{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T11:14:39Z","timestamp":1758280479221},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2009,11,11]],"date-time":"2009-11-11T00:00:00Z","timestamp":1257897600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"published-print":{"date-parts":[[2011,5]]},"DOI":"10.1007\/s11227-009-0347-9","type":"journal-article","created":{"date-parts":[[2009,11,10]],"date-time":"2009-11-10T09:34:58Z","timestamp":1257845698000},"page":"129-163","source":"Crossref","is-referenced-by-count":15,"title":["Fast parallel DNA-based algorithms for molecular computation: discrete logarithm"],"prefix":"10.1007","volume":"56","author":[{"given":"Weng-Long","family":"Chang","sequence":"first","affiliation":[]},{"given":"Shu-Chien","family":"Huang","sequence":"additional","affiliation":[]},{"given":"Kawuu Weicheng","family":"Lin","sequence":"additional","affiliation":[]},{"given":"Michael","family":"Ho","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,11,11]]},"reference":[{"key":"347_CR1","first-page":"282","volume-title":"Minaturization","author":"RP Feynman","year":"1961","unstructured":"Feynman RP (1961) In: Gilbert DH (ed) Minaturization. Reinhold, New York, pp 282\u2013296"},{"issue":"11","key":"347_CR2","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1126\/science.7973651","volume":"266","author":"L Adleman","year":"1994","unstructured":"Adleman L (1994) Molecular computation of solutions to combinatorial problems. Science 266(11):1021\u20131024","journal-title":"Science"},{"issue":"6","key":"347_CR3","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"22","author":"W Diffie","year":"1976","unstructured":"Diffie W, Hellman M (1976) New directions in cryptography. IEEE Trans Inf Theory 22(6):644\u2013654","journal-title":"IEEE Trans Inf Theory"},{"key":"347_CR4","series-title":"DIMACS: series in discrete mathematics and theoretical computer science","first-page":"31","volume-title":"The 2nd annual workshop on DNA computing, Princeton University","author":"L Adleman","year":"1999","unstructured":"Adleman L, Rothemund PWK, Roweis S, Winfree E (1999) On applying molecular computation to the data encryption standard. In: The 2nd annual workshop on DNA computing, Princeton University. DIMACS: series in discrete mathematics and theoretical computer science. Am Math Soc, Providence, pp 31\u201344"},{"issue":"1","key":"347_CR5","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.biosystems.2004.10.003","volume":"80","author":"M Guo","year":"2005","unstructured":"Guo M, Chang W-L, Ho M, Lu J, Cao J (2005) Is optimal solution of every NP-complete or NP-hard problem determined from its characteristic for DNA-based computing. BioSystems 80(1):71\u201382","journal-title":"BioSystems"},{"issue":"2\u20133","key":"347_CR6","first-page":"242","volume":"372","author":"M Muskulus","year":"2006","unstructured":"Muskulus M, Besozzi D, Brijder R, Cazzaniga P, Houweling S, Pescini D, Rozenberg G (2006) Cycles and communicating classes in membrane systems and molecular dynamics. Theor Comput Sci 372(2\u20133):242\u2013266","journal-title":"Theor Comput Sci"},{"issue":"9","key":"347_CR7","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1145\/1284621.1284647","volume":"50","author":"JH Reif","year":"2007","unstructured":"Reif JH, LaBean TH (2007) Autonomous programmable biomolecular devices using self-assembled DNA nanostructures. Commun ACM 50(9):46\u201353","journal-title":"Commun ACM"},{"issue":"4","key":"347_CR8","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/s11047-006-9006-8","volume":"5","author":"G Wu","year":"2006","unstructured":"Wu G, Seeman NC (2006) Multiplying with DNA. Nat Comput 5(4):427\u2013441","journal-title":"Nat Comput"},{"issue":"11","key":"347_CR9","doi-asserted-by":"crossref","first-page":"2598","DOI":"10.1021\/nl0620684","volume":"6","author":"J Macdonald","year":"2006","unstructured":"Macdonald J, Li Y, Sutovic M, Lederman H, Pendri K, Lu W, Andrews BL, Stefanovic D, Stojanovic