yusuke1997/dblp-id-title huggingface dataset:
Post-Quantum Provably-Secure Authentication and MAC from Mersenne Primes
Streebog compression function as PRF in secret-key settings
The Power of NAPs: Compressing OR-Proofs via Collision-Resistant Hashing
On the security of two blind signatures from code equivalence problems
Weaknesses in the Pseudorandom Bit Generation Algorithms of the Stream Ciphers TPypy and TPy
Design Space Exploration of Galois and Fibonacci Configuration based on Espresso Stream Cipher
Continuous After-the-fact Leakage-Resilient Key Exchange (full version)
Practical MPC+FHE with Applications in Secure Multi-PartyNeural Network Evaluation
Breaking and Repairing Trapdoor-free Group Signature Schemes from Asiacrypt 2004
NovaTEE: Private Clearing and Settlement on Trusted Execution Hardware
Higher Order Side-Channel Attacks Resilient S-boxes
XTR and Tori
Leakage-resilient Algebraic Manipulation Detection Codes with Optimal Parameters
The inspection model for zero-knowledge proofs and efficient Zerocash with secp256k1 keys
Single-Trace Side-Channel Attacks on CRYSTALS-Dilithium: Myth or Reality?
Attribute-Based Encryption for a Subclass of Circuits with Bounded Depth from Lattices
Oblivious Messsage Retrieval
Privacy-Preserving Linear Regression on Distributed Data
Hybrid Anomaly Detection using K-Means Clustering in Wireless Sensor Networks
Differential Cryptanalysis of a Lightweight Block Cipher LELBC
Some results on Sprout
Separating two roles of hashing in one-way message authentication
GraSS: Graph-based Similarity Search on Encrypted Query
Ring Key-Homomorphic Weak PRFs and Applications
An argument on the security of LRBC, a recently proposed lightweight block cipher
mR LWE -CP-ABE a revocable CP-ABE for Post-Quantum Cryptography
Secure Direct Communication Using Quantum Calderbank-Shor-Steane Codes
A New Scheme for Zero Knowledge Proof based on Multivariate Quadratic Problem and Quaternion Algebra
Walsh-Hadamard Transform and Cryptographic Applications in Bias Computing
Modular Inversion Hidden Number Problem- A Lattice Approach
Further Observations on Certificate-Base Encryption and its Generic Construction from Certificateless Public Key Encryption
Rational authentication protocols
A Secure Text Messaging Protocol
On the Degree-Insensitive SI-GDH problem and assumption
Multiparty Homomorphic Encryption: From Theory to Practice
Fast Multiple Point Multiplication on Elliptic Curves over Prime and Binary Fields using the Double-Base Number System
Accumulating Automata and Cascaded Equations Automata for Communicationless Information Theoretically Secure Multi-Party Computation
Evolutionary Design of Trace Form Bent Functions
Implementation and Comparison of Lattice-based Identification Protocols on Smart Cards and Microcontrollers
Secure Merge in Linear Time and O(log log N) Rounds
Areion: Highly-Efficient Permutations and Its Applications (Extended Version)
A Subgradient Algorithm For Computational Distances and Applications to Cryptography
CARPOOL: Secure And Reliable Proof of Location
Critical Round in Multi-Round Proofs: Compositions and Transformation to Trapdoor Commitments
Differentially Private Access Patterns in Secure Computation
The Art of Labeling: Task Augmentation for Private(Collaborative) Learning on Transformed Data
Attacking ECDSA with Nonce Leakage by Lattice Sieving: Bridging the Gap with Fourier Analysis-based Attacks
S-box pipelining using genetic algorithms for high-throughput AES implementations: How fast can we go?
