Rivest, R. L., A. Shamir and L. Adleman “A method for obtaining digital signatures and public-key cryptosystems,” Communications of the ACM, Volume 21, Num. 2, Feb. 1978. Available here. This is the famous paper that introduced the practical public-key encryption system.
Adleman, Leonard M.; Pomerance, Carl; Rumely, Robert S. (1983). "On distinguishing prime numbers from composite numbers," Annals of Mathematics, Vol. 117, Num. 1, pp. 173–206. Available here. In this significant paper the authors describe a new algorithm for primality testing, and prove that it always correctly decides the [non] primality of an integer n in almost polynomial time.
Adleman, L. and M. Huang, “Recognizing primes in random polynomial time,” Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing, pp. 462-469. Available here. This paper is the first in a series that prove the existence of a random polynomial time algorithm for the set of primes.
Adleman, L., “Molecular computation of solutions to combinatorial problems,” Science, Vol. 266, Num. 5187, pp. 1021-1024, November 1994. Available here. This paper describes how the tools of molecular biology were used to solve an instance of the directed Hamiltonian path problem. A small graph was encoded in molecules of DNA, and the "operations" of the computation were performed with standard protocols and enzymes. This experiment demonstrated the feasibility of carrying out computations at the molecular level.
Adleman L.M. and D.R. Heath-Brown. "The first case of Fermat's last theorem," Inventiones Mathematicae, Vol. 79, Num. 2 (June 1985), pp. 409–416. Available here.
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