What Does It Mean for k to Be a Square Modulo m?

  • Thread starter stgermaine
  • Start date
  • Tags
    Square
In summary, "k is a square modulo m" means that there exists a number x such that x^2 is congruent to k modulo m. This is used in cryptography to determine whether a given number is a perfect square modulo a certain modulus.
  • #1
stgermaine
48
0
k is a square modulo m??

\:

Homework Statement


This is a portion of the problem. I have to prove that A holds if and only if k is a square modulo m.

I have no idea what "k is a square modulo m" means.

Homework Equations


The Attempt at a Solution


I've looked it up online and found some PDF's on cryptography.l
My best guess is that "k is a square modulo m" means [itex]x^{2} \equiv k \: (mod\:m)[/itex] has a solution x.

Is that right?
 
Physics news on Phys.org
  • #2


stgermaine said:
\:

Homework Statement


This is a portion of the problem. I have to prove that A holds if and only if k is a square modulo m.

I have no idea what "k is a square modulo m" means.

Homework Equations





The Attempt at a Solution


I've looked it up online and found some PDF's on cryptography.l
My best guess is that "k is a square modulo m" means [itex]x^{2} \equiv k \: (mod\:m)[/itex] has a solution x.

Is that right?

Yes, that's what it means.
 

Related to What Does It Mean for k to Be a Square Modulo m?

What does it mean for K to be a square modulo m?

For a number K to be a square modulo m means that when K is divided by m, the remainder is a perfect square. In other words, there exists a number n such that K ≡ n² (mod m).

How do you determine if K is a square modulo m?

To determine if K is a square modulo m, you can use the Legendre symbol. If the Legendre symbol for K and m is equal to 1, then K is a square modulo m. If the symbol is equal to -1, then K is not a square modulo m.

What is the significance of K being a square modulo m?

The concept of K being a square modulo m is important in number theory and cryptography. It is used in various algorithms and protocols to ensure the security and efficiency of cryptographic systems.

Can K be a square modulo m for any values of K and m?

No, K can only be a square modulo m if the greatest common divisor of K and m is equal to 1. This is known as the fundamental theorem of arithmetic.

What are some applications of K being a square modulo m?

K being a square modulo m has various applications in number theory, cryptography, and computer science. It is used in modular exponentiation, primality testing, and quadratic residues. It is also used in the Diffie-Hellman protocol and other cryptographic systems.

Similar threads

Solve the simultaneous congruence modulo equation
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Congruence and Primes: Proving the Order of an Integer Modulo a Prime
    • Calculus and Beyond Homework Help
Replies
4
Views
997
What is the correct formula for the reduced Chi square?
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Number Theory (2) Homework: Find Integer Orders Modulo 19 & 17
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Chinese Remainder theorem for 2 congruences
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
Help Taking the Limit as K goes to infinity
    • Calculus and Beyond Homework Help
Replies
14
Views
2K
Proving Least Positive Residue Using m-Cycle Permutations
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
Proving Dyadic Squares Interaction Rules
    • Calculus and Beyond Homework Help
Replies
1
Views
2K
Is m the smallest order for an m-cycle in the symmetric group?
    • Calculus and Beyond Homework Help
Replies
3
Views
813
Prove that if p > 3 is a prime number, then p^2 = [....]
    • Calculus and Beyond Homework Help
Replies
16
Views
2K

Hot Threads

Recent Insights

Back
Top