equation Consider the elliptic curve group based on the where a = y² = x³ + ax + b X3 7, b = 2, and p = 11. mod p = (7,3). The order of This curve contains the point P this elliptic curve group is the prime number 8, and therefore we can be sure that P is a primitive element. Another element in this group is Q = (,). The index of Qwith respect to P is the least positive integer d such that Q = dP. What is d, the index of Q?
equation Consider the elliptic curve group based on the where a = y² = x³ + ax + b X3 7, b = 2, and p = 11. mod p = (7,3). The order of This curve contains the point P this elliptic curve group is the prime number 8, and therefore we can be sure that P is a primitive element. Another element in this group is Q = (,). The index of Qwith respect to P is the least positive integer d such that Q = dP. What is d, the index of Q?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Consider the elliptic curve group based on the equation:**
\[ y^2 \equiv x^3 + ax + b \pmod{p} \]
where \( a = 7 \), \( b = 2 \), and \( p = 11 \).
This curve contains the point \( P = (7, 3) \). The order of this elliptic curve group is the prime number 8, and therefore we can be sure that \( P \) is a primitive element. Another element in this group is \( Q = (\ ,\ ) \). The index of \( Q \) with respect to \( P \) is the least positive integer \( d \) such that \( Q = dP \). What is \( d \), the index of \( Q \)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F648d38bc-f5b9-4baf-95bc-853621e34b39%2Fcf08e451-d861-4453-82bb-b92b9fb51051%2Fcmy3a0s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Consider the elliptic curve group based on the equation:**
\[ y^2 \equiv x^3 + ax + b \pmod{p} \]
where \( a = 7 \), \( b = 2 \), and \( p = 11 \).
This curve contains the point \( P = (7, 3) \). The order of this elliptic curve group is the prime number 8, and therefore we can be sure that \( P \) is a primitive element. Another element in this group is \( Q = (\ ,\ ) \). The index of \( Q \) with respect to \( P \) is the least positive integer \( d \) such that \( Q = dP \). What is \( d \), the index of \( Q \)?
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