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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...
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...
Miller Inversion is Easy for the Reduced Tate Pairing on Trace Zero Supersingular Curves
elliptic curve cryptosystem pairing inversion Tate pairing
2019/4/16
We present a simple algorithm for Miller inversion for the reduced Tate pairing on supersingular elliptic curve of trace zero defined over the finite fields with q elements. Our algorithm runs with O(...
Motivated by the potential cryptographic application of building a directed transitive signature scheme, the search for a group with infeasible inversion was initiated in the theses of Hohenberger and...
Efficient Inversion In (Pseudo-)Mersenne Prime Order Fields
finite fields inversion multiplication
2018/11/5
Efficient scalar multiplication algorithms require a single finite field inversion at the end to convert from projective to affine coordinates. This inversion consumes a significant proportion of the ...
On inversion modulo pseudo-Mersenne primes
Elliptic Curves side-channel secure modular inversion
2018/11/2
It is well established that the method of choice for implementing a side-channel secure modular inversion, is to use Fermat's little theorem. So 1/x=xp−2modp1/x=xp−2modp. This can be calcu...
Generic Hardness of Inversion on Ring and Its Relation to Self-Bilinear Map
MCDH unbalanced modulus
2018/5/22
In this paper, we study the generic hardness of the inversion problem on a ring, which is a problem to compute the inverse of a given prime cc by just using additions, subtractions and multiplications...
A Real-time Inversion Attack on the GMR-2 Cipher Used in the Satellite Phones
Satellite Phone Stream Cipher GMR-2
2017/7/6
The GMR-2 cipher is a kind of stream cipher currently being used in Inmarsat satellite phones. It has been proven that such cipher can be cracked using only one frame known keystream but with a modera...
A Note on “Outsourcing Large Matrix Inversion Computation to a Public Cloud”
Cloud computing outsourcing computation
2016/5/9
We remark that the Lei et al.'s scheme [IEEE Transactions on Cloud Computing, 1 (1), 78-87, 2013] fails, because the verifying equation does not hold over the infinite field R. For the field R, the co...
Exponent-inversion Signatures and IBE under Static Assumptions
Dual form signature Identity-based encryption Exponent inversion
2016/1/23
Boneh-Boyen signatures are widely used in many advanced cryptosystems. It has a structure of “inversion in the exponent”, and its unforgeability against q chosen-messages attack is proven under the ...
Performance Increasing Approaches For Binary Field Inversion
binary field multiplicative inversion Extended Euclidean Algorithm
2016/1/8
Authors propose several approaches for increasing performance of multiplicative inversion algorithm in binary fields based on Extended Euclidean Algorithm (EEA). First approach is based on Extended Eu...
Finding Small Solutions of a Class of Simultaneous Modular Equations and Applications to Modular Inversion Hidden Number Problem and Inversive Congruential Generator
Modular Inversion Hidden Number Problem Inversive Congruential Generator
2016/1/6
In this paper we revisit the modular inversion hidden number
problem and the inversive congruential pseudo random number generator
and consider how to more efficiently attack them in terms of fewer
...
Optimal software-implemented Itoh--Tsujii inversion for GF($2^m$)
finite fields inversion number theory
2016/1/5
Field inversion in F2m dominates the cost of modern software implementations of certain elliptic
curve cryptographic operations, such as point encoding/hashing into elliptic curves. [7, 6, 2]
Itoh–T...
Improving Modular Inversion in RNS using the Plus-Minus Method
Hardware Implementation ECC RSA
2016/1/3
The paper describes a new RNS modular inversion algorithm
based on the extended Euclidean algorithm and the plus-minus trick. In
our algorithm, comparisons over large RNS values are replaced by chea...
Highly Efficient GF(2^8) Inversion Circuit Based on Redundant GF Arithmetic and Its Application to AES Design
GF(2^8) inversion S-Box AES
2015/12/24
This paper proposes a compact and efficient GF(2^8) inversion circuit design based on a combination of non-redundant and redundant Galois Field (GF) arithmetic. The proposed design utilizes redundant ...