Alice Silverberg -- Bibliography

• Click here for articles published in the AWM Newsletter, MAA Focus, San Francisco Chronicle, Mathematical Intelligencer, etc.

• Realizing orders as group rings, H. W. Lenstra Jr., A. Silverberg, D. M. H. van Gent, Journal of Algebra 641 (2024), 391-428, https://doi.org/10.1016/j.jalgebra.2023.11.017.

• Quantum Money from Quaternion Algebras, Daniel M. Kane, Shahed Sharif, Alice Silverberg, Mathematical Cryptology 2, no. 1 (2022), 60-83.

• "Mathematicians for Equal Opportunity", in "Fifty Years of Women in Mathematics", eds. J. Beery, S. Greenwald, and C. Kessel, Association for Women in Mathematics Series 28 (2022), Springer, 49-53, https://doi.org/10.1007/978-3-030-82658-1_8.

• Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant, Eric Rains, Karl Rubin, Travis Scholl, Shahed Sharif, Alice Silverberg, Algebra & Number Theory 15-3 (2021), 711-727, https://doi.org/10.2140/ant.2021.15.711.

• Problem #1366 on multiparty key agreement, A. Silverberg, Pi Mu Epsilon Journal, Volume 15, No. 2 (2020), pp. 120-121, and Volume 15, No. 3 (2020).

• Explicit arithmetic of Jacobians of generalized Legendre curves over global function fields, Lisa Berger, Chris Hall, René Pannekoek, Jennifer Park, Rachel Pries, Shahed Sharif, Alice Silverberg, Douglas Ulmer, Memoirs of the American Mathematical Society, Volume 266, Number 1295 (2020), 134 pages, https://doi.org/10.1090/memo/1295.

• Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves, Dan Boneh, Darren Glass, Daniel Krashen, Kristin Lauter, Shahed Sharif, Alice Silverberg, Mehdi Tibouchi, Mark Zhandry, Journal of Mathematical Cryptology 14, no. 1 (2020), 5-14.

• Mathematics and Cryptography: A Marriage of Convenience? A. Silverberg, Advances in Cryptology --- EUROCRYPT 2020, Proceedings, Part I, Lecture Notes in Computer Science 12105 (2020), Springer, 3-9.

• Memories of Goro Shimura (multiple authors), Notices of the American Mathematical Society 67, no. 5 (2020), 677-689.

• Testing isomorphism of lattices over CM-orders, H. W. Lenstra Jr. and A. Silverberg, SIAM Journal on Computing 48, no. 4 (2019), 1300-1334.

• Universal gradings of orders, H. W. Lenstra Jr. and A. Silverberg, Archiv der Mathematik, https://doi.org/10.1007/s00013-018-1228-3, 111, no. 6 (2018), 579-597, Selected as a Distinguished Article.

• "What can I learn from this?" or: Some things I wish I'd learned sooner, MAA FOCUS 38, no. 1, February/March 2018, 12-15.

• Algorithms for commutative algebras over the rational numbers, H. W. Lenstra Jr. and A. Silverberg, doi:10.1007/s10208-016-9336-6, Foundations of Computational Mathematics 18, no. 1, (2018), 159-180.

• Arithmetic properties of the Frobenius traces defined by a rational abelian variety (with two appendices by J-P. Serre), Alina Carmen Cojocaru, Rachel Davis, Alice Silverberg, Katherine E. Stange, doi:10.1093/imrn/rnw058, International Mathematics Research Notices 2017, no.12, 3557-3602.

• Lattices with symmetry, H. W. Lenstra Jr. and A. Silverberg (Invited Paper, due to "Revisiting the Gentry-Szydlo Algorithm" having been selected as one of the best papers at the conference Crypto 2014), Journal of Cryptology 30 (2017), 760-804.

• Roots of unity in orders, H. W. Lenstra Jr. and A. Silverberg, Foundations of Computational Mathematics 17, no. 3, (2017), 851-877, doi:10.1007/s10208-016-9304-1.

• Through the Cryptographer's Looking-Glass, and what Alice found there, A. Silverberg, Notices of the American Mathematical Society 64, no. 1, January 2017, 10-11.

• Collected Papers of Goro Shimura, Volume V: 2002-2012, Alice Silverberg and Hiroyuki Yoshida (editors), Springer (2016).

• Determining cyclicity of finite modules, H. W. Lenstra Jr. and A. Silverberg, Journal of Symbolic Computation 73 (2016), 153-156.

• A framework for deterministic primality proving using elliptic curves with complex multiplication, A. Abatzoglou, A. Silverberg, A. V. Sutherland, A. Wong, Mathematics of Computation 85 (2016), 1461-1483.

• Isogenies of abelian varieties over finite fields, A. Silverberg, Yu. G. Zarhin, in Designs, Codes and Cryptography 77 (2015), 427-439.

• Some remarks on primality proving and elliptic curves, A. Silverberg, Advances in Mathematics of Communications 8, no. 4 (2014), 427-436.

• Lattices with symmetry, and the extended tensor algebra, H. W. Lenstra Jr. and A. Silverberg, in Mathematisches Forschungsinstitut Oberwolfach Reports 11, no. 3 (2014), 1966-1967.

• Revisiting the Gentry-Szydlo Algorithm, H. W. Lenstra Jr. and A. Silverberg, in Advances in Cryptology --- CRYPTO 2014, Lecture Notes in Computer Science 8616 (2014), Springer, 280-296.

• On elliptic curves with an isogeny of degree 7, R. Greenberg, K. Rubin, A. Silverberg, and M. Stoll, American Journal of Mathematics 136 (2014), 77-109.

• Fully Homomorphic Encryption for Mathematicians, A. Silverberg, in WIN 2: Research Directions in Number Theory, eds. C. David, M. Lalin, and M. Manes, Contemporary Mathematics 606, American Mathematical Society and Centre de Recherches Mathématiques (2013), 111-123.

• Ranks "cheat sheet", A. Silverberg, in WIN 2: Research Directions in Number Theory, eds. C. David, M. Lalin, and M. Manes, Contemporary Mathematics 606, American Mathematical Society and Centre de Recherches Mathématiques (2013), 101-110.

• Deterministic elliptic curve primality proving for a special sequence of numbers, A. Abatzoglou, A. Silverberg, A. V. Sutherland, A. Wong, in ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium, eds. E. W. Howe and K. S. Kedlaya, Open Book Series 1, Mathematical Sciences Publishers, Berkeley (2013), 1-20.

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

• Introduction to Elliptic Curves, A. Silverberg, in Arithmetic of L-functions, IAS/Park City Mathematics Series 18, American Mathematical Society, Providence, RI (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 Arithmetic, Geometry, Cryptography and Coding Theory 2009, eds. D. Kohel and R. Rolland, 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, eds. C. G. Melles, J-P. Brasselet, G. Kennedy, K. Lauter, and L. McEwan, Contemporary Mathematics 324, American Mathematical Society, Providence, RI (2003), 71-90; corrected version and published version.

• 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 (Fort Worth, TX, 1996), 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. A. C. Adolphson, S. Sperber, and M. 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; Corrigendum, Compositio Mathematica 154 (2018), 594.

• 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.