Most of today’s public key cryptosystems are based on two hard mathematical problems: factoring large integers and discrete logarithm problem. With possible advent of quantum computers, these problems can become solvable. This paper describes the NTRU cryptosystem, cryptosystem that is known to not be vulnerable to quantum computer based attacks. It consists of two algorithms: NTRUEncrypt, which is used for encryption, and NTRUSign, which is used for digital signatures. NTRUEncrypt is lattice-based public key cryptosystem and is based on the shortest vector problems. Operations are based on objects in a polynomial ring with convolution multiplication and all polynomials in the ring have integer coefficients. Breaking the NTRUEncrypt cryptosystem is related with problem of lattice reduction. Some of lattice reduction algorithms used to break NTRUEncrypt are LLL algorithm and BKZ-LLL algorithm. LLL algoritham calculates an LLL reduced basis, i.e. short and nearly orthonogal basis. NTRUSign is a public key cryptography digital signature algorithm. A digital signature is a scheme for verifying the authenticity of a digital document. Transcript of NTRUSign signatures leaks information about private key. To prevent leaks is recommended to use preturbation in message before the signature itself is calculated.