Alice Silverberg -- Bibliography

• Choosing the correct elliptic curve in the CM method, K. Rubin and A. Silverberg, preprint.

• PARI/GP implementations of algorithms, and pre-computed polynomials, associated with "Choosing the correct elliptic curve in the CM method"

• Point counting on reductions of CM elliptic curves, K. Rubin and A. Silverberg, preprint.

• Using Abelian Varieties to Improve Pairing-Based Cryptography, K. Rubin and A. Silverberg, to appear in Journal of Cryptology.

• Applications to cryptography of twisting commutative algebraic groups, A. Silverberg, to appear in Discrete Applied Mathematics.

• Compression in finite fields and torus-based cryptography, K. Rubin and A. Silverberg, SIAM Journal on Computing 37, no. 5 (2008), 1401-1428.

• Twisting commutative algebraic groups, B. Mazur, K. Rubin, and A. Silverberg, Journal of Algebra 314, no. 1 (2007), 419-438.

• The distribution of ranks in families of quadratic twists of elliptic curves, A. Silverberg, in Ranks of Elliptic Curves and Random Matrix Theory, Cambridge University Press (2007), 171-176.

• Twists of elliptic curves of rank at least four, K. Rubin and A. Silverberg, in Ranks of Elliptic Curves and Random Matrix Theory, Cambridge University Press (2007), 177-188.

• Alice in NUMB3Rland, A. Silverberg, MAA Focus 26, no. 8 (2006), 12-13.

• Women at Harvard, A. Silverberg, Remarks at an AWM Panel "Lawrence Summers: One Year Later" (with reference links), AWM Newsletter 36 (2006), 17-20.

• A Reed-Solomon Code for Disk Storage, and Efficient Recovery Computations for Erasure-Coded Disk Storage, M. S. Manasse, C. A. Thekkath, and A. Silverberg, in Distributed Data and Structures 6 (WDAS 2004), eds. Karl Aberer and Manfred Hauswirth, Carleton-Scientific (2006), 51-61.

• Practical Cryptography in High Dimensional Tori, M. van Dijk, R. Granger, D. Page, K. Rubin, A. Silverberg, M. Stam, and D. Woodruff, in Advances in Cryptology --- EUROCRYPT 2005, Lecture Notes in Computer Science 3494 (2005), Springer, 234-250.

• Compression for Trace Zero Subgroups of Elliptic Curves, A. Silverberg, Trends in Mathematics 8 (2005), 93-100.

• Inertia groups and abelian surfaces, A. Silverberg and Yu. G. Zarhin, Journal of Number Theory 110 (2005), 178-198.

• Using primitive subgroups to do more with fewer bits, K. Rubin and A. Silverberg, in Algorithmic Number Theory (ANTS VI), Lecture Notes in Computer Science 3076 (2004), Springer, 18-41.

• Algebraic tori in cryptography, K. Rubin and A. Silverberg, in High Primes and Misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams, Fields Institute Communications Series 41, American Mathematical Society, Providence, RI (2004), 317-326.

• Torus-based cryptography, K. Rubin and A. Silverberg, in Advances in Cryptology --- CRYPTO 2003, Lecture Notes in Computer Science 2729 (2003), Springer, 349-365.

• Arnold Ross (1906 - 2002), Memorial Article (multiple authors), Notices of the American Mathematical Society 50, no. 6 (2003), 664.

• Applications of List Decoding to Tracing Traitors, A. Silverberg, J. Staddon, and J. Walker, IEEE Transactions on Information Theory 133, no. 5 (2003), 1312-1318.

• Applications of Multilinear Forms to Cryptography, D. Boneh and A. Silverberg, in Topics in Algebraic and Noncommutative Geometry, Contemporary Mathematics 324, American Mathematical Society, Providence, RI (2003), 71-90.

• Hierarchical ID-Based Cryptography, C. Gentry and A. Silverberg, in Advances in Cryptology --- ASIACRYPT 2002, Lecture Notes in Computer Science 2501 (2002), Springer, 548-566; extended version in Cryptology ePrint Archive: Report 2002/056.

• Securing MIPv6 Binding Updates Using Address Based Keys (ABKs), S. Okazaki, A. Desai, C. Gentry, J. Kempf, A. Silverberg, and Y. L. Yin, Internet-Draft.

