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The Function-Inversion Problem: Barriers and Opportunities
breaking block ciphers forging signatures
2019/9/19
The task of function inversion is central to cryptanalysis: breaking block ciphers, forging signatures, and cracking password hashes are all special cases of the function-inversion problem. In 1980, H...
A New Method for Geometric Interpretation of Elliptic Curve Discrete Logarithm Problem
Intersection of Curves Grobner Basis Vanishing Ideals
2019/9/19
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DL...
Quantum Algorithms for the Approximate k-List Problem and their Application to Lattice Sieving
approximate k-list problem cryptanalysis distributed computation
2019/9/16
The Shortest Vector Problem (SVP) is one of the mathematical foundations of lattice based cryptography. Lattice sieve algorithms are amongst the foremost methods of solving SVP. The asymptotically fas...
At CRYPTO 2017, Rosca et al. introduce a new variant of the Learning With Errors (LWE) problem, called the Middle-Product LWE (MP-LWE). The hardness of this new assumption is based on the hardness of ...
On the Degree-Insensitive SI-GDH problem and assumption
public-key cryptography supersingular isogeny Diffie-Hellman
2019/8/19
Fujioka, Takashima, Terada and Yoneyama, in their 2018 work on an authenticated key exchange protocol using supersingular isogenies, use new assumptions in their security proof of the scheme. In parti...
Low-Memory Attacks against Two-Round Even-Mansour using the 3-XOR Problem
Even-Mansour Cryptanalysis 3-XOR
2019/8/19
The iterated Even-Mansour construction is an elegant construction that idealizes block cipher designs such as the AES. In this work we focus on the simplest variant, the 2-round Even-Mansour construct...
On the Quantum Complexity of the Continuous Hidden Subgroup Problem
Quantum Algorithm Hidden Subgroup Period Finding
2019/6/19
The Hidden Subgroup Problem (HSP) aims at capturing all problems that are susceptible to be solvable in quantum polynomial time following the blueprints of Shor's celebrated algorithm. Successful solu...
New Results on Modular Inversion Hidden Number Problem and Inversive Congruential Generator
Modular inversion hidden number problem inversive congruential generator lattice
2019/6/3
The Modular Inversion Hidden Number Problem (MIHNP), introduced by Boneh, Halevi and Howgrave-Graham in Asiacrypt 2001, is briefly described as follows: Let MSBδ(z)MSBδ(z) refer to the δδ most signifi...
The Mersenne Low Hamming Combination Search Problem can be reduced to an ILP Problem
Post-Quantum Cryptography Cryptanalysis Public-Key Cryptography Integer Linear Programming
2019/5/13
In 2017, Aggarwal, Joux, Prakash, and Santha proposed an innovative NTRU-like public-key cryptosystem that was believed to be quantum resistant, based on Mersenne prime numbers q=2N−1q=2N−...
On the complexity of the Permuted Kernel Problem
Cryptanalysis Identification scheme complexity
2019/4/23
In this document, we investigate the complexity of an old-time combinatorial problem - namely Permuted Kernel Problem (PKP) - about which no new breakthrough were reported for a while. PKP is an NP-co...
Improved Classical Cryptanalysis of the Computational Supersingular Isogeny Problem
Post-quantum cryptography supersingular elliptic curves isogenies
2019/3/21
Two recent papers have made significant advances towards a better understanding of the concrete hardness of the computational supersingular isogeny (CSSI) problem; this problem underlies the supersing...
Algorithms for CRT-variant of Approximate Greatest Common Divisor Problem
CCK-ACD Lattice orthogonal lattice attack
2019/3/1
The approximate greatest common divisor problem (ACD) and its variants have been used to construct many cryptographic primitives. In particular, variants of the ACD problem based on Chinese remainder ...
Link Prediction is an important and well-studied problem for social networks. Given a snapshot of a graph, the link prediction problem predicts which new interactions between members are most likely t...
On the Asymptotics of Solving the LWE Problem Using Coded-BKW with Sieving
public-key cryptography LWE
2019/1/9
The Learning with Errors problem (LWE) has become a central topic in recent cryptographic research. In this paper, we present a new solving algorithm combining important ideas from previous work on im...
On the Security of the Multivariate Ring Learning with Errors Problem
cryptanalysis lattice techniques public-key cryptography
2018/11/6
The Multivariate Ring Learning with Errors (mm-RLWE) problem was introduced in 2015 by Pedrouzo-Ulloa, Troncoso-Pastoriza and Pérez-González. Instead of working over a polynomial residue ring with one...