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Background on Combinatorial Group Theoryaphs where a complete exposition of these techniques is given. For an exposition of Nielsen’s and Schreier’s methods, we recommend [96], whereas [95] has, in our opinion, a better exposition of Whitehead’s and Tietze’s methods.

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Using Decision Problems in Public Key Cryptographyecision problems may allow us to address (to some extent) the following challenge of public key cryptography: to design a cryptosystem that would be secure against (at least, some) “brute force” attacks by an adversary with essentially unlimited computational capabilities.

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Philosophical Perspectives on Brain Dataecision problems may allow us to address (to some extent) the following challenge of public key cryptography: to design a cryptosystem that would be secure against (at least, some) “brute force” attacks by an adversary with essentially unlimited computational capabilities.

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Canonical Non-commutative Cryptographyom the canonical paradigm of a public-key protocol based on a one-way function. We include here the ground-breaking Anshel-Anshel-Goldfeld protocol [1] as well as protocols that are closer in spirit to classical protocols based on commutative (semi)groups.

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Ways of the Scientific World-Conception,In Section 4.1, we have outlined some of the requirements on the platform group in a protocol based on the conjugacy search problem. Most of these requirements apply, in fact, to platform groups in any “canonical” (i.e., based on a one-way function) cryptographic protocol, so we summarize these general requirements here.