1998/01/01 by Igor Semaev · 2 citations
Computer Science · Mathematics · #Cryptography and Residue Arithmetic #Algebraic Geometry and Number Theory #Coding theory and cryptography
paper · pdf · doi:10.1090/s0025-5718-98-00887-4
openalex publication_date 1998/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
We show that to solve the discrete log problem in a subgroup of order <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of an elliptic curve over the finite field of characteristic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> one needs <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper O left-parenthesis ln p right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ln</mml:mi> <mml:mo> </mml:mo> <mml:mi>p</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">O(ln p)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> operations in this field.