Computationally Data-Independent Memory Hard Functions
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Computationally Data-Independent Memory Hard Functions
Computationally Data-Independent Memory Hard Functions Mohammad Hassan Ameri∗ Jeremiah Blocki† Samson Zhou‡ November 18, 2019 Abstract Memory hard functions (MHFs) are an important cryptographic primitive that are used to design egalitarian proofs of work and in the construction of moderately expensive key-derivation functions resistant to brute-force attacks. Broadly speaking, MHFs can be divided into two categories: data-dependent memory hard functions (dMHFs) and data-independent memory hard functions (iMHFs). iMHFs are resistant to certain side-channel attacks as the memory access pattern induced by the honest evaluation algorithm is independent of the potentially sensitive input e.g., password. While dMHFs are potentially vulnerable to side-channel attacks (the induced memory access pattern might leak useful information to a brute-force attacker), they can achieve higher cumulative memory complexity (CMC) in comparison than an iMHF. In particular, any iMHF that can be evaluated in N steps on a sequential machine has CMC at 2 most N log log N . By contrast, the dMHF scrypt achieves maximal CMC Ω(N 2) — though O log N the CMC of scrypt would be reduced to just (N) after a side-channel attack. In this paper, we introduce the notion ofO computationally data-independent memory hard functions (ciMHFs). Intuitively, we require that memory access pattern induced by the (ran- domized) ciMHF evaluation algorithm appears to be independent from the standpoint of a computationally bounded eavesdropping attacker — even if the attacker selects the initial in- put. We then ask whether it is possible to circumvent known upper bound for iMHFs and build a ciMHF with CMC Ω(N 2). -
Características Y Aplicaciones De Las Funciones Resumen Criptográficas En La Gestión De Contraseñas
Características y aplicaciones de las funciones resumen criptográficas en la gestión de contraseñas Alicia Lorena Andrade Bazurto Instituto Universitario de Investigación en Informática Escuela Politécnica Superior Características y aplicaciones de las funciones resumen criptográficas en la gestión de contraseñas ALICIA LORENA ANDRADE BAZURTO Tesis presentada para aspirar al grado de DOCTORA POR LA UNIVERSIDAD DE ALICANTE DOCTORADO EN INFORMÁTICA Dirigida por: Dr. Rafael I. Álvarez Sánchez Alicante, julio 2019 Índice Índice de tablas .................................................................................................................. vii Índice de figuras ................................................................................................................. ix Agradecimiento .................................................................................................................. xi Resumen .......................................................................................................................... xiii Resum ............................................................................................................................... xv Abstract ........................................................................................................................... xvii 1 Introducción .................................................................................................................. 1 1.1 Objetivos ...............................................................................................................4 -
Argon2: the Memory-Hard Function for Password Hashing and Other Applications
Argon2: the memory-hard function for password hashing and other applications Designers: Alex Biryukov, Daniel Dinu, and Dmitry Khovratovich University of Luxembourg, Luxembourg [email protected], [email protected], [email protected] https://www.cryptolux.org/index.php/Argon2 https://github.com/P-H-C/phc-winner-argon2 https://github.com/khovratovich/Argon2 Version 1.3 of Argon2: PHC release February 29, 2016 Contents 1 Introduction 2 2 Definitions 3 2.1 Motivation . 3 2.2 Model for memory-hard functions . 4 3 Specification of Argon2 4 3.1 Inputs . 4 3.2 Operation . 5 3.3 Indexing . 6 3.4 Compression function G ......................................... 7 4 Features 8 4.1 Available features . 8 4.2 Possible future extensions . 9 5 Security analysis 9 5.1 Ranking tradeoff attack . 9 5.2 Memory optimization attack . 9 5.3 Attack on iterative compression function . 10 5.4 Security of Argon2 to generic attacks . 10 5.5 Security of Argon2 to ranking tradeoff attacks . 11 5.6 Security of Argon2i to generic tradeoff attacks on random graphs . 12 5.7 Summary of tradeoff attacks . 12 6 Design rationale 12 6.1 Indexing function . 12 6.2 Implementing parallelism . 13 6.3 Compression function design . 15 6.3.1 Overview . 15 6.3.2 Design criteria . 15 6.4 User-controlled parameters . 15 7 Performance 16 7.1 x86 architecture . 16 8 Applications 16 1 9 Recommended parameters 17 10 Conclusion 17 A Permutation 18 P B Additional functionality 19 C Change log 19 C.1 v.1.3 . 19 C.2 v1.2.1 { February 1st, 2016 . -
Performance Analysis of Cryptographic Hash Functions Suitable for Use in Blockchain
