NPTEL Computational Number Theory and Algebra Assignment 10 Answer

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NPTEL Computational Number Theory and Algebra Assignment

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1 point

Let |v||v| be the length of the shortest vector v in a given lattice. Which of the following is true for the LLL algorithm?

LLL finds the shortest vector v in the lattice.

LLL finds a vector in lattice whose length ≤2n|v|≤2n|v|

LLL finds the largest vector in the lattice.

LLL finds a vector in lattice whose length ≥2n|v|≥2n|v|

Ans  – A

1 point

Suppose a client uses NTRU cryptosystem to communicate with his/her bank. Let the ciphertext e generated by client to send message m to Bank be, e = m + prh (mod q), where p,r,q and h are as discussed in lectures. Which of the following parameters is kept secret by client so that no adversary can recover m from e?

 p

 q

 h

 r

Ans  –  B

1 point

Which of the following is true for all a∈(Z/<n>)∗a∈(Z/<n>)∗?

an≡a(modn)an≡a(modn) if n is prime.

an≡a(modn)an≡a(modn) only if n is prime.

an≡a(modn)an≡a(modn) if and only if n is prime.

All of these.

Ans  –  D

1 point

Recall the Legendre symbol (ap)(ap) where pp is prime and a∈Za∈Z. Which of the following is true?

1. (ap)=ap−12modp(ap)=ap−12modp.

2. aa is a quadratic residue in F∗pFp∗ iff (ap)=1(ap)=1.

 Only 1.

 Only 2.

 Both 1 and 2.

 Neither 1 nor 2.

Ans  –  C

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1 point

Which of the following is true about Carmichael numbers?

 There are finitely many Carmichael numbers.

 There are infinite Carmichael numbers.

 Fermat test passes many but not all Carmichael numbers.

 561 is not a Carmichael number.

Ans  –  D

1 point

Which of the following is true?

 Efficient integer factoring implies efficient primality testing.

 Efficient primality testing implies efficient integer factoring.

 Efficient integer factoring does not imply efficient primality testing.

 None of the above.

Ans  –  B

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