Leonard M. Adleman

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An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: (1) Couriers or other secure means are not needed to transmit keys, since a message can be enciphered using an encryption key publicly revealed by the intented(More)
Recently Rothemund and Winfree [6] have considered the program size complexity of constructing squares by self-assembly. Here, we consider the time complexity of such constructions using a natural generalization of the Tile Assembly Model defined in [6]. In the generalized model, the Rothemund-Winfree construction of <italic>n \times n</italic> squares(More)
In this paper some theoretical and (potentially) practical aspects of quantum computing are considered. Using the tools of transcendental number theory it is demonstrated that quantum Turing machines (QTM) with rational amplitudes are sufficient to define the class of bounded error quantum polynomial time (BQP) introduced by Bernstein and Vazirani [Proc.(More)
The use of randomness in computation was first studied in abstraction by Gill [4]. In recent years its use in both practical and theoretical areas has become apparent. Strassen and Solovay [10]; Miller [7]; and Rabin [8] have used it to transform primality testing into a (for many purposes) tractible problem. We can see in retrospect that it was implicit in(More)
We introduce a new model of molecular computation that we call the sticker model. Like many previous proposals it makes use of DNA strands as the physical substrate in which information is represented and of separation by hybridization as a central mechanism. However, unlike previous models, the stickers model has a random access memory that requires no(More)
In 1870 Bouniakowsky [2 J publ ished an algorithm to solve the congruence aX _ bMOD (q). While his algorithm contained several clever ideas useful for small numbers, its asymptotic complexity was O(q). Despite its long history, no fast algorithm has ever emerged for the Discrete Logarithm Problem and the best published method, due to Shanks [lOJ requires(More)