Alice Silverberg -- Bibliography

• Fully Homomorphic Encryption for Mathematicians, A. Silverberg, to appear in the WIN2 Proceedings.

• Ranks "cheat sheet", A. Silverberg, to appear in the WIN2 Proceedings.

• On elliptic curves with an isogeny of degree 7, R. Greenberg, K. Rubin, A. Silverberg, and M. Stoll, to appear in the American Journal of Mathematics.

• Deterministic elliptic curve primality proving for a special sequence of numbers, A. Abatzoglou, A. Silverberg, A. V. Sutherland, A. Wong, to appear in Algorithmic Number Theory (ANTS X), Mathematical Sciences Publishers.

• Arithmetic of L-functions, C. Popescu, K. Rubin, A. Silverberg (eds.), IAS/Park City Mathematics Series 18, American Mathematical Society, Providence (2011), 499 pp.

• Introduction to Elliptic Curves, A. Silverberg, in Arithmetic of L-functions, IAS/Park City Mathematics Series 18, American Mathematical Society, Providence (2011), 155-167.

• Finding composite order ordinary elliptic curves using the Cocks-Pinch method, D. Boneh, K. Rubin, and A. Silverberg, Journal of Number Theory 131 (2011), 832-841.

• Group order formulas for reductions of CM elliptic curves, A. Silverberg, in Proceedings of the Conference on Arithmetic, Geometry, Cryptography and Coding Theory, Contemporary Mathematics, 521, American Mathematical Society, Providence, RI (2010), 107-120.

• Choosing the correct elliptic curve in the CM method, K. Rubin and A. Silverberg, Mathematics of Computation 79, no. 269 (2010), 545-561.

• 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, Journal of Number Theory 129, no. 12 (2009), 2903-2923.

• Using Abelian Varieties to Improve Pairing-Based Cryptography, K. Rubin and A. Silverberg, Journal of Cryptology 22, no. 3 (2009), 330-364.

• Applications to cryptography of twisting commutative algebraic groups, A. Silverberg, Discrete Applied Mathematics 156 (2008), 3122-3138.

• 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.

• 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), 296-309.

• 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.