A message recovery attack on multivariate polynomial trapdoor function
Cybersecurity guarantees the exchange of information through a public channel in a secure way. That is the data must be protected from unauthorized parties and transmitted to the intended parties with confidentiality and integrity. In this work, we mount an attack on a cryptosystem based on multivar...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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PeerJ Inc.
2023-08-01
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| Series: | PeerJ Computer Science |
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| Online Access: | https://peerj.com/articles/cs-1521.pdf |
| _version_ | 1797732215779491840 |
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| author | Rashid Ali Muhammad Mubashar Hussain Shamsa Kanwal Fahima Hajjej Saba Inam |
| author_facet | Rashid Ali Muhammad Mubashar Hussain Shamsa Kanwal Fahima Hajjej Saba Inam |
| author_sort | Rashid Ali |
| collection | DOAJ |
| description | Cybersecurity guarantees the exchange of information through a public channel in a secure way. That is the data must be protected from unauthorized parties and transmitted to the intended parties with confidentiality and integrity. In this work, we mount an attack on a cryptosystem based on multivariate polynomial trapdoor function over the field of rational numbers Q. The developers claim that the security of their proposed scheme depends on the fact that a polynomial system consisting of 2n (where n is a natural number) equations and 3n unknowns constructed by using quasigroup string transformations, has infinitely many solutions and finding exact solution is not possible. We explain that the proposed trapdoor function is vulnerable to a Gröbner basis attack. Selected polynomials in the corresponding Gröbner basis can be used to recover the plaintext against a given ciphertext without the knowledge of the secret key. |
| first_indexed | 2024-03-12T12:10:10Z |
| format | Article |
| id | doaj.art-eb797cca5be5415eb012ecf4ab033a35 |
| institution | Directory Open Access Journal |
| issn | 2376-5992 |
| language | English |
| last_indexed | 2024-03-12T12:10:10Z |
| publishDate | 2023-08-01 |
| publisher | PeerJ Inc. |
| record_format | Article |
| series | PeerJ Computer Science |
| spelling | doaj.art-eb797cca5be5415eb012ecf4ab033a352023-08-30T15:05:12ZengPeerJ Inc.PeerJ Computer Science2376-59922023-08-019e152110.7717/peerj-cs.1521A message recovery attack on multivariate polynomial trapdoor functionRashid Ali0Muhammad Mubashar Hussain1Shamsa Kanwal2Fahima Hajjej3Saba Inam4Department of Mathematics, Capital University of Science and Technology, Islamabad, PakistanDepartment of Mathematics, University of Punjab, Jhelum, PakistanDepartment of Mathematical Sciences, Fatima Jinnah Women University, Rawalpindi, Rawalpindi, PakistanDepartment of Information Systems, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, Riyadh, Saudi ArabiaDepartment of Mathematical Sciences, Fatima Jinnah Women University, Rawalpindi, Rawalpindi, PakistanCybersecurity guarantees the exchange of information through a public channel in a secure way. That is the data must be protected from unauthorized parties and transmitted to the intended parties with confidentiality and integrity. In this work, we mount an attack on a cryptosystem based on multivariate polynomial trapdoor function over the field of rational numbers Q. The developers claim that the security of their proposed scheme depends on the fact that a polynomial system consisting of 2n (where n is a natural number) equations and 3n unknowns constructed by using quasigroup string transformations, has infinitely many solutions and finding exact solution is not possible. We explain that the proposed trapdoor function is vulnerable to a Gröbner basis attack. Selected polynomials in the corresponding Gröbner basis can be used to recover the plaintext against a given ciphertext without the knowledge of the secret key.https://peerj.com/articles/cs-1521.pdfMultivariate polynomial systemGröbner basisAlgebraic cryptanalysisPublic key cryptosystem |
| spellingShingle | Rashid Ali Muhammad Mubashar Hussain Shamsa Kanwal Fahima Hajjej Saba Inam A message recovery attack on multivariate polynomial trapdoor function PeerJ Computer Science Multivariate polynomial system Gröbner basis Algebraic cryptanalysis Public key cryptosystem |
| title | A message recovery attack on multivariate polynomial trapdoor function |
| title_full | A message recovery attack on multivariate polynomial trapdoor function |
| title_fullStr | A message recovery attack on multivariate polynomial trapdoor function |
| title_full_unstemmed | A message recovery attack on multivariate polynomial trapdoor function |
| title_short | A message recovery attack on multivariate polynomial trapdoor function |
| title_sort | message recovery attack on multivariate polynomial trapdoor function |
| topic | Multivariate polynomial system Gröbner basis Algebraic cryptanalysis Public key cryptosystem |
| url | https://peerj.com/articles/cs-1521.pdf |
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