Let be the group of braids on strands and its standard generators. Define two subgroups and of
as follows:
and
Clearly,
and
commute elementwise.
The Ko-Lee protocol [1] is the following sequence of operations:
(0) One of the parties (say, Alice) publishes a random element (the ``base" word).
(1) Alice chooses a word as a product of generators of and their inverses. The word is Alice's private key.
(2) Bob chooses a word as a product of generators of and their inverses. The word is Bob's private key.
(3) Alice sends a normal form of the element to Bob and Bob sends a normal form of the element to Alice.
(4) Alice computes a normal form of and Bob computes a normal form of
Since in , the normal forms of and coincide.
Thus Alice and Bob have the same normal form called their shared secret key.
Parameters
Under construction ...
Known Attacks
Under construction ...
Challenges
Under construction ...
References
K.H.Ko, S.J.Lee, J.H.Han, J.Kang, C.Park.
New public-key Cryptosystem using braid groups. CRYPTO'2000,
LNCS 1880, pp.166-183, 2000.
R.Gennaro, D.Micciancio.
Cryptoanalysis of a pseudorandom generator based on braid groups.
Advances in Cryptology, EUROCRYPT 2002, LNCS 2332, pp.1-13, 2002.
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be the group of braids on 
strands and 
its standard generators. Define two subgroups 
and 
of 
and
Clearly,
(the ``base" word).
as a product of generators of 
as a product of generators of 
to Bob and Bob sends a normal form of the element 
to Alice.
and Bob computes a normal form of 
Since 
in 
and 
coincide.
Thus Alice and Bob have the same normal form called their shared secret key.