A New Variant of the McEliece Cryptosystem Based on QC-LDPC and QC-MDPC Codes

This letter presents a new version of the McEliece cryptosystem based on quasi-cyclic (QC) low density parity check codes and QC moderate density parity check codes. A modified self-shrinking generator is used to obtain random bits, which are utilized in the cryptosystem. It is shown that this system is secure against known structural and decoding attacks.

[1]  Mohammad Reza Aref,et al.  Squaring attacks on McEliece public-key cryptosystems using quasi-cyclic codes of even dimension , 2016, Des. Codes Cryptogr..

[2]  Roberto Garello,et al.  Quasi-Cyclic Low-Density Parity-Check Codes in the McEliece Cryptosystem , 2007, 2007 IEEE International Conference on Communications.

[3]  V. Sidelnikov,et al.  A public-key cryptosystem based on binary Reed-Muller codes , 1994 .

[4]  D.J.C. MacKay,et al.  Good error-correcting codes based on very sparse matrices , 1997, Proceedings of IEEE International Symposium on Information Theory.

[5]  Ayoub Otmani,et al.  Cryptanalysis of Two McEliece Cryptosystems Based on Quasi-Cyclic Codes , 2008, Math. Comput. Sci..

[6]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[7]  Elwyn R. Berlekamp,et al.  On the inherent intractability of certain coding problems (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[8]  Mohammad Reza Aref,et al.  Cryptanalysis of McEliece cryptosystem variants based on quasi-cyclic low-density parity check codes , 2016, IET Inf. Secur..

[9]  G. A. Karpunin.  On the key space of the McEliece cryptosystem based on binary Reed–Muller codes , 2004 .

[10]  Anne Canteaut,et al.  A New Algorithm for Finding Minimum-Weight Words in a Linear Code: Application to McEliece’s Cryptosystem and to Narrow-Sense BCH Codes of Length , 1998 .

[11]  Nicolas Sendrier,et al.  Worst case QC-MDPC decoder for McEliece cryptosystem , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[12]  Enrico Thomae,et al.  Decoding Random Linear Codes in Õ(20.054n) , 2012 .

[13]  Paulo S. L. M. Barreto,et al.  Compact McEliece Keys from Goppa Codes , 2009, IACR Cryptol. ePrint Arch..

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

[15]  Ayoub Otmani,et al.  Weak Keys for the Quasi-Cyclic MDPC Public Key Encryption Scheme , 2016, AFRICACRYPT.

[16]  Eugene Prange,et al.  The use of information sets in decoding cyclic codes , 1962, IRE Trans. Inf. Theory.

[17]  Thomas A. Berson,et al.  Failure of the McEliece Public-Key Cryptosystem Under Message-Resend and Related-Message Attack , 1997, CRYPTO.

[18]  Ali Kanso.  Modified self-shrinking generator , 2010, Comput. Electr. Eng..

[19]  Tanja Lange,et al.  Attacking and defending the McEliece cryptosystem , 2008, IACR Cryptol. ePrint Arch..

[20]  Hugo Krawczyk,et al.  The Shrinking Generator , 1994, CRYPTO.

[21]  Bin Zhang,et al.  New Guess-and-Determine Attack on the Self-Shrinking Generator , 2006, ASIACRYPT.

[22]  Alexander Meurer,et al.  Decoding Random Linear Codes in $\tilde{\mathcal{O}}(2^{0.054n})$ , 2011, ASIACRYPT.

[23]  Amin Shokrollahi,et al.  Cryptanalysis of the Sidelnikov Cryptosystem , 2007, EUROCRYPT.

[24]  J. Rosenthal,et al.  Using low density parity check codes in the McEliece cryptosystem , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[25]  Willi Meier,et al.  The Self-Shrinking Generator , 1994, EUROCRYPT.

[26]  Paulo S. L. M. Barreto,et al.  MDPC-McEliece: New McEliece variants from Moderate Density Parity-Check codes , 2013, 2013 IEEE International Symposium on Information Theory.

[27]  Alexander May,et al.  On Computing Nearest Neighbors with Applications to Decoding of Binary Linear Codes , 2015, EUROCRYPT.

[28]  Thomas Johansson,et al.  A Key Recovery Attack on MDPC with CCA Security Using Decoding Errors , 2016, ASIACRYPT.

[29]  Antoine Joux,et al.  Decoding Random Binary Linear Codes in 2n/20: How 1+1=0 Improves Information Set Decoding , 2012, IACR Cryptol. ePrint Arch..