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Subject: [digest] 2025 Week 27
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## In this issue

1. [2023/1524] SoK: Signatures With Randomizable Keys
2. [2025/372] KLPT=C2=B2: Algebraic Pathfinding in Dimension Two and ...
3. [2025/1194] Private coins extension with verifiable encryption
4. [2025/1195] On symbolic computations and Post Quantum ...
5. [2025/1196] Limits on the Power of Private Constrained PRFs
6. [2025/1197] How to Copy-Protect All Puncturable Functionalities ...
7. [2025/1198] Brief Comments on Rijndael-256 and the Standard ...
8. [2025/1199] HypSCA: A Hyperbolic Embedding Method for Enhanced ...
9. [2025/1200] Tricycle: Private Transformer Inference with ...
10. [2025/1201] BitBatSPIR: Efficient Batch Symmetric Private ...
11. [2025/1202] t-Probing (In-)Security - Pitfalls on Noise Assumptions
12. [2025/1203] Breaking The Authenticated Encryption scheme HiAE
13. [2025/1204] A search to distinguish reduction for the ...
14. [2025/1205] Generic Construction of Threshold Ring Signatures ...
15. [2025/1206] New Upper and Lower Bounds for Perfectly Secure MPC
16. [2025/1207] Copy-Protection from UPO, Revisited
17. [2025/1208] End-to-End Encrypted Git Services
18. [2025/1209] RingSG: Optimal Secure Vertex-Centric Computation ...
19. [2025/1210] A Generalized Approach to Root-based Attacks ...
20. [2025/1211] May the Force $\textit{not}$ Be with you: Brute- ...
21. [2025/1212] All Proof of Work But No Proof of Play
22. [2025/1213] Tightly Secure Public-Key Encryption with Equality ...
23. [2025/1214] Hobbit: Space-Efficient zkSNARK with Optimal Prover ...
24. [2025/1215] Highly Scalable Searchable Symmetric Encryption for ...
25. [2025/1216] Ring-LWR based Commitments and ZK-PoKs with ...

## 2023/1524

* Title: SoK: Signatures With Randomizable Keys
* Authors: Sof=C3=ADa Celi, Scott Griffy, Lucjan Hanzlik, Octavio Perez Kempn=
er, Daniel Slamanig
* [Permalink](https://eprint.iacr.org/2023/1524)
* [Download](https://eprint.iacr.org/2023/1524.pdf)

### Abstract

Digital signature schemes with specific properties have recently seen various=
 real-world applications with a strong emphasis on privacy-enhancing technolo=
gies. They have been extensively used to develop anonymous credentials scheme=
s and to achieve an even more comprehensive range of functionalities in the d=
ecentralized web.

Substantial work has been done to formalize different types of signatures whe=
re an allowable set of transformations can be applied to message-signature pa=
irs to obtain new related pairs. Most of the previous work focused on transfo=
rmations with respect to the message being signed, but little has been done t=
o study what happens when transformations apply to the signing keys. A first =
attempt to thoroughly formalize such aspects was carried by Derler and Slaman=
ig (ePrint'16, Designs, Codes and Cryptography'19), followed by the more rece=
nt efforts by Backes et al. (ASIACRYPT'18) and Eaton et al. (ePrint'23). Howe=
ver, the literature on the topic is vast and different terminology is used ac=
ross contributions, which makes it difficult to compare related works and und=
erstand the range of applications covered by a given construction.

In this work, we present a unified view of signatures with randomizable keys =
and revisit their security properties. We focus on state-of-the-art construct=
ions and related applications,identifying existing challenges. Our systematiz=
ation allows us to highlight gaps, open questions and directions for future r=
esearch on signatures with randomizable keys.



## 2025/372

* Title: KLPT=C2=B2: Algebraic Pathfinding in Dimension Two and Applications
* Authors: Wouter Castryck, Thomas Decru, P=C3=A9ter Kutas, Abel Laval, Chris=
tophe Petit, Yan Bo Ti
* [Permalink](https://eprint.iacr.org/2025/372)
* [Download](https://eprint.iacr.org/2025/372.pdf)

