Character sums with division polynomials

Igor E. Shparlinski; Katherine E. Stange

doi:10.4153/CMB-2011-126-x

Character sums with division polynomials

Igor E. Shparlinski^*, Katherine E. Stange

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We obtain nontrivial estimates of quadratic character sums of division polynomialsΨ_n(P), n = 1, 2, . . . , evaluated at a given point P on an elliptic curve over a finite field of q elements. Our bounds are nontrivial if the order of P is at least q^1/2+ε for some fixed ε > 0. This work is motivated by an open question about statistical indistinguishability of some cryptographically relevant sequences that was recently brought up by K. Lauter and the second author.

Original language	English
Pages (from-to)	850-857
Number of pages	8
Journal	Canadian Mathematical Bulletin
Volume	55
Issue number	4
DOIs	https://doi.org/10.4153/CMB-2011-126-x
Publication status	Published - Dec 2012

Access to Document

10.4153/CMB-2011-126-x

Cite this

@article{39d78778124245708ca11ddc2acc1a0a,

title = "Character sums with division polynomials",

abstract = "We obtain nontrivial estimates of quadratic character sums of division polynomialsΨn(P), n = 1, 2, . . . , evaluated at a given point P on an elliptic curve over a finite field of q elements. Our bounds are nontrivial if the order of P is at least q1/2+ε for some fixed ε > 0. This work is motivated by an open question about statistical indistinguishability of some cryptographically relevant sequences that was recently brought up by K. Lauter and the second author.",

author = "Shparlinski, \{Igor E.\} and Stange, \{Katherine E.\}",

year = "2012",

month = dec,

doi = "10.4153/CMB-2011-126-x",

language = "English",

volume = "55",

pages = "850--857",

journal = "Canadian Mathematical Bulletin",

issn = "0008-4395",

publisher = "Canadian Mathematical Society",

number = "4",

}

TY - JOUR

T1 - Character sums with division polynomials

AU - Shparlinski, Igor E.

AU - Stange, Katherine E.

PY - 2012/12

Y1 - 2012/12

N2 - We obtain nontrivial estimates of quadratic character sums of division polynomialsΨn(P), n = 1, 2, . . . , evaluated at a given point P on an elliptic curve over a finite field of q elements. Our bounds are nontrivial if the order of P is at least q1/2+ε for some fixed ε > 0. This work is motivated by an open question about statistical indistinguishability of some cryptographically relevant sequences that was recently brought up by K. Lauter and the second author.

AB - We obtain nontrivial estimates of quadratic character sums of division polynomialsΨn(P), n = 1, 2, . . . , evaluated at a given point P on an elliptic curve over a finite field of q elements. Our bounds are nontrivial if the order of P is at least q1/2+ε for some fixed ε > 0. This work is motivated by an open question about statistical indistinguishability of some cryptographically relevant sequences that was recently brought up by K. Lauter and the second author.

UR - https://www.scopus.com/pages/publications/84871772074

U2 - 10.4153/CMB-2011-126-x

DO - 10.4153/CMB-2011-126-x

M3 - Article

AN - SCOPUS:84871772074

SN - 0008-4395

VL - 55

SP - 850

EP - 857

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

IS - 4

ER -

Character sums with division polynomials

Abstract

Access to Document

Other files and links

Fingerprint

Cite this