A simple power analysis attack on a McEliece cryptoprocessor

The security of McEliece public-key cryptosystem is based on the difficulty of the decoding problem which is NP-hard. In this article, we propose a simple power analysis attack on this cryptosystem. The attack exploits an information leakage, which results from the relation between the error vector weight and the iteration number of the extended Euclidean algorithm used in Patterson Algorithm. Executing the proposed attacks enables the extraction of the secret error vector, and thus the plain text with minimal overhead. A countermeasure is presented which removes the information leakage and prevents the simple power analysis attack. The attack procedure and the countermeasure are applied to a cryptoprocessor implementation of the McEliece cryptosystem running on a FPGA platform.

[1]  Christof Paar,et al.  Practical Power Analysis Attacks on Software Implementations of McEliece , 2010, PQCrypto.

[2]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[3]  Abdulhadi Shoufan,et al.  A Novel Processor Architecture for McEliece Cryptosystem and FPGA Platforms , 2009, 2009 20th IEEE International Conference on Application-specific Systems, Architectures and Processors.

[4]  Francisco Rodríguez-Henríquez,et al.  Cryptographic Algorithms on Reconfigurable Hardware (Signals and Communication Technology) , 2006 .

[5]  Shu Lin,et al.  Error control coding : fundamentals and applications , 1983 .

[6]  Arnaud Tisserand,et al.  FPGA Implementation of a Recently Published Signature Scheme , 2004 .

[7]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[8]  Y. Tsunoo,et al.  Cryptanalysis of Block Ciphers Implemented on Computers with Cache , 2002 .

[9]  Erik Tews,et al.  Side Channels in the McEliece PKC , 2008, PQCrypto.

[10]  Ralph C. Merkle,et al.  A Certified Digital Signature , 1989, CRYPTO.

[11]  Francisco Rodríguez-Henríquez,et al.  Cryptographic Algorithms on Reconfigurable Hardware , 2010 .

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

[13]  Paul C. Kocher,et al.  Differential Power Analysis , 1999, CRYPTO.

[14]  Nicholas J. Patterson,et al.  The algebraic decoding of Goppa codes , 1975, IEEE Trans. Inf. Theory.

[15]  Victor S. Miller,et al.  Use of Elliptic Curves in Cryptography , 1985, CRYPTO.

[16]  Taher ElGamal,et al.  A public key cyryptosystem and signature scheme based on discrete logarithms , 1985 .

[17]  Christof Zalka,et al.  Shor's discrete logarithm quantum algorithm for elliptic curves , 2003, Quantum Inf. Comput..

[18]  Paul C. Kocher,et al.  Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems , 1996, CRYPTO.

[19]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

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

[21]  Mohamed El-Hadedy,et al.  High Performance Implementation of a Public Key Block Cipher - MQQ, for FPGA Platforms , 2008, 2008 International Conference on Reconfigurable Computing and FPGAs.

[22]  T. Elgamal A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.

[23]  Whitfield Diffie,et al.  Analysis of a Public Key Approach Based on Polynomial Substitution , 1985, CRYPTO.

[24]  Christof Paar,et al.  A Stochastic Model for Differential Side Channel Cryptanalysis , 2005, CHES.

[25]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

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

[27]  Abdulhadi Shoufan,et al.  A Timing Attack against Patterson Algorithm in the McEliece PKC , 2009, ICISC.

[28]  Andrey Bogdanov,et al.  Fast multivariate signature generation in hardware: The case of rainbow , 2008, 2008 International Conference on Application-Specific Systems, Architectures and Processors.