Impossibility of Secure Multi-Party Products in Non-Abelian Groups
Hardware Penetration Testing Knocks Your SoCs Off
Modes of Encryption Secure against Blockwise-Adaptive Chosen-Plaintext Attack
On Privacy Losses in the Trusted Agent Model (Abstract)
Bounded Fully Homomorphic Signature Schemes
Multi-Authority ABE from Lattices without Random Oracles
DMM: Distributed Matrix Mechanism for Differentially-Private Federated Learning using Packed Secret Sharing
An Efficient Parallel Algorithm for Skein Hash Functions
Fuzzy PSI via Oblivious Protocol Routing
Non-Interactive CCA2-Secure Threshold Cryptosystems: Achieving Adaptive Security in the Standard Model Without Pairings
A Theoretical Study of Kolmogorov-Smirnov Distinguishers: Side-Channel Analysis vs. Differential Cryptanalysis
A Signature-Based Gröbner Basis Algorithm with Tail-Reduced Reductors (M5GB)
Feistel Like Construction of Involutory Binary Matrices With High Branch Number
Regional Blackouts: Protection of Broadcast Content on 3G Networks
Using Learning with Rounding to Instantiate Post-Quantum Cryptographic Algorithms
On the order of the polynomial x p -x-a
Computational Records with Aging Hardware: Controlling Half the Output of SHA-256
Elliptic Curves for Pairing Applications
Sublinear Distributed Product Checks on Replicated Secret-Shared Data over ℤ 2 k without Ring Extensions
Overview of the Candidates for the Password Hashing Competition - And their Resistance against Garbage-Collector Attacks
Symphony of Speeds: Harmonizing Classic McEliece Cryptography with GPU Innovation
Nopenena Untraceable Payments: Defeating Graph Analysis with Small Decoy Sets
Obtaining Universally Composable Security: Towards the Bare Bones of Trust
Towards Leakage Exploitation Optimality in Profiled Side-Channel Attacks
Cryptanalysis of a privacy-preserving behavior-oriented authentication scheme
Not optimal but efficient: a distinguisher based on the Kruskal-Wallis test
Kaweichel, an Extension of Blowfish for 64-Bit Architectures
Out of the Box Testing
Improved Preimage Attack on One-block MD4
TEDT, a Leakage-Resilient AEAD mode for High (Physical) Security Applications
SoK: Instruction Set Extensions for Cryptographers
Security of the Misty Structure Beyond the Birthday Bound
Efficient Arithmetic on Hessian Curves over Fields of Characteristic Three
Equivalence between MAC and PRF for Blockcipher based Constructions
OML: Open, Monetizable, and Loyal AI
IEEE P1363.1 Draft 10: Draft Standard for Public Key Cryptographic Techniques Based on Hard Problems over Lattices
Quantum Security of the Legendre PRF
Polynomial-Time Key Recovery Attack on the Lau-Tan Cryptosystem Based on Gabidulin Codes
Forward Security in Threshold Signature Schemes
Size-Hiding in Private Set Intersection: what can be done and how to do it without random oracles
Routing Protocol Based Shared and Session Key Exchange Protocol for Wireless Mobile Ad-hoc Network
Casting out Primes: Bignum Arithmetic for Zero-Knowledge Proofs
Learning from Leakage: Database Reconstruction from Just a Few Multidimensional Range Queries
Low-Complexity Deep Convolutional Neural Networks on Fully Homomorphic Encryption Using Multiplexed Convolutions
Kachina - Foundations of Private Smart Contracts
PMNS revisited for consistent redundancy and equality test
Prouï¬ & Rivain's Formal Security Proof of Masking, Revisited: Tight Bounds in the Noisy Leakage Model
The Fourier Entropy-Influence conjecture holds for a log-density 1 class of cryptographic Boolean functions
Cryptanalysis of the CFVZ cryptosystem
Comment on "Attribute-Based Signatures for Supporting Anonymous Certification" by N. Kaaniche and M. Laurent (ESORICS 2016)
New record in the number of qubits for a quantum implementation of AES
Repudiable Ring Signature: Stronger Security and Logarithmic-Size
Beale Cipher 1 and Cipher 3: Numbers With No Messages
Efficient Low-Latency Masking of Ascon without Fresh Randomness
On the anonymity of one authenticated key agreement scheme for mobile vehicles-assisted precision agricultural IoT networks
Horizontal Clustering Side-Channel Attacks on Embedded ECC Implementations (Extended Version)
Communication-Efficient BFT Protocols Using Small Trusted Hardware to Tolerate Minority Corruption
Doubly Efficient Interactive Proofs over Infinite and Non-Commutative Rings
On a Threshold Group Signature Scheme and a Fair Blind Signature Scheme
IBE-IBE: Intent-Based Execution through Identity-Based Encryption and Auctions
Notion of Algebraic Immunity and Its evaluation Related to Fast Algebraic Attacks
Privacy-Preserving Shape Matching with Leveled Homomorphic Encryption
Extending Oblivious Transfers Efficiently - How to get Robustness Almost for Free
SCA Evaluation and Benchmarking of Finalists in the NIST Lightweight Cryptography Standardization Process
