Categorical composable cryptography: extended version
We formalize the simulation paradigm of cryptography in terms of category theory and show that protocols secure against abstract attacks form a symmetric monoidal category, thus giving an abstract model of composable security definitions in cryptography. Our model is able to incorporate computationa...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2023-12-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/9979/pdf |
| _version_ | 1797268532350681088 |
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| author | Anne Broadbent Martti Karvonen |
| author_facet | Anne Broadbent Martti Karvonen |
| author_sort | Anne Broadbent |
| collection | DOAJ |
| description | We formalize the simulation paradigm of cryptography in terms of category
theory and show that protocols secure against abstract attacks form a symmetric
monoidal category, thus giving an abstract model of composable security
definitions in cryptography. Our model is able to incorporate computational
security, set-up assumptions and various attack models such as colluding or
independently acting subsets of adversaries in a modular, flexible fashion. We
conclude by using string diagrams to rederive the security of the one-time pad,
correctness of Diffie-Hellman key exchange and no-go results concerning the
limits of bipartite and tripartite cryptography, ruling out e.g., composable
commitments and broadcasting. On the way, we exhibit two categorical
constructions of resource theories that might be of independent interest: one
capturing resources shared among multiple parties and one capturing resource
conversions that succeed asymptotically. |
| first_indexed | 2024-04-25T01:33:58Z |
| format | Article |
| id | doaj.art-f375eb0b0257403dad24e5bd5825554c |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:33:58Z |
| publishDate | 2023-12-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-f375eb0b0257403dad24e5bd5825554c2024-03-08T10:43:59ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742023-12-01Volume 19, Issue 410.46298/lmcs-19(4:30)20239979Categorical composable cryptography: extended versionAnne BroadbentMartti KarvonenWe formalize the simulation paradigm of cryptography in terms of category theory and show that protocols secure against abstract attacks form a symmetric monoidal category, thus giving an abstract model of composable security definitions in cryptography. Our model is able to incorporate computational security, set-up assumptions and various attack models such as colluding or independently acting subsets of adversaries in a modular, flexible fashion. We conclude by using string diagrams to rederive the security of the one-time pad, correctness of Diffie-Hellman key exchange and no-go results concerning the limits of bipartite and tripartite cryptography, ruling out e.g., composable commitments and broadcasting. On the way, we exhibit two categorical constructions of resource theories that might be of independent interest: one capturing resources shared among multiple parties and one capturing resource conversions that succeed asymptotically.https://lmcs.episciences.org/9979/pdfcomputer science - cryptography and securitymathematics - category theory |
| spellingShingle | Anne Broadbent Martti Karvonen Categorical composable cryptography: extended version Logical Methods in Computer Science computer science - cryptography and security mathematics - category theory |
| title | Categorical composable cryptography: extended version |
| title_full | Categorical composable cryptography: extended version |
| title_fullStr | Categorical composable cryptography: extended version |
| title_full_unstemmed | Categorical composable cryptography: extended version |
| title_short | Categorical composable cryptography: extended version |
| title_sort | categorical composable cryptography extended version |
| topic | computer science - cryptography and security mathematics - category theory |
| url | https://lmcs.episciences.org/9979/pdf |
| work_keys_str_mv | AT annebroadbent categoricalcomposablecryptographyextendedversion AT marttikarvonen categoricalcomposablecryptographyextendedversion |