Howard loves Polly

Polly two - a public key cryptosystem based on Polly cracker

She loves me--she loves me not.

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He Loves Me Not.

Sir In the article in your current issue on making so-called ‘orphan drugs’ available via the NHS, it seems to be tacitly assumed that our overriding duty as physicians and surgeons is to prolong the existence of our patients whether or not that is their main preoccupation and what our overpopulated world needs. We do not of course ever ‘save’ lives when we prolong them unless we concern oursel...

Polly Cracker, Revisited

In this work, we initiate the formal treatment of cryptographic constructions (“Polly Cracker”) based on the hardness of computing remainders modulo an ideal. We start by formalising and studying the relation between the ideal remainder problem and the problem of computing a Gröbner basis. We show both positive and negative results. On the negative side, we define a symmetric Polly Cracker encr...

Lattice Polly Cracker cryptosystems

Using Gröbner bases for the construction of public key cryptosystems has been often attempted, but has always failed. We review the reason for these failures, and show that only ideals generated by binomials may give a successful cryptosystem. As a consequence, we concentrate on binomial ideals that correspond to Euclidean lattices. We show how to build a cryptosystem based on lattice ideals an...