Charles V. Schaefer, Jr. School of Engineering and Science
 
 
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Ko-Lee Key Exschange

Introduction

Let 482 be the group of braids on 483 strands and 484 its standard generators. Define two subgroups 485 and 486 of 482 as follows: 487 and 488 Clearly, 485 and 486 commute elementwise. The Ko-Lee protocol [1] is the following sequence of operations:

(0) One of the parties (say, Alice) publishes a random element 489 (the ``base" word).

(1) Alice chooses a word 490 as a product of generators of 485 and their inverses. The word 490 is Alice's private key.

(2) Bob chooses a word 491 as a product of generators of 486 and their inverses. The word 491 is Bob's private key.

(3) Alice sends a normal form of the element 492 to Bob and Bob sends a normal form of the element 493 to Alice.

(4) Alice computes a normal form of 494 and Bob computes a normal form of 495 Since 496 in 482, the normal forms of 497 and 498 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

  1. 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.
  2. R.Gennaro, D.Micciancio. Cryptoanalysis of a pseudorandom generator based on braid groups. Advances in Cryptology, EUROCRYPT 2002, LNCS 2332, pp.1-13, 2002.