MN (2006) Medium scale integration of molecular logic gates in an automaton. Nano Lett 6(11):2598\u20132603","journal-title":"Nano Lett"},{"key":"347_CR10","doi-asserted-by":"crossref","first-page":"268301","DOI":"10.1103\/PhysRevLett.93.268301","volume":"93","author":"A Ekani-Nkodo","year":"2004","unstructured":"Ekani-Nkodo A, Kumar A, Fygenson DK (2004) Joining and scission in the self assembly of nanotubes from DNA tiles. Phys Rev Lett 93:268301","journal-title":"Phys Rev Lett"},{"key":"347_CR11","doi-asserted-by":"crossref","first-page":"021913","DOI":"10.1103\/PhysRevE.74.021913","volume":"74","author":"M Dehnert","year":"2006","unstructured":"Dehnert M, Helm WE, H\u00fctt M-Th (2006) Informational structure of two closely related eukaryotic genomes. Phys Rev E 74:021913","journal-title":"Phys Rev E"},{"key":"347_CR12","doi-asserted-by":"crossref","first-page":"2814","DOI":"10.1021\/nl0619406","volume":"6","author":"BK M\u00fcller","year":"2006","unstructured":"M\u00fcller BK, Reuter A, Simmel FC, Lamb DC (2006) Single-pair FRET characterization of DNA tweezers. Nano Lett 6:2814\u20132820","journal-title":"Nano Lett"},{"issue":"1","key":"347_CR13","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1137\/060651100","volume":"49","author":"RM Dirks","year":"2007","unstructured":"Dirks RM, Bois JS, Schaeffer JM, Winfree E, Pierce NA (2007) Thermodynamic analysis of interacting nucleic acid strands. SIAM Rev 49(1):65\u201388","journal-title":"SIAM Rev"},{"key":"347_CR14","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1126\/science.7725098","volume":"268","author":"R Lipton","year":"1995","unstructured":"Lipton R (1995) DNA solution of hard computational problems. Science 268:542\u2013545","journal-title":"Science"},{"issue":"1","key":"347_CR15","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.biosystems.2005.09.005","volume":"83","author":"C-W Yeh","year":"2006","unstructured":"Yeh C-W, Chu C-P, Wu K-R (2006) Molecular solutions to the binary integer programming problem based on DNA computation. Biosystems 83(1):56\u201366","journal-title":"Biosystems"},{"issue":"9\u201310","key":"347_CR16","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1016\/j.parco.2004.07.014","volume":"30","author":"M Guo","year":"2004","unstructured":"Guo M, Ho M, Chang W-L (2004) Fast parallel molecular solution to the dominating-set problem on massively parallel bio-computing. Parallel Comput 30(9\u201310):1109\u20131125","journal-title":"Parallel Comput"},{"key":"347_CR17","volume-title":"Theoretical and experimental DNA computation","author":"M Amos","year":"2005","unstructured":"Amos M (2005) Theoretical and experimental DNA computation. Springer, Berlin"},{"issue":"7","key":"347_CR18","first-page":"1782","volume":"E-87D","author":"M Ho","year":"2004","unstructured":"Ho M, Chang W-L, Guo M, Yang LT (2004) Fast parallel solution for set-packing and clique problems by DNA-based computing. IEICE Trans Inf Syst E-87D(7):1782\u20131788","journal-title":"IEICE Trans Inf Syst"},{"issue":"5","key":"347_CR19","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1016\/j.future.2003.10.010","volume":"20","author":"W-L Chang","year":"2004","unstructured":"Chang W-L, Guo M, Ho M (2004) Towards solution of the set-splitting problem on gel-based DNA computing. Future Gener Comput Syst 20(5):875\u2013885","journal-title":"Future Gener Comput Syst"},{"issue":"3","key":"347_CR20","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/S0303-2647(03)00149-7","volume":"72","author":"W-L Chang","year":"2003","unstructured":"Chang W-L, Guo M (2003) Solving the set-cover problem and the problem of exact cover by 3-sets in the Adleman-Lipton\u2019s model. BioSystems 72(3):263\u2013275","journal-title":"BioSystems"},{"key":"347_CR21","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.biosystems.2004.11.009","volume":"80","author":"M Ho","year":"2005","unstructured":"Ho M (2005) Fast parallel molecular solutions for DNA-based supercomputing: the subset-product