A New Generation of "Cholaphanes": Steroid-Derived Macrocyclic Hosts with Enhanced Solubility and Controlled Flexibility

The macrocyclic "cholaphanes" 3a-c were synthesized from the inexpensive steroid cholic acid. Like earlier relatives they feature substantial cavities with inward-directed hydroxyl groups, suitable for binding polar molecules such as carbohydrates in nonpolar media. New features are the externally directed alkyl chains, promoting solubility in organic solvents, and (in the case of 3b/c) reduced conformational freedom resulting from truncation of the steroidal side-chain. In particular, modeling shows that the smallest macrocycle 3c possesses very little flexibility, preferring an open conformation which is also revealed in the X-ray crystal structure of its pentahydrate. NMR studies indicated that all three cholaphanes form 1:1 complexes with octyl beta-D-glucoside in CDCl(3), with K(a) = 600-1560 M(-)(1). Cholaphanes 3b/c proved able to extract methyl beta-D-glucoside from aqueous solutions into CHCl(3). The transport of methyl beta-D-glucoside across a chloroform barrier was also demonstrated for 3c.     

A public-key cryptosystem utilizing cyclotomic fields

While it is well-known that the RSA public-key cryptosystem can be broken if its modulusN can be factored, it is not known whether there are other ways of breaking RSA. This paper presents a public-key scheme which necessarily requires knowledge of the factorization of its modulus in order to be broken. Rabin introduced the first system whose security is equivalent to the difficulty of factoring the modulus. His scheme is based on squaring (cubing) for encryption and extracting square (cube) roots for decryption. This introduces a 14 (19) ambiguity in the decryption. Various schemes which overcome this problem have been introduced for both the quadratic and cubic case. We generalize the ideas of Williams' cubic system to larger prime exponents. The cases of higher prime order introduce a number of problems not encountered in the quadratic and cubic cases, namely the existence of fundamental units in the underlying cyclotomic field, the evaluation of higher power residue symbols, and the increased difficulty of Euclidean division in the field.