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The authors propose new cryptosystems based on self-distributive systems that are defined by Conjugator Searching Problems (CSP) in noncommutative groups. Under the newly developed cryptographic assumptions, the basic construction is proven IND-CPA secure in the standard model. Then, they describe two extensions: The first is proven IND-CCA secure in the random oracle model, while the second achieves the IND-CCA security in the standard model. Moreover, the proposal is instantiated with braid groups, and leads to a new braid-based encryption scheme and its security is directly rooted in the intractability assumption of CSP in braid groups.
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