Theory of linear and integer programming
Theory of linear and integer programming
A survey of fast exponentiation methods
Journal of Algorithms
Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Lattice Attacks on Digital Signature Schemes
Designs, Codes and Cryptography
Handbook of Applied Cryptography
Handbook of Applied Cryptography
ElectroMagnetic Analysis (EMA): Measures and Counter-Measures for Smart Cards
E-SMART '01 Proceedings of the International Conference on Research in Smart Cards: Smart Card Programming and Security
Weierstraß Elliptic Curves and Side-Channel Attacks
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Some baby-step giant-step algorithms for the low hamming weight discrete logarithm problem
Mathematics of Computation
The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces
Designs, Codes and Cryptography
On the Bounded Sum-of-Digits Discrete Logarithm Problem in Finite Fields
SIAM Journal on Computing
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Unified point addition formulæ and side-channel attacks
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
A new security model for authenticated key agreement
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
A secure and efficient authenticated Diffie-Hellman protocol
EuroPKI'09 Proceedings of the 6th European conference on Public key infrastructures, services and applications
Using equivalence classes to accelerate solving the discrete logarithm problem in a short interval
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
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For elliptic curve based cryptosystems, the discrete logarithm problem must be hard to solve. But even when this is true from a mathematical point of view, side-channel attacks could be used to reveal information about the key if proper countermeasures are not used. In this paper, we study the difficulty of the discrete logarithm problem when partial information about the key is revealed by side channel attacks. We provide algorithms to solve the discrete logarithm problem for generic groups with partial knowledge of the key which are considerably better than using a square-root attack on the whole key or doing an exhaustive search using the extra information, under two different scenarios. In the first scenario, we assume that a sequence of contiguous bits of the key is revealed. In the second scenario, we assume that partial information on the "Square and Multiply Chain" is revealed.