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Number Theory

Encryption with Number Theory

Concept Quizzes

Public-Key Encryption
Diffie-Hellman
RSA

RSA

Solving which of the following problems would allow one to break RSA encryption?

Boolean Satisfiability problem Integer Factorization problem Traveling Salesman problem Vertex Cover problem

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by Brilliant Staff

Alice chooses a public key of $n=187$ and $e=3$ . What is her private key?

53 78 107 160

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by Brilliant Staff

Bob's public key is $426759435605268851$ and $e=3$ . Alice uses ASCII encryption and sends the ciphertext $c=298049520771754739$ . Which of the following was Alice's original message?

BOO CAT DOG EGG

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Mallory discovers many public keys, including the following:

$n=70441807$ , $e=3$
$n=10645627$ , $e=17$
$n=63339281$ , $e=65537$
$n=24864431$ , $e=257$
$n=89221291$ , $e=17$

What number can Mallory discover is the prime factor of one (or more) of these keys, without needing to factor any of them, making use of a vulnerability of RSA?

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Knowing which of the following would allow an attacker to efficiently break the RSA encryption?

c

, the ciphertext

e

, the exponent

n

, the product of two primes

\phi(n)

, the totient function of

n

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by Brilliant Staff

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