How to prove yourself: practical solutions to identification and signature problems
Proceedings on Advances in cryptology---CRYPTO '86
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
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Discrete Logarithms: The Past and the Future
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Some baby-step giant-step algorithms for the low hamming weight discrete logarithm problem
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Practical threshold signatures
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An improved fast signature scheme without online multiplication
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Analysis of Low Hamming Weight Products
Discrete Applied Mathematics
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CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
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IEEE Transactions on Information Theory
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ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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CT-RSA'07 Proceedings of the 7th Cryptographers' track at the RSA conference on Topics in Cryptology
Public key cryptography and RFID tags
CT-RSA'07 Proceedings of the 7th Cryptographers' track at the RSA conference on Topics in Cryptology
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We describe a new variant of the well known Baby-Step Giant-Step algorithm in the case of some discrete logarithms with a special structure. More precisely, we focus on discrete logarithms equal to products in groups of unknown order. As an example of application, we show that this new algorithm enables to cryptanalyse a variant of the GPS scheme proposed by Girault and Lefranc at CHES 2004 conference in which the private key is equal to the product of two sub-private keys of low Hamming weight. We also describe a second attack based on a known variant of the Baby-Step Giant-Step algorithm using the low Hamming weight of the sub-private keys.