A method for exchange of information I over a communications link, a communications system including a data processor for carrying out the method, and computer readable media for providing program code to the data processor. The system receives a signal transmitted over the link, the signal being generated in accordance with a braid group based cryptosystem; transforming the signal to obtain a word expressive of a braid in B.sub.n, braid encoding the information; and transforming the word into a word in novel standard form to recover the information. Word is represented by arrays a[m], a[m] in {0, 1, . . . , n-1}, and p[m], p[m] in {-1, 1}, and transforming the word to a standard form includes: inputting the arrays a[m], and p[m]; processing a[m] and p[m] to obtain array b[s], b[s] in {0, 1, . . . , n-1} and representing a positive braid word P, and variable r, .DELTA..sup.rP being a word in standard form representative of the braid; and outputting b[s] and r. In one embodiment of the invention the information I is an encryption key.