problem. BioSystems 80:233\u2013250","journal-title":"BioSystems"},{"issue":"1\u20132","key":"347_CR22","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.biosystems.2006.06.001","volume":"88","author":"CV Henkel","year":"2007","unstructured":"Henkel CV, B\u00e4ck T, Kok JN, Rozenberg G, Spaink HP (2007) DNA computing of solutions to knapsack problems. Biosystems 88(1\u20132):156\u2013162","journal-title":"Biosystems"},{"issue":"1","key":"347_CR23","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1109\/TNB.2007.909012","volume":"6","author":"W-L Chang","year":"2007","unstructured":"Chang W-L (2007) Fast parallel DNA-based algorithms for molecular computation: the set-partition problem. IEEE Trans Nanobiosci 6(1):346\u2013353","journal-title":"IEEE Trans Nanobiosci"},{"issue":"2","key":"347_CR24","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1109\/TNB.2005.850474","volume":"4","author":"W-L Chang","year":"2005","unstructured":"Chang W-L, Ho M, Guo M (2005) Fast parallel molecular algorithms for DNA-based computation: factoring integers. IEEE Trans Nanobiosci 4(2):149\u2013163","journal-title":"IEEE Trans Nanobiosci"},{"key":"347_CR25","series-title":"DIMACS series in discrete mathematics and theoretical computer science","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1090\/dimacs\/027\/04","volume-title":"Proceedings of the 1st DIMACS workshop on DNA based computers, 1995","author":"D Boneh","year":"1996","unstructured":"Boneh D, Dunworth C, Lipton RJ (1996) Breaking DES using a molecular computer. In: Proceedings of the 1st DIMACS workshop on DNA based computers, 1995. DIMACS series in discrete mathematics and theoretical computer science, vol 27. Am Math Soc, Providence, pp 37\u201366"},{"key":"347_CR26","doi-asserted-by":"crossref","first-page":"13921","DOI":"10.1021\/ja803318t","volume":"130","author":"DY Zhang","year":"2008","unstructured":"Zhang DY, Winfree E (2008) Dynamic allosteric control of noncovalent DNA catalysis reactions. J\u00a0Am Chem Soc 130:13921\u201313926","journal-title":"J\u00a0Am Chem Soc"},{"issue":"2","key":"347_CR27","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.biosystems.2003.11.001","volume":"73","author":"W-L Chang","year":"2004","unstructured":"Chang W-L, Ho M, Guo M (2004) Molecular solutions for the subset-sum problem on DNA-based supercomputing. BioSystems 73(2):117\u2013130","journal-title":"BioSystems"},{"issue":"5805","key":"347_CR28","doi-asserted-by":"crossref","first-page":"1585","DOI":"10.1126\/science.1132493","volume":"314","author":"G Seelig","year":"2006","unstructured":"Seelig G, Soloveichik D, Zhang D-Y, Winfree E (2006) Enzyme-free nucleic acid logic circuits. Science 314(5805):1585\u20131588","journal-title":"Science"},{"issue":"1\u20133","key":"347_CR29","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.tcs.2004.12.032","volume":"334","author":"L Kari","year":"2005","unstructured":"Kari L, Konstantinidis S, Sos\u00edk P (2005) On properties of bond-free DNA languages. Theor Comput Sci 334(1\u20133):131\u2013159","journal-title":"Theor Comput Sci"},{"key":"347_CR30","series-title":"Lecture notes in computer science series","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/3-540-44992-2_3","volume-title":"Proceedings of the 6th international conference on DNA computation","author":"RS Braich","year":"2001","unstructured":"Braich RS, Johnson C, Rothemund PWK, Hwang D, Chelyapov N, Adleman LM (2001) Solution of a satisfiability problem on a gel-based DNA computer. In: Proceedings of the 6th international conference on DNA computation. Lecture notes in computer science series, vol 2054. Springer, Berlin, pp 27\u201342"},{"issue":"5567","key":"347_CR31","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1126\/science.1069528","volume":"296","author":"LM Adleman","year":"2002","unstructured":"Adleman LM, Braich RS, Johnson C, Rothemund PWK, Hwang D, Chelyapov N (2002) Solution of a 20-variable 3-SAT problem on a DNA computer. Science 