A New Technique in Rank Metric Code-Based Encryption
We propose a rank metric codes based encryption based on the hard problem of rank syndrome decoding problem. We propose a new encryption with a public key matrix by considering the adding of a random distortion matrix over F q m of full column rank n. We show that IND-CPA security is achie...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2018-10-01
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| Series: | Cryptography |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2410-387X/2/4/32 |
| _version_ | 1828153867410341888 |
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| author | Terry Shue Chien Lau Chik How Tan |
| author_facet | Terry Shue Chien Lau Chik How Tan |
| author_sort | Terry Shue Chien Lau |
| collection | DOAJ |
| description | We propose a rank metric codes based encryption based on the hard problem of rank syndrome decoding problem. We propose a new encryption with a public key matrix by considering the adding of a random distortion matrix over F q m of full column rank n. We show that IND-CPA security is achievable for our encryption under assumption of the Decisional Rank Syndrome Decoding problem. Furthermore, we also prove some bounds for the number of matrices of a fixed rank with entries over a finite field. Our proposal allows the choice of the error terms with rank up to r 2 , where r is the error-correcting capability of a code. Our encryption based on Gabidulin codes has public key size of 13 . 68 KB, which is 82 times smaller than the public key size of McEliece Cryptosystem based on Goppa codes. For similar post-quantum security level of 2 140 bits, our encryption scheme has a smaller public key size than the key size suggested by LOI17 Encryption. |
| first_indexed | 2024-04-11T22:31:46Z |
| format | Article |
| id | doaj.art-243c00091c384aae996a2e8c764003d6 |
| institution | Directory Open Access Journal |
| issn | 2410-387X |
| language | English |
| last_indexed | 2024-04-11T22:31:46Z |
| publishDate | 2018-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Cryptography |
| spelling | doaj.art-243c00091c384aae996a2e8c764003d62022-12-22T03:59:22ZengMDPI AGCryptography2410-387X2018-10-01243210.3390/cryptography2040032cryptography2040032A New Technique in Rank Metric Code-Based EncryptionTerry Shue Chien Lau0Chik How Tan1Temasek Laboratories, National University of Singapore, T-Lab Building, 5A, Engineering Drive 1, #09-02, Singapore 117411, SingaporeTemasek Laboratories, National University of Singapore, T-Lab Building, 5A, Engineering Drive 1, #09-02, Singapore 117411, SingaporeWe propose a rank metric codes based encryption based on the hard problem of rank syndrome decoding problem. We propose a new encryption with a public key matrix by considering the adding of a random distortion matrix over F q m of full column rank n. We show that IND-CPA security is achievable for our encryption under assumption of the Decisional Rank Syndrome Decoding problem. Furthermore, we also prove some bounds for the number of matrices of a fixed rank with entries over a finite field. Our proposal allows the choice of the error terms with rank up to r 2 , where r is the error-correcting capability of a code. Our encryption based on Gabidulin codes has public key size of 13 . 68 KB, which is 82 times smaller than the public key size of McEliece Cryptosystem based on Goppa codes. For similar post-quantum security level of 2 140 bits, our encryption scheme has a smaller public key size than the key size suggested by LOI17 Encryption.http://www.mdpi.com/2410-387X/2/4/32code-based cryptographyMcEliecepublic key encryptionprovable security |
| spellingShingle | Terry Shue Chien Lau Chik How Tan A New Technique in Rank Metric Code-Based Encryption Cryptography code-based cryptography McEliece public key encryption provable security |
| title | A New Technique in Rank Metric Code-Based Encryption |
| title_full | A New Technique in Rank Metric Code-Based Encryption |
| title_fullStr | A New Technique in Rank Metric Code-Based Encryption |
| title_full_unstemmed | A New Technique in Rank Metric Code-Based Encryption |
| title_short | A New Technique in Rank Metric Code-Based Encryption |
| title_sort | new technique in rank metric code based encryption |
| topic | code-based cryptography McEliece public key encryption provable security |
| url | http://www.mdpi.com/2410-387X/2/4/32 |
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