Algebraic Cryptanalysis of CTRU Cryptosystem

Generalisations of NTRU cryptosystem

“…So, search space will be square times than that of NTRU. This variant of NTRU had got speed improvement by a factor of O ( k 1.624 ) over NTRU for the same bit of information .…”

“…In 2008, Nitin Vats saw that CTRU has importance because the attacks based on LLL algorithm and CRT are avoided on it. So he presented a polynomial time algorithm that breaks CTRU for all recommended parameters that were built to make CTRU secure against Popov normal form attack .…”

“…Later, Nitin Vats gave algebraic cryptanalysis of CTRU cryptosystem in 2008 . They showed that this cryptosystem overcomes lattice attack but is totally insecure against more easy Linear algebra attacks.…”

“…In 2009, Nitin Vats gave a paper entitled, NNRU, a non‐commutative analogue of NTRU. In this paper, they presented a scheme based on NTRU in which they did the calculations during encryption and decryption non‐commutatively, so that the system will be secured against lattice attack (presented by Shamir in 1997 ) because lattice‐based attack is the most common attack on NTRU cryptosystem.…”

“…In this case, the attacker can get the maximum bits of information. Lattice attack ‐ We can attack this cryptosystem if we can construct a lattice from public key ( h , H ) in which vector ( f w , c g ) lies. The author proved that one can not make such a lattice . So, this attack will not work for this cryptosystem. Comparison ‐ Because matrix multiplication in this scheme is strictly non‐abelian; therefore, the attacker will have to find out two ring elements.…”