Algebraic attack on NTRU using Witt vectors and Gröbner bases

An Algebraic Approach to NTRU (q = 2) via Witt Vectors and Overdetermined Systems of Nonlinear Equations

We use the theory of Witt vectors to develop an algebraic approach for studying the NTRU primitive with q parameter equal to a power of two. This results in a system of nonlinear algebraic equations over F2 having many symmetries, which is reminiscent of the approach of Courtois, Murphy, Pieprzyk, Robshaw and others for studying the structure of block ciphers such as the AES. We study whether t...

An Algebraic Approach to NTRU (q = 2n) via Witt Vectors and Overdetermined Systems of Nonlinear Equations

Non-Commutative Gröbner Bases in Poincaré-Birkhoff-Witt Extensions

Commutative Gröbner Bases are a well established technique with many applications, including polynomial solving and constructive approaches to commutative algebra and algebraic geometry. Noncommutative Gröbner Bases are a focus of much recent research activity. For example, combining invariant theory and elimination theory, or elimination in moving frames of partial differential operators invar...

TECHNISCHE UNIVERSITEIT EINDHOVEN Department of Mathematics and Computing Science MASTER ’ S

Recently, a special kind of cryptanalysis coined as the algebraic attack has gained a lot of attention. In this thesis, we clarify this attack and discuss the threat to common ciphers. Among the known attacks, one can roughly distinguish between two classes. The first consists of structural attacks that focus on specific properties of a certain cipher. The second includes inversion attacks, whi...

QTRU: A Lattice Attack Resistant Version of NTRU

We propose QTRU, a probabilistic and multi-dimensional public key cryptosystem based on the NTRU public key cryptosystem using quaternion algebra. QTRU encrypts four data vectors in each encryption session and the only other major difference between NTRU and QTRU is that the underlying algebraic structure has been changed to a non-commutative algebraic structure. As a result, QTRU inherits the ...