Torus-Based Cryptography
Karl Rubin,Alice Silverberg +1 more
- 17 Aug 2003
- pp 349-365
TL;DR: The concept of torus-based cryptography is introduced, a new public key system called CEILIDH is given, and other discrete log based systems including Lucas-based systems and XTR are compared.
read more
Abstract: We introduce the concept of torus-based cryptography, give a new public key system called CEILIDH, and compare it to other discrete log based systems including Lucas-based systems and XTR. Like those systems, we obtain small key sizes. While Lucas-based systems and XTR are essentially restricted to exponentiation, we are able to perform multiplication as well. We also disprove the open conjectures from [2], and give a new algebro-geometric interpretation of the approach in that paper and of LUC and XTR.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
VSH, an efficient and provable collision-resistant hash function
Scott Contini,Arjen K. Lenstra,Ron Steinfeld +2 more
- 28 May 2006
TL;DR: VSH, very smooth hash, a new S-bit hash function that is provably collision-resistant assuming the hardness of finding nontrivial modular square roots of very smooth numbers modulo an S- bit composite, is introduced.
Chameleon Hashing Without Key Exposure
Xiaofeng Chen,Fangguo Zhang,Kwangjo Kim +2 more
- 27 Sep 2004
TL;DR: Chameleon signatures as mentioned in this paper are based on hash-and-sign paradigm, where a chameleon hash function is used to compute the cryptographic message digest and simultaneously provide the properties of non-repudiation and non-transferability for the signed message, i.e., the designated recipient is capable of verifying the validity of the signature, but cannot disclose the contents of the signed information to convince any third party without the signer's consent.
On Small Characteristic Algebraic Tori in Pairing-Based Cryptography
TL;DR: In this article, the Tate pairing on an elliptic curve over a finite field may be viewed as an element of an algebraic torus and transfer techniques recently developed for torus-based cryptography to pairing-based cryptosystems, resulting in more efficient computations and lower bandwidth requirements.
Squaring in cyclotomic subgroups
TL;DR: New squaring formulae for cyclotomic subgroups of the multiplicative group of certain finite fields using a compressed representation of elements having the property that decompression can be performed at a very low cost are proposed.
Practical cryptography in high dimensional tori
Marten van Dijk,Robert Granger,Daniel Page,Karl Rubin,Alice Silverberg,Martijn Stam,David P. Woodruff +6 more
- 22 May 2005
TL;DR: A new method is given that compresses orders of magnitude faster than the original, while also speeding up the decompression and improving on the compression factor (by a constant term).
52
References
•Book
Handbook of Applied Cryptography
Alfred Menezes,Scott A. Vanstone,Paul C. van Oorschot +2 more
- 01 Jan 1996
TL;DR: A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols.
15K
•Book
Adeles and algebraic groups
André Weil
- 01 Jan 1982
TL;DR: Ono and Ono as mentioned in this paper gave a short survey of subsequent research on Adele-Geometry and the Tamagawa numbers, including the case of the local measure and the convergence factor.
557
•Book
Algebraic Groups and Their Birational Invariants
V. Voskresenskiĭ
- 28 Jul 1998
TL;DR: In this paper, the main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, algebraic groups, Tamagawa numbers, $R$-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas.
336
The XTR Public Key System
Arjen K. Lenstra,Eric R. Verheul +1 more
- 20 Aug 2000
TL;DR: The XTR public key system as discussed by the authors is based on a new method to represent elements of a subgroup of a multiplicative group of a finite field, which leads to substantial savings both in communication and computational overhead without compromising security.
•Journal Article
The XTR public key system
Arjen K. Lenstra,Eric R. Verheul +1 more
TL;DR: This paper introduces the XTR public key system, a new method to represent elements of a subgroup of a multiplicative group of a finite field that leads to substantial savings both in communication and computational overhead without compromising security.
246
Related Papers (5)
Arjen K. Lenstra,Eric R. Verheul +1 more
Alfred Menezes,Scott A. Vanstone,Paul C. van Oorschot +2 more
- 01 Jan 1996