speed) then RSA would probably be rendered
useless, but for the moment it seems to be OK. A piece of warning may
however be in order: There are some choices of keys for RSA that are
easily broken, even if the number ''N'' by itself is hard to factorize.
Presumably code libraries that generate RSA cryptos have a lot of
built-in checks to avoid outputting one of these inferior sets of keys.
----'''2004Sept2 [PS]''' [Salvatore Sanfilippo] has created a Pure-Tcl bignum package (attached to http://wiki.hping.org/108 ). Using this a (naive!) implementation of RSA is rather trivial to do:
'''[PS] 2004-09-02''':
[Salvatore Sanfilippo] has created a [http://wiki.hping.org/108%|%Pure-Tcl
bignum package]. Using this a (naive!) implementation of RSA is rather trivial
to do:
====== source bignum.tcl
set P 61
set Q 53
set PQ 3233
set E 17
set D 2753
# Turn into bignums:
set pub [fromstr $E]
set pri [fromstr $D]
set pq [fromstr $PQ]
set text "Salvatore does amaze!"
proc rsa { c key pq } {
#puts "RSA: [tostr $c] [tostr $key] [tostr $pq]"
return [powm $c $key $pq]
}
proc encrypt { text key pq } {
set crypted {}
foreach char [split $text ""] {
lappend crypted [tostr [rsa [fromstr [scan $char %c]] $key $pq]]
}
return $crypted
} return $crypted
}
proc decrypt { crypt key pq } {
set plain ""
foreach cypher $crypt {
append plain [format %c [tostr [rsa [fromstr $cypher] $key $pq]]]
}
return $plain
} return $plain
}
puts "Plain: $text"
set cypher [encrypt $text $pri $pq]
puts "Encrypt: $cypher"
puts "Decrypt: [decrypt $cypher $pub $pq]"
======
Mind you - this is not how real implementation of RSA would work... Direct encryption of a plain-text with RSA ''<shudder>''. -- Pascal.
20041109 [Twylite] - See [RSA in Tcl] for a more complete implementation. [Tcllib] also has a pure Tcl math::bignum package.
** Other Page Contributors **
[Twylite]:
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