• Securing IPv6 Neighbor Discovery Using Address Based Keys (ABKs), J. Kempf, C. Gentry, and A. Silverberg, Internet-Draft.

• Supersingular abelian varieties in cryptology, K. Rubin and A. Silverberg, in Advances in Cryptology --- CRYPTO 2002, Lecture Notes in Computer Science 2442 (2002), Springer, 336-353; for an earlier version see "The best and worst of supersingular abelian varieties in cryptology", Cryptology ePrint Archive, Report 2002/006.

• Ranks of elliptic curves, K. Rubin and A. Silverberg, Bulletin of the American Mathematical Society 39 (2002), 455-474.

• Polarizations on abelian varieties, A. Silverberg and Yu. G. Zarhin, Mathematical Proceedings of the Cambridge Philosophical Society 133, no. 2 (2002), 223-233.

• Rank frequencies for quadratic twists of elliptic curves, K. Rubin and A. Silverberg, Experimental Mathematics 10, no. 4 (2001), 559-569.

• Electronic Appendix to Rank frequencies for quadratic twists of elliptic curves, K. Rubin and A. Silverberg --- Mathematica notebook.

• Electronic Appendix to Rank frequencies for quadratic twists of elliptic curves, K. Rubin and A. Silverberg --- PARI file.

• Efficient Traitor Tracing Algorithms using List Decoding, A. Silverberg, J. Staddon, and J. Walker, in Advances in Cryptology --- ASIACRYPT 2001, Lecture Notes in Computer Science 2248 (2001), Springer, 175-192.

• Emmy Noether in Erlangen, A. Silverberg, Mathematical Intelligencer 23, no. 3 (2001), 44-49.

• Symplectic representations of inertia groups, A. Silverberg and Yu. G. Zarhin, Journal of Algebra 238 (2001), 400-410.

• Open Questions in Arithmetic Algebraic Geometry, A. Silverberg, in Arithmetic Algebraic Geometry (Park City, UT, 1999), Institute for Advanced Study/Park City Mathematics Series 9, American Mathematical Society, Providence, RI (2001), 83-142.

• Polarizations on abelian varieties and self-dual l-adic representations of inertia groups, A. Silverberg and Yu. G. Zarhin, Compositio Mathematica 126 (2001), 25-45.

• Etale cohomology and reduction of abelian varieties, A. Silverberg and Yu. G. Zarhin, Bulletin de la Société Mathématique de France 129 (2001), 141-157.

• Ranks of elliptic curves in families of quadratic twists, K. Rubin and A. Silverberg, Experimental Mathematics 9 (2000), 583-590.

• Mod 2 representations of elliptic curves, K. Rubin and A. Silverberg, Proceedings of the American Mathematical Society 129 (2001), 53-57.

• Reduction of abelian varieties, A. Silverberg and Yu. G. Zarhin, in The Arithmetic and Geometry of Algebraic Cycles, eds. B. B. Gordon et al., Kluwer Academic Publishers (2000), 495-513.

• Mod 6 representations of elliptic curves, K. Rubin and A. Silverberg, in Automorphic Forms, Automorphic Representations, and Arithmetic, Proceedings of Symposia in Pure Mathematics 66, Part 1, eds. Robert S. Doran, Ze-Li Dou, George T. Gilbert, AMS, Providence, RI (1999), 213-220.

• Subgroups of inertia groups arising from abelian varieties, A. Silverberg and Yu. G. Zarhin, Journal of Algebra 209 (1998), 94-107.

• Semistable reduction of abelian varieties over extensions of small degree, A. Silverberg and Yu. G. Zarhin, Journal of Pure and Applied Algebra 132, no. 2 (1998), 179-193.

• Connectedness extensions for abelian varieties, A. Silverberg and Yu. G. Zarhin, Mathematische Zeitschrift 228, no. 2 (1998), 387-403.

• Explicit families of elliptic curves with prescribed mod N representations, A. Silverberg, in Modular Forms and Fermat's Last Theorem, eds. Gary Cornell, Joseph H. Silverman, Glenn Stevens, Springer-Verlag, Berlin-Heidelberg-New York (1997), 447-461.

• Hodge groups of abelian varieties with purely multiplicative reduction, A. Silverberg and Yu. G. Zarhin, Izvestija Akad. Nauk SSSR Ser. Mat. 60 (1996), 149-158.

• Variations on a theme of Minkowski and Serre, A. Silverberg and Yu. G. Zarhin, Journal of Pure and Applied Algebra 111 (1996), 285-302.

