Proof of Stake (PoS) blockchain systems require weighted threshold signatures where participants' voting powers reflect their stakes. As stakes change dynamically through deposits and withdrawals, efficient weight and threshold adjustments are essential for maintaining system security and availability without downtime. However, existing approaches face critical limitations: (1) virtualization-based schemes require$O(w)$operations (signatures) per participant with weight$w$; (2) dynamic threshold / paricipants schemes do not support weighted participants; (3) schemes with both properties require trusted dealers or$O(n^{2})$re-setup, causing temporary unavailability. This paper introduces Active Weighted Signature (AWS), enabling dynamic adjustments without trusted dealers or re-setup. We propose Generalized Lagrange Interpolation (GLI), encoding weights as polynomial derivatives rather than virtualized participants, and instantiate AWS through$ {\sf ADAPT}$by applying GLI to the Schnorr-based threshold signature${\sf FROST}$. Our implementation shows that$ {\sf ADAPT}$achieves comparable efficiency to${\sf FROST}$for key generation, while weight and threshold adjustments complete in 4.1-22.3% of re-setup time. For uneven weight distributions,$ {\sf ADAPT}$achieves sub-linear scaling: 49× weight difference requires only 3.29× computation versus 49× in virtualization.

Fully Homomorphic Encryption over the Torus (TFHE) is a homomorphic encryption scheme which supports efficient Boolean operations over encrypted bits. TFHE has a unique feature in that the evaluation of each binary gate is followed by a bootstrapping procedure to refresh the noise of a ciphertext. In particular, this gate bootstrapping involves two algorithms called the blind rotation and key-switching.

Abstract The authors present a classical polynomial‐time attack against the branching program obfuscator of Fernando–Rasmussen–Sahai (for short FRS, Asiacrypt’17) (with one zerotest parameter), which is robust against all known classical cryptanalyses on obfuscators when instantiated with the CLT13 multilinear map. The first step is to recover a plaintext modulus of the CLT13 multilinear map. To achieve the goal, the Coron and Notarnicola (Asiacrypt’19) algorithm is applied. However, because of parameter issues, the algorithm cannot be used directly. In order to detour the issue, the authors convert an FRS obfuscator into a new programme containing a small message space. Through the conversion, the authors obtain two zerotest parameters and encodings of zero except for two non‐zero slots. Then, they are used to mitigate parameter constraints of the message space recovering algorithm. Then, a cryptanalysis of the FRS obfuscation based on the recovered message space is proposed. The authors show that there exist two functionally equivalent programmes such that their obfuscated programmes are computationally distinguishable. Thus, the FRS scheme does not satisfy the desired security without any additional constraints.

Abstract A simultaneous Diophantine approximation (SDA) algorithm takes instances of the partial approximate common divisor (PACD) problem as input and outputs a solution. While several encryption schemes have been published and their securities depend on the presumed hardness of variant of the PACD problem, fewer studies have attempted to extend the SDA algorithm to be applicable to these variants. In this study, the SDA algorithm is extended to solve the general PACD problem. In order to proceed, first the variants of the PACD problem are classified and how to extend the SDA algorithm for each is suggested. Technically, the authors show that a short vector of some lattice used in the SDA algorithm gives an algebraic relation between secret parameters. Then, all the secret parameters can be recovered by finding this short vector. It is also confirmed experimentally that this algorithm works well.

In this paper, we describe a polynomial time cryptanalysis of the (approximate) multilinear map proposed by Coron, Lepoint, and Tibouchi in Crypto13 (CLT13). This scheme includes a zero-testing functionality that determines whether the message of a given encoding is zero or not. This functionality is useful for designing several of its applications, but it leaks unexpected values, such as linear combinations of the secret elements. By collecting the outputs of the zero-testing algorithm, we construct a matrix containing the hidden information as eigenvalues, and then recover all the secret elements of the CLT13 scheme via diagonalization of the matrix. In addition, we provide polynomial time algorithms to directly break the security assumptions of many applications based on the CLT13 scheme. These algorithms include solving subgroup membership, decision linear, and graded external Diffie–Hellman problems. These algorithms mainly rely on the computation of the determinants of the matrices and their greatest common divisor, instead of performing their diagonalization.