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The hidden number problem with the trace and bit security of XTR and LUC
 XTR AND LUC’, LECT. NOTES IN COMP. SCI
, 2002
"... We consider a certain generalization of the hidden number problem introduced by Boneh and Venkatesan in 1996. Considering the XTR variation of DiffieHellman, we apply our results to show security of the log 1/2 p most significant bits of the secret, in analogy to the results known for the classical ..."
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Cited by 12 (8 self)
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We consider a certain generalization of the hidden number problem introduced by Boneh and Venkatesan in 1996. Considering the XTR variation of DiffieHellman, we apply our results to show security of the log 1/2 p most significant bits of the secret, in analogy to the results known
Speeding up XTR
 In Boyd [29
"... Abstract. This paper describes several speedups and simpli¯cations for XTR. The most important results are new XTR double and single exponentiation methods where the latter requires a cheap precomputation. Both methods are on average more than 60 % faster than the old methods, thus more than doubli ..."
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Cited by 27 (3 self)
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Abstract. This paper describes several speedups and simpli¯cations for XTR. The most important results are new XTR double and single exponentiation methods where the latter requires a cheap precomputation. Both methods are on average more than 60 % faster than the old methods, thus more than
Looking beyond XTR
 IN ADVANCES IN CRYPTOLOGY — ASIACRYPT 2002, LECT. NOTES IN COMP. SCI. 2501
, 2002
"... XTR is a general methodthat can be appliedto discrete logarithm based cryptosystems in extension fields of degree six, providing a compact representation of the elements involved. In this paper we present a precise formulation of the BrouwerPellikaanVerheul conjecture, originally posedin [4], con ..."
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Cited by 14 (0 self)
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XTR is a general methodthat can be appliedto discrete logarithm based cryptosystems in extension fields of degree six, providing a compact representation of the elements involved. In this paper we present a precise formulation of the BrouwerPellikaanVerheul conjecture, originally posedin [4
A Comparison of CEILIDH and XTR
 IN ALGORITHMIC NUMBER THEORY SYMPOSIUM (ANTS), SPRINGERVERLAG LNCS 3076
, 2004
"... We give a comparison of the performance of the recently proposed torusbased public key cryptosystem CEILIDH, and XTR. Underpinning both systems is the mathematics of the two dimensional algebraic torus T6(Fp). However, while they both attain the same discrete logarithm security and each achieve ..."
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Cited by 9 (6 self)
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We give a comparison of the performance of the recently proposed torusbased public key cryptosystem CEILIDH, and XTR. Underpinning both systems is the mathematics of the two dimensional algebraic torus T6(Fp). However, while they both attain the same discrete logarithm security and each
Evidence that XTR is more secure than supersingular elliptic curve cryptosystems
 J. Cryptology
, 2001
"... Abstract. We show that finding an efficiently computable injective homomorphism from the XTR subgroup into the group of points over GF(p 2) of a particular type of supersingular elliptic curve is at least as hard as solving the DiffieHellman problem in the XTR subgroup. This provides strong evidenc ..."
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Cited by 95 (5 self)
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Abstract. We show that finding an efficiently computable injective homomorphism from the XTR subgroup into the group of points over GF(p 2) of a particular type of supersingular elliptic curve is at least as hard as solving the DiffieHellman problem in the XTR subgroup. This provides strong
An Overview of the XTR Public Key System
 IN PUBLICKEY CRYPTOGRAPHY AND COMPUTATIONAL NUMBER THEORY, VERLAGES WALTER DE GRUYTER
, 2000
"... XTR is a new method to represent elements of a subgroup of a multiplicative group of a finite field. Application of XTR in cryptographic protocols leads to substantial savings both in communication and computational overhead without compromising security. This paper describes and explains the techn ..."
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Cited by 10 (1 self)
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XTR is a new method to represent elements of a subgroup of a multiplicative group of a finite field. Application of XTR in cryptographic protocols leads to substantial savings both in communication and computational overhead without compromising security. This paper describes and explains
Faster and smaller hardware implementation of XTR
 In Proceedings of SPIE, Symposium on Optics & photonics, Advanced Signal Processing Algorithms, Architectures, and Implementations
, 2006
"... Modular multiplication is the core of most Public Key Cryptosystems and therefore its implementation plays a crucial role in the overall efficiency of asymmetric cryptosystems. Hardware approaches provide advantages over software in the framework of efficient dedicated accelerators. The concerns of ..."
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Cited by 1 (0 self)
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of the hereafter techniques stand as stateoftheart, the combination described here is unique and particularly efficient in the context of constrained hardware design of XTR cryptosystem. Our solution is implemented on an FPGA platform and compared with previous results. The areatime ratio is improved by around
Unbelievable Security: Matching AES security using public key systems
 PROCEEDINGS ASIACRYPT 2001, LNCS 2248, SPRINGERVERLAG 2001, 67–86
, 2001
"... The Advanced Encryption Standard (AES) provides three levels of security: 128, 192, and 256 bits. Given a desired level of security for the AES, this paper discusses matching public key sizes for RSA and the ElGamal family of protocols. For the latter both traditional multiplicative groups of finit ..."
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Cited by 52 (4 self)
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The Advanced Encryption Standard (AES) provides three levels of security: 128, 192, and 256 bits. Given a desired level of security for the AES, this paper discusses matching public key sizes for RSA and the ElGamal family of protocols. For the latter both traditional multiplicative groups
New LFSRBased Cryptosystems and the Trace Discrete Log Problem (TraceDLP)
 IN: SEQUENCE AND THEIR APPLICATIONS – SETA 2004. LECTURE
, 2004
"... In order to reduce key sizes and bandwidth, cryptographic systems have been proposed using minimal polynomials to represent finite field elements. These systems are essentially equivalent to systems based on characteristic sequences generated by a linear feedback shift register (LFSR). We propose a ..."
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Cited by 6 (1 self)
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problem, the Trace Discrete Logarithm Problem (TraceDLP). The TraceDLP and its variants are discussed and their relationship with wellknown finite fieldbased computational problems is examined. In addition, we prove the equivalence between several LFSRbased computational problems and their finite
Using Primitive Subgroups to Do More with Fewer Bits
, 2004
"... This paper gives a survey of some ways to improve the ef ciency of discrete logbased cryptography by using the restriction of scalars and the geometry and arithmetic of algebraic tori and abelian varieties. ..."
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Cited by 16 (3 self)
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This paper gives a survey of some ways to improve the ef ciency of discrete logbased cryptography by using the restriction of scalars and the geometry and arithmetic of algebraic tori and abelian varieties.
Results 1  10
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130