### Abstract

Following Ibukiyama, Katsura and Oort, all  principally polarized superspecia=
l abelian surfaces over $\overline{\mathbb{F}}_p$ can be represented by a cer=
tain type of $2 \times 2$ matrix $g$, having entries in the quaternion algebr=
a $B_{p,\infty}$. We present a heuristic polynomial-time algorithm which, upo=
n input of two such matrices $g_1, g_2$, finds a "connecting matrix" represen=
ting a polarized isogeny of smooth degree between the corresponding surfaces.=
 Our algorithm should be thought of as a two-dimensional analog of the KLPT a=
lgorithm from 2014 due to Kohel, Lauter, Petit and Tignol for finding a conne=
cting ideal of smooth norm between two given maximal orders in $B_{p, \infty}=
$.=20
=20
The KLPT algorithm has proven to be a versatile tool in isogeny-based cryptog=
raphy, and our analog has similar applications; we discuss two of them in det=
ail. First, we show that it yields a polynomial-time solution to a two-dimens=
ional analog of the so-called constructive Deuring correspondence: given a ma=
trix $g$ representing a superspecial principally polarized abelian surface, r=
ealize the latter as the Jacobian of a genus-$2$ curve (or, exceptionally, as=
 the product of two elliptic curves if it concerns a product polarization). S=
econd, we show that, modulo a plausible assumption, Charles-Goren-Lauter styl=
e hash functions from superspecial principally polarized abelian surfaces req=
uire a trusted set-up. Concretely, if the matrix $g$ associated with the star=
ting surface is known then collisions can be produced in polynomial time. We =
deem it plausible that all currently known methods for generating a starting =
surface indeed reveal the corresponding matrix. As an auxiliary tool, we pres=
ent an efficient method for converting polarized isogenies of powersmooth deg=
ree into the corresponding connecting matrix, a step for which a previous app=
roach by Chu required super-polynomial (but sub-exponential) time.



## 2025/1194

* Title: Private coins extension with verifiable encryption
* Authors: Oleg Fomenko
* [Permalink](https://eprint.iacr.org/2025/1194)
* [Download](https://eprint.iacr.org/2025/1194.pdf)

### Abstract

This paper introduces a protocol for verifiable encryption of values committe=
d using Pedersen commitments. It enables a recipient to decrypt the hidden am=
ount while proving its consistency with the original commitment, without reve=
aling the value publicly. The construction combines symmetric encryption with=
 zero-knowledge proofs and is made non-interactive via the Fiat-Shamir heuris=
tic. The protocol is particularly useful in blockchain settings where confide=
ntial but verifiable value transfers are required.



## 2025/1195

* Title: On symbolic computations and Post Quantum Cryptography with Lie Geom=
etries.
* Authors: Vasyl Ustimenko
* [Permalink](https://eprint.iacr.org/2025/1195)
* [Download](https://eprint.iacr.org/2025/1195.pdf)

### Abstract

Assume that the global density of multivariate map  over the commutative ring=
 is the total number of its coefficients. In the case of finite commutative r=
ing K with the multiplicative group  K* containing more than 2 elements we su=
ggest multivariate public keys in n variables with the public rule of global =
density O(n) and degree O(1). Another public keys  use public rule of global =
density O(n) and degree O(n) together with the space of plaintexts (K*)^n and=
 the space of ciphertext K^n . We consider examples of protocols of Noncommut=
ative Cryptography implemented on the platform of  endomorphisms of which all=
ow the con-version of mentioned above multivariate public keys into protocol =
based cryptosystems of El Gamal type. The cryptosystems and protocols are des=
igned in terms of analogue of geometries of Chevalley groups over commutative=
 rings  and their temporal versions.



## 2025/1196

* Title: Limits on the Power of Private Constrained PRFs
* Authors: Mengda Bi, Chenxin Dai, Yaohua Ma
* [Permalink](https://eprint.iacr.org/2025/1196)
* [Download](https://eprint.iacr.org/2025/1196.pdf)

### Abstract

Private constrained PRFs are constrained PRFs where the constrained key hides=
 information about the predicate circuit. Although there are many constructio=
ns and applications of PCPRF, its relationship to basic cryptographic primiti=
ves, such as one-way functions and public-key encryptions, has been unclear. =
For example, we don't know whether one-way functions imply PCPRFs for general=
 predicates, nor do we know whether 1-key secure PCPRF for all polynomial-siz=
ed predicates imply public-key primitives such as public-key encryption and s=
ecret-key agreement.
   =20
    In this work, we prove the black-box separation between a 1-key secure PC=
PRF for any predicate and a secret-key agreement, which is the first black-bo=
x separation result about PCPRF. Specifically, we prove that there exists an =
oracle relative to which 1-key secure PCPRFs exist while secret-key agreement=
 does not. Our proof is based on the simulation-based technique proposed by I=
mpagliazzo and Rudich (STOC 89). The main technical challenge in generalizing=
 the simulation-based technique to PCPRF is the issue of \textit{unfaithfulne=
ss} of Eve's simulation to the real world because our oracle is more complica=
ted than a random oracle. We introduce a new technique which we call the ``we=
ighting" technique and show how to leverage it to circumvent the issue of unf=
aithfulness in the proof framework of Impagliazzo and Rudich.



## 2025/1197

* Title: How to Copy-Protect All Puncturable Functionalities Without Conjectu=
res: A Unified Solution to Quantum Protection
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