I. J. Computer Network and Information Security, 2021, 2, 1-15 Published Online April 2021 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijcnis.2021.02.01 Performance Analysis of Cryptographic Hash Functions Suitable for Use in Blockchain Alexandr Kuznetsov1 , Inna Oleshko2, Vladyslav Tymchenko3, Konstantin Lisitsky4, Mariia Rodinko5 and Andrii Kolhatin6 1,3,4,5,6 V. N. Karazin Kharkiv National University, Svobody sq., 4, Kharkiv, 61022, Ukraine E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] 2 Kharkiv National University of Radio Electronics, Nauky Ave. 14, Kharkiv, 61166, Ukraine E-mail: [email protected] Received: 30 June 2020; Accepted: 21 October 2020; Published: 08 April 2021 Abstract: A blockchain, or in other words a chain of transaction blocks, is a distributed database that maintains an ordered chain of blocks that reliably connect the information contained in them. Copies of chain blocks are usually stored on multiple computers and synchronized in accordance with the rules of building a chain of blocks, which provides secure and change-resistant storage of information. To build linked lists of blocks hashing is used. Hashing is a special cryptographic primitive that provides one-way, resistance to collisions and search for prototypes computation of hash value (hash or message digest). In this paper a comparative analysis of the performance of hashing algorithms that can be used in modern decentralized blockchain networks are conducted. Specifically, the hash performance on different desktop systems, the number of cycles per byte (Cycles/byte), the amount of hashed message per second (MB/s) and the hash rate (KHash/s) are investigated. -
Just in Time Hashing
Just in Time Hashing Benjamin Harsha Jeremiah Blocki Purdue University Purdue University West Lafayette, Indiana West Lafayette, Indiana Email: [email protected] Email: [email protected] Abstract—In the past few years billions of user passwords prove and as many users continue to select low-entropy have been exposed to the threat of offline cracking attempts. passwords, finding it too difficult to memorize multiple Such brute-force cracking attempts are increasingly dangerous strong passwords for each of their accounts. Key stretching as password cracking hardware continues to improve and as serves as a last line of defense for users after a password users continue to select low entropy passwords. Key-stretching breach. The basic idea is to increase guessing costs for the techniques such as hash iteration and memory hard functions attacker by performing hash iteration (e.g., BCRYPT[75] can help to mitigate the risk, but increased key-stretching effort or PBKDF2 [59]) or by intentionally using a password necessarily increases authentication delay so this defense is hash function that is memory hard (e.g., SCRYPT [74, 74], fundamentally constrained by usability concerns. We intro- Argon2 [12]). duce Just in Time Hashing (JIT), a client side key-stretching Unfortunately, there is an inherent security/usability algorithm to protect user passwords against offline brute-force trade-off when adopting traditional key-stretching algo- cracking attempts without increasing delay for the user. The rithms such as PBKDF2, SCRYPT or Argon2. If the key- basic idea is to exploit idle time while the user is typing in stretching algorithm cannot be computed quickly then we their password to perform extra key-stretching. -
Moderately Hard Functions: Definition, Instantiations, and Applications?
Moderately Hard Functions: Definition, Instantiations, and Applications? Jo¨elAlwen1 and Bj¨ornTackmann2 1 IST, Vienna, Austria, [email protected] 2 IBM Research { Zurich, Switzerland, [email protected] Abstract. Several cryptographic schemes and applications are based on functions that are both reasonably efficient to compute and moderately hard to invert, including client puzzles for Denial-of-Service protection, password protection via salted hashes, or recent proof-of-work blockchain systems. Despite their wide use, a definition of this concept has not yet been distilled and formalized explicitly. Instead, either the applications are proven directly based on the assumptions underlying the function, or some property of the function is proven, but the security of the ap- plication is argued only informally. The goal of this work is to provide a (universal) definition that decouples the efforts of designing new moder- ately hard functions and of building protocols based on them, serving as an interface between the two. On a technical level, beyond the mentioned definitions, we instantiate the model for four different notions of hardness. We extend the work of Alwen and Serbinenko (STOC 2015) by providing a general tool for proving security for the first notion of memory-hard functions that allows for provably secure applications. The tool allows us to recover all of the graph-theoretic techniques developed for proving security under the older, non-composable, notion of security used by Alwen and Serbinenko. As an application of our definition of moderately hard functions, we prove the security of two different schemes for proofs of effort (PoE). We also formalize and instantiate the concept of a non-interactive proof of effort (niPoE), in which the proof is not bound to a particular communication context but rather any bit-string chosen by the prover. -
On the Economics of Offline Password Cracking