Leakage Assessment in Fault Attacks: A Deep Learning Perspective
Superposition Attacks on Pseudorandom Schemes based on Two or Less Permutations
Faster indifferentiable hashing to elliptic $\mathbb{F}_{\!q^2}$-curves
SNARGs for Bounded Depth Computations from Sub-Exponential LWE
Chicken or the Egg - Computational Data Attacks or Physical Attacks
Client-oblivious OPRAM
Attacks and Remedies for Randomness in AI: Cryptanalysis of PHILOX and THREEFRY
BAM BAM!! On Reliability of EMFI for in-situ Automotive ECU Attacks
Encryption Performance Improvements of the Paillier Cryptosystem
Identity-Based Matchmaking Encryption, Revisited: Strong Security and Practical Constructions from Standard Classical and Post-Quantum Assumptions
An error in the mixed adversary protocol by Fitzi, Hirt and Maurer
Simple and Practical Single-Server Sublinear Private Information Retrieval
Official Arbitration and its Application to Secure Cloud Storage
Performance Improvements of ZK-Prover for rWasm: A Sound and Efficient AIR for 32-bit Division and Remainder
A Short Note on a Weight Probability Distribution Related to SPNs
Optimal TNFS-secure pairings on elliptic curves with even embedding degree
How to Generate and use Universal Parameters
Hydra: Succinct Fully Pipelineable Interactive Arguments of Knowledge
Verifiable computation using multiple provers
GearBox: An Efficient UC Sharded Ledger Leveraging the Safety-Liveness Dichotomy
Improved lower bound on the number of balanced symmetric functions over GF(p)
Looking at the NIST Lightweight Candidates from a Masking Point-of-View
Fly Away: Lifting Fault Security through Canaries and the Uniform Random Fault Model
Self-Differential Cryptanalysis of Up to 5 Rounds of SHA-3
Attacks and Modifications of CJC's E-voting Scheme
Webb Protocol: A cross-chain private application and governance protocol
Attacks based on Conditional Correlations against the Nonlinear Filter Generator
Distributed Broadcast Encryption for Confidential Interoperability across Private Blockchains
Ideally HAWKward: How Not to Break Module-LIP
An extension of Overbeck's attack with an application to cryptanalysis of Twisted Gabidulin-based schemes
A Cryptographic Analysis of the TLS 1.3 draft-10 Full and Pre-shared Key Handshake Protocol
The Round Complexity of Proofs in the Bounded Quantum Storage Model
Universally Composable Secure Two and Multi-party Computation in the Corruptible Tamper-Proof Hardware Token Model
Cryptanalysis of Aggregate Γ-Signature and Practical Countermeasures in Application to Bitcoin
Characterizing NTRU-Variants Using Group Ring and Evaluating their Lattice Security
A Random Number Generator Based on Isogenies Operations
Improved Bounds on the Threshold Gap in Ramp Secret Sharing
X509CLOUD - Framework for a Ubiquitous PKI
ID-based Encryption Scheme Secure against Chosen Ciphertext Attacks
Robust Fuzzy Extractors and Helper Data Manipulation Attacks Revisited: Theory vs Practice
Decentralized Finance (DeFi): A Survey
Practical Passive Leakage-Abuse Attacks Against Symmetric Searchable Encryption
Differential Cache Trace Attack Against CLEFIA
Entropy Estimation of Physically Unclonable Functions
On the construction of digest functions for manual authentication protocols
Security Analysis of Aggregate signature and Batch verification signature schemes
Simple is COOL: Graded Dispersal and its Applications for Byzantine Fault Tolerance
Closing the Efficiency Gap between Synchronous and Network-Agnostic Consensus
BlockMaze: An Efficient Privacy-Preserving Account-Model Blockchain Based on zk-SNARKs
Revisiting Proxy Re-Encryption: Forward Secrecy, Improved Security, and Applications
Weakness of Key Predistribution Scheme Proposed by J. Dong et al
Optimal security proofs for PSS and other signature schemes
And Paper-Based is Better? Towards Comparability of Classic and Cryptographic Voting Schemes
Theoretical cryptanalysis of the Klimov-Shamir number generator TF-1
Endomorphisms for Faster Cryptography on Elliptic Curves of Moderate CM Discriminants, II
Polynomial time reduction from approximate shortest vector problem to the principle ideal porblem for lattices in cyclotomic rings
Fast Correlation Attacks on Grain-like Small State Stream Ciphers and Cryptanalysis of Plantlet, Fruit-v2 and Fruit-80
A New Cryptographic Algorithm
Generation of two "independent" points on an elliptic curve of j-invariant ≠q 0, 1728
Construction and Filtration of Lightweight Formalized MDS Matrices
Two new infinite families of APN functions in triviariate form
Decentralized Multi-Client Functional Encryption with Strong Security
Cyptanalysis CDHP , BDHP and Tate pairing under certain conditions The Tate pairing is less secure than Weil
CuFDFB: Fast and Private Computation on Non-Linear Functions Using FHE
Extractors Against Side-Channel Attacks: Weak or Strong?
