We propose the new rank-metric code-based cryptosystem LIGA which is based on the hardness of list decoding and interleaved decoding of Gabidulin codes. LIGA is an improved variant of the Faure–Loidreau (FL) system, which was broken in a structural attack by Gaborit, Otmani, and Talé Kalachi (GOT, 2018). We keep the FL encryption and decryption algorithms, but modify the insecure key generation algorithm. Our crucial observation is that the GOT attack is equivalent to decoding an interleaved Gabidulin code. The new key generation algorithm constructs public keys for which all polynomial-time interleaved decoders fail—hence LIGA resists the GOT attack. We also prove that the public-key encryption version of LIGA is IND-CPA secure in the standard model and the key encapsulation mechanisms version is IND-CCA2 secure in the random oracle model, both under hardness assumptions of formally defined problems related to list decoding and interleaved decoding of Gabidulin codes. We propose and analyze various exponential-time attacks on these problems, calculate their work factors, and compare the resulting parameters to NIST proposals. The strengths of LIGA are short ciphertext sizes and (relatively) small key sizes. Further, LIGA guarantees correct decryption and has no decryption failure rate. It is not based on hiding the structure of a code. Since there are efficient and constant-time algorithms for encoding and decoding Gabidulin codes, timing attacks on the encryption and decryption algorithms can be easily prevented.
Bibliographical noteFunding Information:
The work of J. Renner and A. Wachter-Zeh was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 801434). S. Puchinger received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 713683. We would like to thank Johan Rosenkilde for proposing the “moving to a close error” attack. Also, we are thankful to Michael Schelling for his observation that decryption of the FL system can be seen as error-erasure decoding. Further, we thank Pierre Loidreau for his valuable comments on a previous version of this paper. We are also grateful to Alessandro Neri for fruitful discussions that helped to achieve the results in Appendix .
© 2021, The Author(s).
- Code-based cryptography
- Gabidulin codes
- Interleaved decoding
- List decoding
- Rank-metric codes