New number-theoretic cryptographic primitives
This paper introduces new prq-based one-way functions and companion signature schemes. The new signature schemes are interesting because they do not belong to the two common design blueprints, which are the inversion of a trapdoor permutation and the Fiat–Shamir transform. In the basic signature sch...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2020-08-01
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| Series: | Journal of Mathematical Cryptology |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/jmc-2019-0035 |
| _version_ | 1798026334046257152 |
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| author | Brier Éric Ferradi Houda Joye Marc Naccache David |
| author_facet | Brier Éric Ferradi Houda Joye Marc Naccache David |
| author_sort | Brier Éric |
| collection | DOAJ |
| description | This paper introduces new prq-based one-way functions and companion signature schemes. The new signature schemes are interesting because they do not belong to the two common design blueprints, which are the inversion of a trapdoor permutation and the Fiat–Shamir transform. In the basic signature scheme, the signer generates multiple RSA-like moduli ni = pi2qi and keeps their factors secret. The signature is a bounded-size prime whose Jacobi symbols with respect to the ni’s match the message digest. The generalized signature schemes replace the Jacobi symbol with higher-power residue symbols. Given of their very unique design, the proposed signature schemes seem to be overlooked “missing species” in the corpus of known signature algorithms. |
| first_indexed | 2024-04-11T18:34:49Z |
| format | Article |
| id | doaj.art-ecbb31c89b9e4fcaa5b0ff5bc936ff81 |
| institution | Directory Open Access Journal |
| issn | 1862-2976 1862-2984 |
| language | English |
| last_indexed | 2024-04-11T18:34:49Z |
| publishDate | 2020-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Mathematical Cryptology |
| spelling | doaj.art-ecbb31c89b9e4fcaa5b0ff5bc936ff812022-12-22T04:09:20ZengDe GruyterJournal of Mathematical Cryptology1862-29761862-29842020-08-0114122423510.1515/jmc-2019-0035jmc-2019-0035New number-theoretic cryptographic primitivesBrier Éric0Ferradi Houda1Joye Marc2Naccache David3Ingenico, Valence, FranceNTT Secure Platform Laboratories, Tokyo, JapanOneSpan, Brussels, BelgiumÉcole normale supérieure, Paris, FranceThis paper introduces new prq-based one-way functions and companion signature schemes. The new signature schemes are interesting because they do not belong to the two common design blueprints, which are the inversion of a trapdoor permutation and the Fiat–Shamir transform. In the basic signature scheme, the signer generates multiple RSA-like moduli ni = pi2qi and keeps their factors secret. The signature is a bounded-size prime whose Jacobi symbols with respect to the ni’s match the message digest. The generalized signature schemes replace the Jacobi symbol with higher-power residue symbols. Given of their very unique design, the proposed signature schemes seem to be overlooked “missing species” in the corpus of known signature algorithms.https://doi.org/10.1515/jmc-2019-0035r-th power residue symbolr-th order imprintprq modulinumber theoryone-way functionsdigital signaturescryptographic primitives94a6011t7111a1511r18 |
| spellingShingle | Brier Éric Ferradi Houda Joye Marc Naccache David New number-theoretic cryptographic primitives Journal of Mathematical Cryptology r-th power residue symbol r-th order imprint prq moduli number theory one-way functions digital signatures cryptographic primitives 94a60 11t71 11a15 11r18 |
| title | New number-theoretic cryptographic primitives |
| title_full | New number-theoretic cryptographic primitives |
| title_fullStr | New number-theoretic cryptographic primitives |
| title_full_unstemmed | New number-theoretic cryptographic primitives |
| title_short | New number-theoretic cryptographic primitives |
| title_sort | new number theoretic cryptographic primitives |
| topic | r-th power residue symbol r-th order imprint prq moduli number theory one-way functions digital signatures cryptographic primitives 94a60 11t71 11a15 11r18 |
| url | https://doi.org/10.1515/jmc-2019-0035 |
| work_keys_str_mv | AT briereric newnumbertheoreticcryptographicprimitives AT ferradihouda newnumbertheoreticcryptographicprimitives AT joyemarc newnumbertheoreticcryptographicprimitives AT naccachedavid newnumbertheoreticcryptographicprimitives |