Security Features of an Asymmetric Cryptosystem based on the Diophantine Equation Discrete Log Problem
A Simple Provably Secure Key Exchange Scheme Based on the Learning with Errors Problem
Crypto Dark Matter on the Torus: Oblivious PRFs from shallow PRFs and FHE
On Plausible Tree Hash Modes for SHA-3
On the Importance of Pooling Layer Tuning for Profiling Side-channel Analysis
Improved Security Analysis of PMAC
Partitioning Oracles from Weak Key Forgeries
On the Hardness of Trivium and Grain with respect to Generic Time-Memory-Data Tradeoff Attacks
On Computing the Multidimensional Scalar Multiplication on Elliptic Curves
Related-Key Differential Slide Attack Against Fountain V1
Almost All Discrete Log Bits Are Simultaneously Secure
Optimal Security Reductions for Unique Signatures: Bypassing Impossibilities with A Counterexample
Fully Secure Anonymous Hierarchical Identity-Based Encryption with Constant Size Ciphertexts
Seamless Switching Between PBS and WoPBS for Scalable TFHE
Improved Framework of Related-key Differential Neural Distinguisher and Applications to the Standard Ciphers
Abelian varieties with prescribed embedding degree
Adaptive attack for a possible PKE scheme using FESTA trapdoor functions in the wrong way
General Secret Sharing Based on the Chinese Remainder Theorem
Private Laconic Oblivious Transfer with Preprocessing
Towards Lightweight Side-Channel Security and the Leakage-Resilience of the Duplex Sponge
First-Order Hardware Sharings of the AES
Optimal pairing revisited
Transforming Secure Comparison Protocol from Passive to Active Adversary Model
Extended Double-Base Number System with applications to Elliptic Curve Cryptography
Highly Controlled, Fine-grained Delegation of Signing Capabilities
Too Easy Fault Injection Attacks on Learning with Rounding (LWR)
A New Construction of Time Capsule Signature
UnSplit: Data-Oblivious Model Inversion, Model Stealing, and Label Inference Attacks Against Split Learning
Practical Large-Scale Proof-of-Stake Asynchronous Total-Order Broadcast
Elastic Block Ciphers
Improvements on two password-based authentication protocols
Summation polynomials and the discrete logarithm problem on elliptic curves
Towards Better Integral Distinguishers over 픽 p Based on Exact Coefficients of Monomials
Precise Fault-Injections using Voltage and Temperature Manipulation for Differential Cryptanalysis
Certified-Everlasting Quantum NIZK Proofs
Cryptanalysis and Security Enhancement of an Advanced Authentication Scheme using Smart Cards, and a Key Agreement Scheme for Two-Party Communication
Noise*: A Library of Verified High-Performance Secure Channel Protocol Implementations (Long Version)
Frodo: Take off the ring! Practical, Quantum-Secure Key Exchange from LWE
A Multi-Function Provable Data Possession Scheme in Cloud Computing
On the (In)security of SNARKs in the Presence of Oracles
Cryptanalysis of Round-Reduced SIMON32 Based on Deep Learning
Exploring Kaneko's bound: On multi-edges, loops and the diameter of the supersingular ℓ-isogeny graph
Location Leakage in Distance Bounding: Why Location Privacy does not Work
New Results on Unconditionally Secure Multireceiver Manual Authentication
Certificateless Signcryption without Pairing
Breaking the Rabin-Williams digital signature system implementation in the Crypto++ library
AKE Zoo: 100 two-party protocols (to be continued)
Sum-check Is All You Need: An Opinionated Survey on Fast Provers in SNARK Design
Provably weak instances of Ring-LWE
k-Round MPC from k-Round OT via Garbled Interactive Circuits
Anamorphic Authenticated Key Exchange: Double Key Distribution under Surveillance
An analysis of the C class of bent functions
Improved OR Composition of Sigma-Protocols
Analysis of the End-by-Hop Protocol for Secure Aggregation in Sensor Networks
