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Papers by Benjamin Smith

Research paper thumbnail of Three-Year Outcomes With Hypofractionated Versus Conventionally Fractionated Whole-Breast Irradiation: Results of a Randomized, Noninferiority Clinical Trial

Journal of Clinical Oncology, 2018

Purpose The adoption of hypofractionated whole-breast irradiation (HF-WBI) remains low, in part b... more Purpose The adoption of hypofractionated whole-breast irradiation (HF-WBI) remains low, in part because of concerns regarding its safety when used with a tumor bed boost or in patients who have received chemotherapy or have large breast size. To address this, we conducted a randomized, multicenter trial to compare conventionally fractionated whole-breast irradiation (CF-WBI; 50 Gy/25 fx + 10 to 14 Gy/5 to 7 fx) with HF-WBI (42.56 Gy/16 fx + 10 to 12.5 Gy/4 to 5 fx). Patients and Methods From 2011 to 2014, 287 women with stage 0 to II breast cancer were randomly assigned to CF-WBI or HF-WBI, stratified by chemotherapy, margin status, cosmesis, and breast size. The trial was designed to test the hypothesis that HF-WBI is not inferior to CF-WBI with regard to the proportion of patients with adverse cosmetic outcome 3 years after radiation, assessed using the Breast Cancer Treatment Outcomes Scale. Secondary outcomes included photographically assessed cosmesis scored by a three-physicia...

Research paper thumbnail of Comparative Toxicities and Cost of Intensity-Modulated Radiotherapy, Proton Radiation, and Stereotactic Body Radiotherapy Among Younger Men With Prostate Cancer

Journal of clinical oncology : official journal of the American Society of Clinical Oncology, Jan 21, 2018

Purpose To compare the toxicities and cost of proton radiation and stereotactic body radiotherapy... more Purpose To compare the toxicities and cost of proton radiation and stereotactic body radiotherapy (SBRT) with intensity-modulated radiotherapy (IMRT) for prostate cancer among men younger than 65 years of age with private insurance. Methods Using the MarketScan Commercial Claims and Encounters database, we identified men who received radiation for prostate cancer between 2008 and 2015. Patients undergoing proton therapy and SBRT were propensity score-matched to IMRT patients on the basis of clinical and sociodemographic factors. Proportional hazards models compared the cumulative incidence of urinary, bowel, and erectile dysfunction toxicities by treatment. Cost from a payer's perspective was calculated from claims and adjusted to 2015 dollars. Results A total of 693 proton therapy patients were matched to 3,465 IMRT patients. Proton therapy patients had a lower risk of composite urinary toxicity (33% v 42% at 2 years; P < .001) and erectile dysfunction (21% v 28% at 2 years;...

Research paper thumbnail of Distortion maps for genus two curves

Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, ... more Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated since the full torsion subgroup has rank 2g. In this paper we prove that distortion maps always exist for supersingular curves of genus g>1 and we construct distortion maps in genus 2 (for

Research paper thumbnail of Distortion maps for supersingular genus two curves

Journal of Mathematical Cryptology, 2009

Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, ... more Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated, since the full torsion subgroup has rank 2g. In this paper, we prove that distortion maps always exist for supersingular curves of genus g > 1. We also give several examples of curves of genus 2 with explicit distortion maps for embedding degrees 4, 5, 6, and 12.

Research paper thumbnail of Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic Curves

Journal of Cryptology, 2009

We describe the use of explicit isogenies to translate instances of the Discrete Logarithm Proble... more We describe the use of explicit isogenies to translate instances of the Discrete Logarithm Problem (DLP) from Jacobians of hyperelliptic genus 3 curves to Jacobians of non-hyperelliptic genus 3 curves, where they are vulnerable to faster index calculus attacks. We provide explicit formulae for isogenies with kernel isomorphic to (Z/2Z) 3 (over an algebraic closure of the base field) for any hyperelliptic genus 3 curve over a field of characteristic not 2 or 3. These isogenies are rational for a positive fraction of all hyperelliptic genus 3 curves defined over a finite field of characteristic p > 3. Subject to reasonable assumptions, our constructions give an explicit and efficient reduction of instances of the DLP from hyperelliptic to non-hyperelliptic Jacobians for around 18.57% of all hyperelliptic genus 3 curves over a given finite field. We conclude with a discussion on extending these ideas to isogenies with more general kernels.

Research paper thumbnail of Families of explicitly isogenous Jacobians of variable-separated curves

LMS Journal of Computation and Mathematics, 2011

We construct six infinite series of families of pairs of curves (X,Y) of arbitrarily high genus, ... more We construct six infinite series of families of pairs of curves (X,Y) of arbitrarily high genus, defined over number fields, together with an explicit isogeny from the Jacobian ofXto the Jacobian ofYsplitting multiplication by 2, 3 or 4. For each family, we compute the isomorphism type of the isogeny kernel and the dimension of the image of the family in the appropriate moduli space. The families are derived from Cassou-Noguès and Couveignes’ explicit classification of pairs (f,g) of polynomials such thatf(x1)−g(x2) is reducible.Supplementary materials are available with this article.

