The Hidden Number Problem in Extension Fields and Its Applications

2002 ◽  
pp. 105-117 ◽  
Author(s):  
María Isabel González Vasco ◽  
Mats Näslund ◽  
Igor E. Shparlinski
Keyword(s):  
Number Problem ◽  
Hidden Number Problem

Cryptanalysis of elliptic curve hidden number problem from PKC 2017

2019 ◽  
Vol 88 (2) ◽  
pp. 341-361
Author(s):  
Jun Xu ◽  
Lei Hu ◽  
Santanu Sarkar
Keyword(s):  
Elliptic Curve ◽  
Number Problem ◽  
Hidden Number Problem

scholarly journals On the modular inversion hidden number problem

2012 ◽  
Vol 47 (4) ◽  
pp. 358-367 ◽  
Author(s):  
San Ling ◽  
Igor E. Shparlinski ◽  
Ron Steinfeld ◽  
Huaxiong Wang
Keyword(s):  
Number Problem ◽  
Hidden Number Problem ◽  
Modular Inversion

scholarly journals Return of the Hidden Number Problem.

2018 ◽  
pp. 146-168 ◽  
Author(s):  
Keegan Ryan
Keyword(s):  
Side Channel ◽  
Proof Of Concept ◽  
Private Key ◽  
Side Channels ◽  
Signature Generation ◽  
Number Problem ◽  
Minimum Number ◽  
Hidden Number Problem ◽  
State Changes ◽  
Full Proof

Side channels have long been recognized as a threat to the security of cryptographic applications. Implementations can unintentionally leak secret information through many channels, such as microarchitectural state changes in processors, changes in power consumption, or electromagnetic radiation. As a result of these threats, many implementations have been hardened to defend against these attacks. Despite these mitigations, this work presents a novel side-channel attack against ECDSA and DSA. The attack targets a common implementation pattern that is found in many cryptographic libraries. In fact, about half of the libraries that were tested exhibited the vulnerable pattern. This pattern is exploited in a full proof of concept attack against OpenSSL, demonstrating that it is possible to extract a 256-bit ECDSA private key using a simple cache attack after observing only a few thousand signatures. The target of this attack is a previously unexplored part of (EC)DSA signature generation, which explains why mitigations are lacking and the issue is so widespread. Finally, estimates are provided for the minimum number of signatures needed to perform the attack, and countermeasures are suggested to protect against this attack.

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