Further Improving Differential-Linear Attacks: Applications to Chaskey and Serpent
An n/2 byzantine node tolerated blockchain sharding approach
Non-Malleable Encryption: Equivalence between Two Notions, and an Indistinguishability-based Characterization
Highly Nonlinear Balanced Boolean Functions with very good Autocorrelation Property
Bridging the Gap: Advanced Tools for Side-Channel Leakage Estimation beyond Gaussian Templates and Histograms
An Improved ID-based Authenticated Group Key Agreement Scheme
An efficient FHE proposal based on the hardness of solving systems of nonlinear multivariate equations (II)
Quantum Augmented Dual Attack
Early Detection and Analysis of Leakage Abuse Vulnerabilities
On Kasami Bent Functions
Usable assembly language for GPUs: a success story
DTLS-HIMMO: Efficiently Securing a Post-Quantum World with a Fully-Collusion Resistant KPS
The Planck Constant and Quantum Fourier Transformation
Optimizing the depth of quantum implementations of linear layers
Attacking Single-Cycle Ciphers on Modern FPGAs featuring Explainable Deep Learning
Privacy-Preserving Billing for e-Ticketing Systems in Public Transportation
Two RSA-based Cryptosystems
Two-server Distributed ORAM with Sublinear Computation and Constant Rounds
An Attack to Universally Composable Commitments from Malicious Physically Uncloneable Functions and how to Avoid it
Some Properties of Modular Addition
Solve Approximate CVP via Variants of Nearest-Colattice
Laurent Polynomial-Based Linear Transformations for Improved Functional Bootstrapping
Protego: A Credential Scheme for Permissioned Blockchains (Extended Version)
Handling vectorial functions by means of their graph indicators
Linear Overhead Robust MPC with Honest Majority Using Preprocessing
Not enough LESS: An improved algorithm for solving Code Equivalence Problems over 픽 q
Pirouette: Query Efficient Single-Server PIR
Finding EM leakages at design stage: a simulation methodology
A Simplified Combinatorial Treatment of Constructions and Threshold Gaps of Ramp Schemes
A fast integer-based batch full-homomorphic encryption scheme over finite field
A New Public Key Cryptosystem Based on Edwards Curves
Automated algebraic analysis of structure-preserving signature schemes
Privacy-preserving Approximate GWAS computation based on Homomorphic Encryption
An efficient semantically secure elliptic curve cryptosystem based on KMOV
TorScan: Tracing Long-lived Connections and Differential Scanning Attacks
DiSSECT: Distinguisher of Standard & Simulated Elliptic Curves via Traits
The Average Transmission Overhead of Broadcast Encryption
Decentralized Multi-Authority Attribute-Based Inner-Product Functional Encryption: Noisy and Evasive Constructions from Lattices
FHE-MENNs: Opportunities and Pitfalls for Accelerating Fully Homomorphic Private Inference with Multi-Exit Neural Networks
MeltdownDetector: A Runtime Approach for Detecting Meltdown Attacks
Comparative Analysis of ResNet and DenseNet for Differential Cryptanalysis of SPECK 32/64 Lightweight Block Cipher
Isogeny-based Cryptography using Isomorphisms of Superspecial Abelian Surfaces
SoK: Validating Bridges as a Scaling Solution for Blockchains
Conditional Constant Function Problem and Its Quantum Solutions: Attacking Feistel Ciphers
On known constructions of APN and AB functions and their relation to each other
Arithmetic Walsh Transform of Boolean Functions with Linear Structures
Privacy-Preserving Friend Search over Online Social Networks
Optimizing NCC-Sign for ARMv8
A security analysis on MQ-Sign
A Composable Look at Updatable Encryption
Towards Minimizing Memory Requirement for Implementation of Hyperelliptic Curve Crytosystems
Improved Bitslice Masking: from Optimized Non-Interference to Probe Isolation
