Illustrate NTRU using lattices
Currently, there is no formal proof of NTRU being based on a lattice problem, but you can find a description of NTRU in terms of lattices in Section 5.2 of [Ber09]. For lattice-based attacks for NTRU you can review [HPS98]. There is, however, a provably-secure variant of NTRU that is ultimately based on the hardness of the SVP problem [SS11].

References:

[Ber09] Post-quantum cryptography (2009). Springer Berlin Heidelberg.   

[HPS98] Hoffstein, J., Pipher, J., &amp; Silverman, J. H. (1998). NTRU: A ring-based public key cryptosystem. In Algorithmic number theory (pp. 267-288)

[SS11] Stehlé, D., &amp; Steinfeld, R. (2011). Making NTRU as secure as worst-case problems over ideal lattices. In Advances in Cryptology–EUROCRYPT 2011 (pp. 27-47).