On the Economics of Offline Password Cracking Jeremiah Blocki Ben Harsha Samson Zhou Purdue University Purdue University Carnegie Mellon University Abstract—We develop an economic model of an offline pass- passwords to offline attacks. Password hashing algorithms word cracker which allows us to make quantitative predictions are a critical last line of defense against an offline attacker about the fraction of accounts that a rational password attacker who has stolen password hash values from an authentication would crack in the event of an authentication server breach. We server. An attacker who has stolen a user’s password hash apply our economic model to analyze recent massive password value can attempt to crack each user’s password offline by breaches at Yahoo!, Dropbox, LastPass and AshleyMadison. comparing the hashes of likely password guesses with the All four organizations were using key-stretching to protect user stolen hash value. Because the attacker can check each guess passwords. In fact, LastPass’ use of PBKDF2-SHA256 with 105 offline it is no longer possible to lockout the adversary after hash iterations exceeds 2017 NIST minimum recommendation several incorrect guesses. by an order of magnitude. Nevertheless, our analysis paints An offline attacker is limited only by the cost of com- a bleak picture: the adopted key-stretching levels provide puting the hash function. Ideally, the password hashing al- insufficient protection for user passwords. In particular, we gorithm should be moderately expensive to compute so that present strong evidence that most user passwords follow a it is prohibitively expensive for an offline attacker to crack Zipf’s law distribution, and characterize the behavior of a most user passwords e.g., by checking millions, billions or rational attacker when user passwords are selected from a even trillions of password guesses for each user. -
Balloon Hashing: a Memory-Hard Function Providing Provable Protection Against Sequential Attacks?
Balloon Hashing: A Memory-Hard Function Providing Provable Protection Against Sequential Attacks? Dan Boneh1, Henry Corrigan-Gibbs1, and Stuart Schechter2 1 Stanford University, Stanford CA 94305, U.S.A. 2 Microsoft Research, Redmond WA 98052, U.S.A. Abstract. We present the Balloon password-hashing algorithm. This is the first practical cryptographic hash function that: (i) has proven memory-hardness properties in the random-oracle model, (ii) uses a pass- word-independent access pattern, and (iii) meets—and often exceeds— the performance of the best heuristically secure password-hashing algo- rithms. Memory-hard functions require a large amount of working space to evaluate efficiently and, when used for password hashing, they dra- matically increase the cost of offline dictionary attacks. In this work, we leverage a previously unstudied property of a certain class of graphs (“random sandwich graphs”) to analyze the memory-hardness of the Bal- loon algorithm. The techniques we develop are general: we also use them to give a proof of security of the scrypt and Argon2i password-hashing functions, in the random-oracle model. Our security analysis uses a se- quential model of computation, which essentially captures attacks that run on single-core machines. Recent work shows how to use massively parallel special-purpose machines (e.g., with hundreds of cores) to at- tack memory-hard functions, including Balloon. We discuss this impor- tant class of attacks, which is outside of our adversary model, and pro- pose practical defenses against them. To motivate the need for security proofs in the area of password hashing, we demonstrate and implement a practical attack against Argon2i that successfully evaluates the func- tion with less space than was previously claimed possible. -
Open Sesame the Password Hashing Competition and Argon2 Jos Wetzels
Open Sesame The Password Hashing Competition and Argon2 Jos Wetzels [email protected] Abstract. In this document we present an overview of the background to and goals of the Password Hashing Competition (PHC) as well as the design of its winner, Argon2, and its security requirements and properties. Keywords: Password Hashing Competition, Argon2, Memory-Hard Hash Functions, GPU-FPGA-ASIC password cracking 1 Background of the Password Hashing Competition (PHC) The Password Hashing Competition (PHC) [1] was an open competition run between 2013 and 2015 by a group of cryptographers that aimed to select one or more pass- word hashing schemes, meeting modern requirements, for recommendation as a (de- facto) standard and ended up selecting the Argon2 [2] scheme as its winner. Given the ubiquity of passwords as a (primary) means of authentication to a range of services (from web services to mobile, desktop or server systems) or data protection systems (eg. disk encryption solutions), the persistence of password re-use [3] and the (in- creasing) trend of credential-holding database breaches [4,5,6] password protection is a topic of continuing importance. The initial measure aimed at limiting the impact of database breaches was the usage of cryptographic hash functions for password storage [7] where passwords aren’t stored as plaintext but as a hash digest. When users au- thenticate their password is hashed and compared to the stored digest. The security properties of (cryptographically secure) hash functions [44] aim to make them practi- cally impossible to invert. In this manner a database compromise doesn’t result in the immediate disclosure of user credentials but aims to force an attacker to mount a brute-force [9] or dictionary attack [10] on the hashes. -
