MaTRU: A New NTRU-Based Cryptosystem

In this paper, we propose a new variant of the NTRU public key cryptosystem – the MaTRU cryptosystem. MaTRU works under the same general principles as the NTRU cryptosystem, except that it operates in a different ring with a different linear transformation for encryption and decryption. In particular, it operates in the ring of k by k matrices of polynomials in R=ℤ[X]/(Xn−1), whereas NTRU operates in the ring ℤ[X]/(Xn−1). Note that an instance of MaTRU has the same number of bits per message as an instance of NTRU when nk2 = N. The improved efficiency of the linear transformation in MaTRU leads to respectable speed improvements by a factor of O(k) over NTRU at the cost of a somewhat larger public key.

[1]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[2]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[3]  Joseph H. Silverman,et al.  Dimension Reduction Methods for Convolution Modular Lattices , 2001, CaLC.

[4]  Phong Q. Nguyen.  The Two Faces of Lattices in Cryptology , 2001, Selected Areas in Cryptography.

[5]  Joseph H. Silverman,et al.  NTRU: A Ring-Based Public Key Cryptosystem , 1998, ANTS.

[6]  William Whyte,et al.  NTRUSIGN: Digital Signatures Using the NTRU Lattice , 2003, CT-RSA.

[7]  Robert H. Deng,et al.  Public Key Cryptography – PKC 2004 , 2004, Lecture Notes in Computer Science.

[8]  Alfred Menezes,et al.  Progress in Cryptology — INDOCRYPT 2002 , 2002, Lecture Notes in Computer Science.

[9]  Robert J. McEliece,et al.  A public key cryptosystem based on algebraic coding theory , 1978 .

[10]  N. Koblitz.  Elliptic curve cryptosystems , 1987 .

[11]  Moti Yung,et al.  Advances in Cryptology — CRYPTO 2002 , 2002, Lecture Notes in Computer Science.

[12]  David Pointcheval,et al.  The Impact of Decryption Failures on the Security of NTRU Encryption , 2003, CRYPTO.

[13]  Joseph H. Silverman,et al.  Random small Hamming weight products with applications to cryptography , 2003, Discret. Appl. Math..

[14]  Marc Joye,et al.  Topics in Cryptology — CT-RSA 2003 , 2003 .

[15]  Antoine Joux,et al.  A Chosen-Ciphertext Attack against NTRU , 2000, CRYPTO.

[16]  Mihir Bellare.  Advances in Cryptology — CRYPTO 2000 , 2000, Lecture Notes in Computer Science.

[17]  Jeffrey Shallit,et al.  Algorithmic Number Theory , 1996, Lecture Notes in Computer Science.

[18]  Joseph H. Silverman,et al.  Cryptography and Lattices , 2001, Lecture Notes in Computer Science.

[19]  Joseph H. Silverman,et al.  Optimizations for NTRU , 2001 .

[20]  Adi Shamir,et al.  Lattice Attacks on NTRU , 1997, EUROCRYPT.

[21]  Igor E. Shparlinski,et al.  A Variant of NTRU with Non-invertible Polynomials , 2002, INDOCRYPT.

[22]  Craig Gentry.  Key Recovery and Message Attacks on NTRU-Composite , 2001, EUROCRYPT.

[23]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[24]  Jintai Ding,et al.  A New Variant of the Matsumoto-Imai Cryptosystem through Perturbation , 2004, Public Key Cryptography.

[25]  Daesung Kwon,et al.  Key Recovery Attacks on NTRU without Ciphertext Validation Routine , 2003, ACISP.

[26]  David Pointcheval,et al.  Analysis and Improvements of NTRU Encryption Paddings , 2002, CRYPTO.

[27]  Hideki Imai,et al.  Public Quadratic Polynominal-Tuples for Efficient Signature-Verification and Message-Encryption , 1988, EUROCRYPT.

[28]  Information Security and Privacy , 1996, Lecture Notes in Computer Science.

[29]  Dan Boneh,et al.  Advances in Cryptology - CRYPTO 2003 , 2003, Lecture Notes in Computer Science.