# A More Compact Representation of XTR Cryptosystem

@article{Shirase2008AMC, title={A More Compact Representation of XTR Cryptosystem}, author={Masaaki Shirase and Dong-Guk Han and Y. Hibino and Howon Kim and Tsuyoshi Takagi}, journal={IEICE Trans. Fundam. Electron. Commun. Comput. Sci.}, year={2008}, volume={91-A}, pages={2843-2850} }

XTR is one of the most efficient public-key cryptosystems that allow us to compress the communication bandwidth of their ciphertext. The compact representation can be achieved by deploying a subgroup Fq2 of extension field Fq6, so that the compression ratio of XTR cryptosystem is 1/3. On the other hand, Dijk et al. proposed an efficient public-key cryptosystem using a torus over Fq30 whose compression ratio is 4/15. It is an open problem to construct an efficient public-key cryptosystem whose…

## 17 Citations

### XTR and Tori

- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2021

The past and the present of XTR are described, including the move to 128-bit security and improvements in finite field DLP, which rendered the original XTR and closely related torus-based cryptosystems no longer competitive with elliptic curves.

### Speeding Up GH-Public Key Cryptosystem Through New Encryption Scheme

- Computer Science, Mathematics
- 2012

A novel Encryption Scheme based on the concepts of GH-PKC is proposed which requires only 8 field multiplications for both encryption and decryption of $2 \log n$ bits and also proposes Nyberg-Rueppel-Type signature scheme based on proposed encryption scheme.

### Discrete Logarithm Cryptography

- Computer Science, Mathematics
- 2010

This thesis proposes new compression techniques and exponentiation algorithms and proposes a new protocol that does not depend on any cryptographic primitive and its security is primarily based on the intractability of the DLP.

### Message transmission for GH-public key cryptosystem

- Computer Science, MathematicsJ. Comput. Appl. Math.
- 2014

### Factor-4 and 6 (De)Compression for Values of Pairings Using Trace Maps

- Mathematics, Computer SciencePairing
- 2012

A decompressible trace representation with additional information is proposed that is as efficient as the affine representation in terms of the costs of compression, decompression and exponentiation, and the size.

### On the k-th order lfsr sequence with public key cryptosystems

- Computer Science, Mathematics
- 2017

A novel encryption scheme based on the concepts of the commutative law of the k-th order linear recurrences over the finite field 𝔽q for k > 2, which is an ephemeral-static, useful in situations like email where the recipient may not be online.

### The Final Exponentiation in Pairing-Based Cryptography

- Mathematics, Computer Science
- 2012

This paper illustrates some algorithms to compute the power of an element in $\mathbb F^{*}_{q^{k}}$ with $k=2,3,4,6,10$ and proposes new formulae for $k =14$ and shows how to define short signature scheme using compressed pairings.

### Factor-4 and 6 compression of cyclotomic subgroups of and

- Mathematics, Computer ScienceJ. Math. Cryptol.
- 2010

It is shown how the pairing values over characteristic two fields can be compressed by a factor of 4, and several algorithms for performing exponentiation in the prime-order subgroups using the compressed representations are presented.

### FACTOR-4 AND 6 COMPRESSION OF

- Mathematics, Computer Science
- 2009

It is shown how the pairing values over characteristic two fields can be compressed by a factor of 4, and several algorithms for performing exponentiation in the prime-order subgroups using the compressed representations are presented and compared.

### A security model of voice eavesdropping protection over SIP-based VoIP with XTR cryptography

- Computer Science, Mathematics2015 12th International Joint Conference on Computer Science and Software Engineering (JCSSE)
- 2015

The present work is to develop an effective security model of voice eavesdropping protection over SIP-based VoIP. It is based on XTR cryptography approach, and a partial encryption scheme accompanied…

## References

SHOWING 1-10 OF 18 REFERENCES

### Compressed XTR

- Computer Science, MathematicsACNS
- 2007

The compressed XTR leads to a factor 6 reduction in the representation size compared to the traditional representation and achieves as twice compactness as XTR.

### Practical Cryptography in High Dimensional Tori

- Computer Science, MathematicsEUROCRYPT
- 2005

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).

### Asymptotically Optimal Communication for Torus-Based Cryptography

- Computer Science, MathematicsCRYPTO
- 2004

A compact and efficient representation of elements of the algebraic torus is introduced that allows for a new discrete-log based public-key system achieving the optimal communication rate, partially answering the conjecture in [4].

### Efficient signature generation by smart cards

- Computer Science, MathematicsJournal of Cryptology
- 2004

An efficient algorithm that preprocesses the exponentiation of a random residue modulo p is presented, which improves the ElGamal signature scheme in the speed of the procedures for the generation and the verification of signatures and also in the bit length of signatures.

### Efficient Algorithms for Pairing-Based Cryptosystems

- Computer Science, MathematicsCRYPTO
- 2002

New techniques to implement recent cryptosystems based on the Tate pairing improve pairing evaluation speed by a factor of about 55 compared to previously known methods in characteristic 3, and attain performance comparable to that of RSA in larger characteristics.

### A Public-Key Cryptosystem and a Digital Signature System BAsed on the Lucas Function Analogue to Discrete Logarithms

- Computer Science, MathematicsASIACRYPT
- 1994

Lucas functions can be used to replace exponentiation to produce alternative cryptosystems that are not susceptible to attacks which rely on the fact that multiplication is closed under exponentiation, since Lucas functions do not exhibit this closure.

### Speeding Up XTR

- Computer ScienceASIACRYPT
- 2001

New XTR double and single exponentiation methods where the latter requires a cheap precomputation are presented that are on average more than 60% faster than the old methods, thus more than doubling the speed of the already fast XTR signature applications.

### Torus-Based Cryptography

- Mathematics, Computer ScienceCRYPTO
- 2003

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.

### Public-key cryptosystems based on cubic finite field extensions

- Computer Science, MathematicsIEEE Trans. Inf. Theory
- 1999

The cryptographic properties of third-order linear feedback shift-register (LFSR) sequences over GF(p) are investigated. A fast computational algorithm for evaluating the kth term of a characteristic…

### Using Cyclotomic Polynomials to Construct Efficient Discrete Logarithm Cryptosystems Over Finite Fields

- Mathematics, Computer ScienceACISP
- 1997

We show how to use cyclotomic polynomials to construct subgroups of multiplicative groups of finite fields that allow very efficient implementation of discrete logarithm based public key…