Investigation of Practical Attacks on the Argon2i Memory-Hard Hash
Investigation of Practical Attacks on the Mitchell Gu Argon2i Memory-hard Hash Function Ryan Berg 6.857 Computer and Network Security Casie Chen Massachusetts Institute of Technology May 18, 2017 Contents 1 Introduction 2 2 Project Statement 2 3 Literature Review 3 4 Background 4 4.1 The Argon2 Hash . .4 4.1.1 The Compression Function H . .5 4.1.2 Indexing . .6 4.1.3 Revisions Made to Argon2i-A . .6 4.1.4 Simplifying Assumptions . .6 4.2 The Alwen-Blocki Attack . .7 4.2.1 Modeling the Hash as a DAG . .7 4.2.2 Attacking the Graph's Depth-Robustness . .7 4.2.3 Light and Balloon Phases of Computation . .8 4.2.4 Parallelization and Amortization . .8 4.2.5 Simulation Results . .9 5 Our Contributions 9 5.1 Modeling the Attack . .9 5.2 Genetic Algorithm Minimization of Depth-Reducing Set S ..... 10 5.3 Additional Layer of Parallelization to Amortize Memory Costs . 14 5.4 Predetermining Actual Reduced Graph Depth . 14 6 Further Research Questions 14 7 Conclusion 15 8 Acknowledgements 15 9 References 15 10 Appendix 16 Mitchell Gu Ryan Berg Final Project 6.857 Computer and Network Security Casie Chen 1 Introduction Modern password hashing functions are designed to protect low-entropy pass- words such as "password" or "123456Seven" that can be brute-forced quickly. These hashing techniques have evolved over time as attacks on them have been developed. When plain hashing of passwords became compromised through pre- computing hashes of common passwords and saving them in rainbow tables, the standard became salted hashing. -
High Complexity Graphs and Parallel Memory-Hard Functions
Memory-Hard Functions Joël Alwen – IST Austria Theory: Quo Vadis? Goal 1: Inform future research direction aiming it in a “useful” direction. Goal 2: Raise awareness of potential implications of recent results for Password- hashing standardization. Some example questions to keep in mind… 1. Computational Model: Too weak / strong for security statements / attacks? If so what is wrong? 2. Complexity Measures: Too weak / strong for security statements / attacks? 3. Statements: Are the type of statements being proven relevant to practice? What more would we like to know? MHF a la Percival • Observation: Computation is cheaper for custom hardware (e.g. ASICs) then general purpose CPUs. • Goal: Functions which require as much memory as possible for a given number of computational steps even in parallel. ⟹ Decrease “evaluations/second per dollar” advantage of ASICs. • Recall: Area x Time (AT) complexity of a circuit evaluating f ≈ dollar cost per unit of rate (rate = # of f evaluations / sec). • Percival: Since high speed memory is expensive in circuits replace “area” with “space” (i.e. memory). MHF a la Percival Definition [Per09]: An MHF is a function f with hardness parameter n such that fn: 1. can be computed on a Random Access Machine (RAM) in T*(n) time. 2. can not be computed on a Parallel RAM (PRAM) with S(n) space and processors and T (n) time such that T(n) x S (n) = O(n2-c) for some c > 0. Data-(in)dependence • Is the honest evaluation algorithms memory access pattern input- dependent? • Yes: data-dependent MHF (dMHF). Example: scrypt, Argon2d. • No: data-independent MHF (iMHF). -
Tight Proofs of Space and Replication
Tight Proofs of Space and Replication Ben Fisch Stanford University Abstract We construct a concretely practical proof-of-space (PoS) with arbitrarily tight security based on stacked depth robust graphs and constant-degree expander graphs. A proof-of-space (PoS) is an interactive proof system where a prover demonstrates that it is persistently using space to store information. A PoS is arbitrarily tight if the honest prover uses exactly N space and for any > 0 the construction can be tuned such that no adversary can pass verification using less than (1 − )N space. Most notably, the degree of the graphs in our construction are independent of , and the number of layers is only O(log(1/)). The proof size is O(d/). The degree d depends on the depth robust graphs, which are only required to maintain Ω(N) depth in subgraphs on 80% of the nodes. Our tight PoS is also secure against parallel attacks. Tight proofs of space are necessary for proof-of-replication (PoRep), which is a publicly verifiable proof that the prover is dedicating unique resources to storing one or more retriev- able replicas of a file. Our main PoS construction can be used as a PoRep, but data extraction is as inefficient as replica generation. We present a second variant of our construction called ZigZag PoRep that has fast/parallelizable data extraction compared to replica generation and maintains the same space tightness while only increasing the number of levels by roughly a factor two. 1 Introduction Proof-of-space (PoS) has been proposed as an alternative to proof-of-work (PoW) for applications such as SPAM prevention, DOS attacks, and Sybil resistance in blockchain-based consensus mechanisms [17, 20, 30].