Braid PublicKey Cryptosystem

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[knot.kaist.ac.kr]
Published : Crypto 2000
Abstract :
The braid groups are infinite noncommutative groups naturally
arising from geometric braids. The braid groups can serve as a good
source to enrich cryptography.
The feature that makes the braid groups useful to cryptography includes
the followings: (i) The word problem is solved via
a fast algorithm which computes the canonical form which can be efficiently
manipulated by computers. (ii) The group operations can be performed
efficiently. (iii) The braid groups have many mathematically
hard problems that can be utilized to design cryptographic primitives.
The efficiency of our systems is demonstrated by their speed and information
rate. Our public key encryption sheme is provably secure.
The foundation of our systems is quite different from
widely used cryptosystems based on number theory, but there are some
similarities in design.
Underlying Problems :
Generalized Conjugacy Problem, Computational DiffieHellman type Problem on Braid Groups
Scheme :
Key generation : Choose randomly x in B_{2n} and
a in UB_{n} . G : hash function.
Public key : pk=(x,a^{1}xa) Private key : sk=a
Encryption : For a given plaintext m, choose randomly r in LB_{n} .
E_{pk}(m,r)=(r^{1}xr, G(r^{1}a^{1}xar)+m)
Decryption : For a ciphertext (c,d), compute
D_{sk}(c,d)=G(a^{1}ca)+d
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