296(5567):499\u2013502","journal-title":"Science"},{"key":"347_CR32","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-0310-7","volume-title":"A course in number theory and cryptography","author":"N Koblitz","year":"1987","unstructured":"Koblitz N (1987) A course in number theory and cryptography. Springer, Berlin. ISBN:0387942939","ISBN":"http:\/\/id.crossref.org\/isbn\/0387942939"},{"key":"347_CR33","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1145\/359340.359342","volume":"21","author":"RL Rivest","year":"1978","unstructured":"Rivest RL, Shamir A, Adleman L (1978) A method for obtaining digital signatures and public-key cryptosystem. Commun ACM 21:120\u2013126","journal-title":"Commun ACM"},{"key":"347_CR34","doi-asserted-by":"crossref","unstructured":"Blakley GR A computer algorithm for calculating product AB modulo M. IEEE Trans Comput c-32(5):497\u2013500","DOI":"10.1109\/TC.1983.1676262"},{"key":"347_CR35","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-4103-8","volume-title":"The biochemistry of the nucleic acids","author":"RL Adams","year":"1986","unstructured":"Adams RL, Knowler JT, Leader DP (1986) The biochemistry of the nucleic acids, 10th edn. Chapman & Hall, London","edition":"10"},{"key":"347_CR36","doi-asserted-by":"crossref","unstructured":"Watson J, Gilman M, Witkowski J, Zoller M (1992) Recombinant DNA, 2nd edn. Scientific American Books","DOI":"10.1016\/0960-8966(92)90050-G"},{"key":"347_CR37","doi-asserted-by":"crossref","unstructured":"Breslauer K, Frank R, Blocker H, Marky L (1986) Predicting DNA duplex stability from the base sequence. Proc Natl Acad Sci 3746\u20133750","DOI":"10.1073\/pnas.83.11.3746"},{"key":"347_CR38","volume-title":"Genetics: a molecular approach","author":"T Brown","year":"1993","unstructured":"Brown T (1993) Genetics: a molecular approach. Chapman & Hall, London"},{"issue":"5","key":"347_CR39","doi-asserted-by":"crossref","first-page":"1484","DOI":"10.1137\/S0097539795293172","volume":"26","author":"PW Shor","year":"1997","unstructured":"Shor PW (1997) Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Comput 26(5):1484\u20131509","journal-title":"SIAM Comput"},{"key":"347_CR40","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1038\/nnano.2009.220","volume":"16","author":"RJ Kershner","year":"2009","unstructured":"Kershner RJ, Bozano LD, Micheel CM, Hung AH, Fornof AR, Cha JN, Rettner CT, Bersani M, Frommer J, Rothemund PWK, Wallraff GM (2009) Placement and orientation of individual DNA shapes on lithographically patterned surfaces. Nat Nanotechnol 16:557\u2013561","journal-title":"Nat Nanotechnol"},{"key":"347_CR41","doi-asserted-by":"crossref","first-page":"6054","DOI":"10.1073\/pnas.0808736106","volume":"106","author":"RD Barish","year":"2009","unstructured":"Barish RD, Schulman R, Rothemund PWK, Winfree E (2009) An information-bearing seed for nucleating algorithmic self-assembly. PNAS 106:6054\u20136059","journal-title":"PNAS"},{"key":"347_CR42","first-page":"518093","volume":"2008","author":"K Li","year":"2008","unstructured":"Li K, Zou S, Xv J (2008) Fast parallel molecular algorithms for DNA-based computation: solving the elliptic curve discrete logarithm problem over GF(2 n ). J Biomed Biotechnol 2008:518093. doi: 10.1155\/2008\/518093","journal-title":"J Biomed Biotechnol"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-009-0347-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11227-009-0347-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-009-0347-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T10:23:59Z","timestamp":1559384639000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11227-009-0347-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,11]]},"references-count":42,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,5]]}},"alternative-id":["347"],"URL":"https:\/\/doi.org\/10.1007\/s11227-009-0347-9","relation":{},"ISSN":["0920-8542","1573-0484"],"issn-type":[{"value":"0920-8542","type":"print"},{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11,11]]}}}