PRCash: Centrally-Issued Digital Currency with Privacy and Regulation
A Unified Method for Improving PRF Bounds for a Class of Blockcipher based MACs
Uniform Black-Box Separations via Non-Malleable Extractors
Efficient Zero Knowledge Arguments for Bilinear Matrix Relations over Finite Fields and Knowledge-Soundness Enhancement via Operations over Extended Field
Fine-Grained Complexity in a World without Cryptography
SILBE: an Updatable Public Key Encryption Scheme from Lollipop Attacks
Revisiting Multi-Key Blind Rotation: Optimized NTRU-based Bootstrapping for MKFHE
A roadmap to fully homomorphic elections: Stronger security, better verifiability
DualMatrix: Conquering zkSNARK for Large Matrix Multiplication
Towards Optimal Parallel Broadcast under a Dishonest Majority
Desynchronization Attack on RAPP Ultralightweight Authentication Protocol
A New Family of Practical Non-Malleable Protocols
Minimizing Non-interactive Zero-Knowledge Proofs Using Fully Homomorphic Encryption
Clock-Controlled Shift Registers for Key-Stream Generation
AKCN-E8: Compact and Flexible KEM from Ideal Lattice
Singular points of UOV and VOX
A note on isogeny-based hybrid verifiable delay functions
On Constructing Universal One-Way Hash Functions from Arbitrary One-Way Functions
A kilobit special number field sieve factorization
Verifiable Computation over Encrypted Data in the Presence of Verification Queries
On Lions and Elligators: An efficient constant-time implementation of CSIDH
Lattice-Based Fully Dynamic Multi-Key FHE with Short Ciphertexts
An Assessment of Differential-Neural Distinguishers
Using Bleichenbacher's Solution to the Hidden Number Problem to Attack Nonce Leaks in 384-Bit ECDSA
Making RSA-PSS Provably Secure Against Non-Random Faults
Climbing and descending tall volcanos
On Measurable Side-Channel Leaks inside ASIC Design Primitives
No-Commit Proofs: Defeating Livelock in BFT
Revisiting Shuffle-Based Private Set Unions with Reduced Communication
Session-state Reveal is stronger than Ephemeral Key Reveal: Attacking the NAXOS Authenticated Key Exchange protocol
sPAR: (Somewhat) Practical Anonymous Router
Distributed Non-Interactive Zero-Knowledge Proofs
Hardness of Computing Individual Bits for Pairing-based One-way Functions
Analysis of Affinely Equivalent Boolean Functions
A Security Analysis of Two Classes of RSA-like Cryptosystems
More on Proofs of Knowledge
Integrative Acceleration of First-Order Boolean Masking for Embedded IoT Devices
A Provably Secure W-OTS + based on MQ Problem
SoK: Off The Chain Transactions
Threat-Adjusting Security: BitFlip as an AI-Ready, Post-Quantum cipher
Security of Quantum-Readout PUFs against quadrature based challenge estimation attacks
Multi-homogeneous XL
Interactive and Noninteractive Zero Knowledge Coincide in the Help Model
TR-31 and AS 2805 (Non)equivalence report
SiGamal: A supersingular isogeny-based PKE and its application to a PRF
Quantum Collision-Resistance of Non-uniformly Distributed Functions: Upper and Lower Bounds
A Novel Duplication Based Countermeasure To Statistical Ineffective Fault Analysis
Decoding Interleaved Gabidulin Codes and Ciphertext-Security for GPT variants
SMART POOL : Practical Decentralized Pooled Mining
Security Analysis of an Authentication Scheme Using Smart Cards
Rhyme: A Fiat-Shamir Lattice-based Signature with 3C Sampling
Grover on Present: Quantum Resource Estimation
PUF Modeling Attacks on Simulated and Silicon Data
Gold OPRF: Post-Quantum Oblivious Power Residue PRF
STP Models of Optimal Differential and Linear Trail for S-box Based Ciphers
TESLA: Tightly-Secure Efficient Signatures from Standard Lattices
An Open Problem on the Bentness of Mesnagerâs Functions
Decomposition formula of the Jacobian group of plane curve