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Consider the elliptic curve group based on the equation y²r³+ ax+b mod p where a = 2, b = 4, and p = 5. This curve contains the point P = (0, 2). The order of this elliptic curve group is the prime number 7, and therefore we can be sure that P is a primitive element. Another element in this group is Q = (2, 1). 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?

Consider the elliptic curve group based on the equation y²r³+ ax+b mod p where a = 2, b = 4, and p = 5. This curve contains the point P = (0, 2). The order of this elliptic curve group is the prime number 7, and therefore we can be sure that P is a primitive element. Another element in this group is Q = (2, 1). 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?

Advanced Engineering Mathematics
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 y² = x³ + ax +b mod p where a = 2, b = 4, and p = 5. This curve contains the point P = (0, 2). The order of this elliptic curve group is the prime number 7, and therefore we can be sure that P is a primitive element. Another element in this group is Q = (2, 1). The index of Qwith respect to P is the least positive integer d such that Q = d.P. What is d, the index of Q?
Transcribed Image Text:Consider the elliptic curve group based on the equation y² = x³ + ax +b mod p where a = 2, b = 4, and p = 5. This curve contains the point P = (0, 2). The order of this elliptic curve group is the prime number 7, and therefore we can be sure that P is a primitive element. Another element in this group is Q = (2, 1). The index of Qwith respect to P is the least positive integer d such that Q = d.P. What is d, the index of Q?
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