Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Rounding in lattices and its cryptographic applications
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
The State of Elliptic Curve Cryptography
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Lattice Attacks on Digital Signature Schemes
Designs, Codes and Cryptography
Cryptography: Theory and Practice
Cryptography: Theory and Practice
Handbook of Applied Cryptography
Handbook of Applied Cryptography
"Pseudo-Random" Number Generation Within Cryptographic Algorithms: The DDS Case
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
An Elliptic Curve Implementation of the Finite Field Digital Signature Algorithm
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Lattice Reduction in Cryptology: An Update
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
On Exponential Sums and Group Generators for Elliptic Curves over Finite Fields
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Security of the most significant bits of the Shamir message passing scheme
Mathematics of Computation
The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces
Designs, Codes and Cryptography
Hidden Number Problem with the Trace and Bit Security of XTR and LUC
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
On the Security of Lenstra's Variant of DSA without Long Inversions
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Hidden number problem with hidden multipliers, timed-release crypto, and noisy exponentiation
Mathematics of Computation
The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces
Designs, Codes and Cryptography
On the hardness of approximating the permanent of structured matrices
Computational Complexity
On the power of simple branch prediction analysis
ASIACCS '07 Proceedings of the 2nd ACM symposium on Information, computer and communications security
Computers and Electrical Engineering
Yet another MicroArchitectural Attack:: exploiting I-Cache
Proceedings of the 2007 ACM workshop on Computer security architecture
Bits Security of the Elliptic Curve Diffie---Hellman Secret Keys
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Information Security Applications
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On the bits of elliptic curve Diffie-Hellman Keys
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
Solving discrete logarithms from partial knowledge of the key
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
High-speed high-security signatures
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Security analysis of an RSA key generation algorithm with a large private key
ISC'11 Proceedings of the 14th international conference on Information security
Experimenting with faults, lattices and the DSA
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Practical modifications of leadbitter et al.'s repeated-bits side-channel analysis on (EC)DSA
WISA'05 Proceedings of the 6th international conference on Information Security Applications
An updated survey on secure ECC implementations: attacks, countermeasures and cost
Cryptography and Security
Finite Fields and Their Applications
On the Uniformity of Distribution of the Elliptic Curve ElGamal Signature
Finite Fields and Their Applications
Using bleichenbacher's solution to the hidden number problem to attack nonce leaks in 384-bit ECDSA
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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Nguyen and Shparlinski have recently presented a polynomial-time algorithm that provably recovers the signer’s secret DSA key when a few consecutive bits of the random nonces k (used at each signature generation) are known for a number of DSA signatures at most linear in log q (q denoting as usual the small prime of DSA), under a reasonable assumption on the hash function used in DSA. The number of required bits is about log1/2q, but can be decreased to log log q with a running time qO(1/log log q) subexponential in log q, and even further to two in polynomial time if one assumes access to ideal lattice basis reduction, namely an oracle for the lattice closest vector problem for the infinity norm. All previously known results were only heuristic, including those of Howgrave-Graham and Smart who introduced the topic. Here, we obtain similar results for the elliptic curve variant of DSA (ECDSA).