Research paper thumbnail of Three-Year Outcomes With Hypofractionated Versus Conventionally Fractionated Whole-Breast Irradiation: Results of a Randomized, Noninferiority Clinical Trial

Journal of Clinical Oncology, 2018

Purpose The adoption of hypofractionated whole-breast irradiation (HF-WBI) remains low, in part b... more Purpose The adoption of hypofractionated whole-breast irradiation (HF-WBI) remains low, in part because of concerns regarding its safety when used with a tumor bed boost or in patients who have received chemotherapy or have large breast size. To address this, we conducted a randomized, multicenter trial to compare conventionally fractionated whole-breast irradiation (CF-WBI; 50 Gy/25 fx + 10 to 14 Gy/5 to 7 fx) with HF-WBI (42.56 Gy/16 fx + 10 to 12.5 Gy/4 to 5 fx). Patients and Methods From 2011 to 2014, 287 women with stage 0 to II breast cancer were randomly assigned to CF-WBI or HF-WBI, stratified by chemotherapy, margin status, cosmesis, and breast size. The trial was designed to test the hypothesis that HF-WBI is not inferior to CF-WBI with regard to the proportion of patients with adverse cosmetic outcome 3 years after radiation, assessed using the Breast Cancer Treatment Outcomes Scale. Secondary outcomes included photographically assessed cosmesis scored by a three-physicia...

Research paper thumbnail of Comparative Toxicities and Cost of Intensity-Modulated Radiotherapy, Proton Radiation, and Stereotactic Body Radiotherapy Among Younger Men With Prostate Cancer

Journal of clinical oncology : official journal of the American Society of Clinical Oncology, Jan 21, 2018

Purpose To compare the toxicities and cost of proton radiation and stereotactic body radiotherapy... more Purpose To compare the toxicities and cost of proton radiation and stereotactic body radiotherapy (SBRT) with intensity-modulated radiotherapy (IMRT) for prostate cancer among men younger than 65 years of age with private insurance. Methods Using the MarketScan Commercial Claims and Encounters database, we identified men who received radiation for prostate cancer between 2008 and 2015. Patients undergoing proton therapy and SBRT were propensity score-matched to IMRT patients on the basis of clinical and sociodemographic factors. Proportional hazards models compared the cumulative incidence of urinary, bowel, and erectile dysfunction toxicities by treatment. Cost from a payer's perspective was calculated from claims and adjusted to 2015 dollars. Results A total of 693 proton therapy patients were matched to 3,465 IMRT patients. Proton therapy patients had a lower risk of composite urinary toxicity (33% v 42% at 2 years; P < .001) and erectile dysfunction (21% v 28% at 2 years;...

Research paper thumbnail of Distortion maps for genus two curves

Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, ... more Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated since the full torsion subgroup has rank 2g. In this paper we prove that distortion maps always exist for supersingular curves of genus g>1 and we construct distortion maps in genus 2 (for

Research paper thumbnail of Distortion maps for supersingular genus two curves

Journal of Mathematical Cryptology, 2009

Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, ... more Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated, since the full torsion subgroup has rank 2g. In this paper, we prove that distortion maps always exist for supersingular curves of genus g > 1. We also give several examples of curves of genus 2 with explicit distortion maps for embedding degrees 4, 5, 6, and 12.

Research paper thumbnail of Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic Curves

Journal of Cryptology, 2009

We describe the use of explicit isogenies to translate instances of the Discrete Logarithm Proble... more We describe the use of explicit isogenies to translate instances of the Discrete Logarithm Problem (DLP) from Jacobians of hyperelliptic genus 3 curves to Jacobians of non-hyperelliptic genus 3 curves, where they are vulnerable to faster index calculus attacks. We provide explicit formulae for isogenies with kernel isomorphic to (Z/2Z) 3 (over an algebraic closure of the base field) for any hyperelliptic genus 3 curve over a field of characteristic not 2 or 3. These isogenies are rational for a positive fraction of all hyperelliptic genus 3 curves defined over a finite field of characteristic p > 3. Subject to reasonable assumptions, our constructions give an explicit and efficient reduction of instances of the DLP from hyperelliptic to non-hyperelliptic Jacobians for around 18.57% of all hyperelliptic genus 3 curves over a given finite field. We conclude with a discussion on extending these ideas to isogenies with more general kernels.

Research paper thumbnail of Families of explicitly isogenous Jacobians of variable-separated curves

LMS Journal of Computation and Mathematics, 2011

We construct six infinite series of families of pairs of curves (X,Y) of arbitrarily high genus, ... more We construct six infinite series of families of pairs of curves (X,Y) of arbitrarily high genus, defined over number fields, together with an explicit isogeny from the Jacobian ofXto the Jacobian ofYsplitting multiplication by 2, 3 or 4. For each family, we compute the isomorphism type of the isogeny kernel and the dimension of the image of the family in the appropriate moduli space. The families are derived from Cassou-Noguès and Couveignes’ explicit classification of pairs (f,g) of polynomials such thatf(x1)−g(x2) is reducible.Supplementary materials are available with this article.