• Rigidity Theorems for Abelian Varieties, A. Silverberg and Yu. G. Zarhin, Doklady Rossiiskoi Akademii Nauk 351, no. 1 (1996), 9-10.

• Connectedness results for l-adic representations associated to abelian varieties, A. Silverberg and Yu. G. Zarhin, Compositio Mathematica 97 (1995), 273-284.

• Families of Elliptic Curves with Constant mod p Representations, K. Rubin and A. Silverberg, in Elliptic curves, modular forms, & Fermat's last theorem (Hong Kong, 1993), eds. John Coates, S. T. Yau, International Press, Cambridge, Massachusetts (1995), 148-161; Second edition: Elliptic Curves, Modular Forms, & Fermat's Last Theorem (1997).

• Semistable reduction and torsion subgroups of abelian varieties, A. Silverberg and Yu. G. Zarhin, Annales de l'Institut Fourier 45, no. 2 (1995), 403-420.

• A report on Wiles' Cambridge lectures, K. Rubin and A. Silverberg, Bulletin of the American Mathematical Society (N. S.) 31, no. 1 (1994), 15-38.

• Isogenies of abelian varieties, A. Silverberg and Yu. G. Zarhin, Journal of Pure and Applied Algebra 90 (1993), 23-37.

• Galois representations attached to points on Shimura varieties, A. Silverberg, in Séminaire de Théorie des Nombres, Paris 1990-91, ed. Sinnou David, Progress in Mathematics 108, Birkhäuser, Boston (1993), 221-240.

• Points of finite order on abelian varieties, A. Silverberg, in p-adic Methods in Number Theory and Algebraic Geometry, eds. Alan C. Adolphson, Steven Sperber, Marvin D. Tretkoff, Contemporary Mathematics 133, American Mathematical Society (1992), 175-193.

• Fields of definition for homomorphisms of abelian varieties, A. Silverberg, Journal of Pure and Applied Algebra 77 (1992), 253-262.

• Canonical models and adelic representations, A. Silverberg, American Journal of Mathematics 114 (1992), 1221-1241.

• Galois Representations and an "Isogeny Theorem" for Points on Shimura Varieties, A. Silverberg, in Proceedings of the Conference on Number Theory and Arithmetical Geometry, March 12-15, 1991, ed. Gerhard Frey, Institut für Experimentelle Mathematik, Universität GH Essen 18 (1991), 8-11.

• Universal families of abelian varieties, A. Silverberg, in Number Theory and Cryptography, ed. John Loxton, London Mathematical Society Lecture Note Series 154, Cambridge University Press (1990), 227-235.

• Abelian varieties with endomorphism algebra structure, A. Silverberg, Forschungsschwerpunkt Komplexe Mannigfaltigkeiten Schriftenreihe, Heft Nr. 5, Universität Erlangen-Nürnberg (1988), 31 pp.

• Torsion points on abelian varieties of CM-type, A. Silverberg, Compositio Mathematica 68 (1988), 241-249.

• Mordell-Weil groups of generic abelian varieties in the unitary case, A. Silverberg, Proceedings of the American Mathematical Society 104 (1988), 723-728.

• Cohomology of fiber systems and Mordell-Weil groups of abelian varieties, A. Silverberg, Duke Mathematical Journal 56 (1988), 41-46.

• Points de torsion des variétés abéliennes de type CM, A. Silverberg, in Problèmes Diophantiens 1985-86, eds. Daniel Bertrand and Michel Waldschmidt, Publications mathématiques de l'Université de Paris VI 79 (1986), exp. no. 7, 12 pp.

• Mordell-Weil groups of generic abelian varieties, A. Silverberg, Inventiones mathematicae 81 (1985), 71-106.

• Finiteness of Mordell-Weil groups of generic abelian varieties, A. Silverberg, Bulletin of the American Mathematical Society 12 (1985), 131-133.

• Mordell-Weil groups of generic polarized abelian varieties, A. Silverberg, Ph.D. thesis, Princeton University (1984), 77 pp.

• The Hardy-Littlewood Circle Method, Mathematics Essay, A. Silverberg, University of Cambridge, England (1980), 30 pp.

• The Signalizer Functor Theorem for Finite Groups, A. Silverberg, Senior Honors Thesis in Mathematics, Harvard University (1979), 37 pp.