Randomness is a necessary ingredient in various computational tasks and especially in Cryptography, yet many existing mechanisms for obtaining randomness suffer from numerous problems. We suggest utilizing the behavior of humans while playing competitive games as an entropy source, in order to enhance the quality of the randomness in the system. This idea has two motivations: (i) results in experimental psychology indicate that humans are able to behave quite randomly when engaged in competitive games in which a mixed strategy is optimal, and (ii) people have an affection for games, and this leads to longer play yielding more entropy overall. While the resulting strings are not perfectly random, we show how to integrate such a game into a robust pseudo-random generator that enjoys backward and forward security.
Randomness is a necessary ingredient in various computational tasks and especially in Cryptography, yet many existing mechanisms for obtaining randomness suffer from numerous problems. We suggest utilizing the behavior of humans while playing competitive games as an entropy source, in order to enhance the quality of the randomness in the system. This idea has two motivations: (i) results in experimental psychology indicate that humans are able to behave quite randomly when engaged in competitive games in which a mixed strategy is optimal, and (ii) people have an affection for games, and this leads to longer play yielding more entropy overall. While the resulting strings are not perfectly random, we show how to integrate such a game into a robust pseudo-random generator that enjoys backward and forward security.
Randomness plays a central role in computer science, in particular cryptography. Almost all cryptographic primitives depend crucially on randomness because randomness and unpredictability in secret keys provides the means for security. Usually one assumes that perfect randomness, a sequence of independently and uniformly distributed bits, are accessible to algorithms. This is a strong assumption. Physical sources of randomness are neither uniformly random, nor produce necessarily independent bits. Therefore, the aim of this thesis is to start from a realistic model of randomness, investigate notions of secrecy and their randomness requirements and finally find practical methods for generation of randomness that matches the requirements of cryptographic primitives. We consider a model of random source where the source output follows one distribution from a set of possible distributions, each with the property that the maximum probability of symbols is bounded and can not be arbitrarily close to 1. This model does not assume independence or uniformity of the output symbols, and is considered to be a realistic model of randomness. From this point, the thesis can be divided into two main parts: In the first part, considering various notions of information theoretic secrecy, a fundamental problem is to find the properties of randomness needed to achieve security in these notions. Traditional cryptographic protocols simply assume perfect randomness and build on this assumption. We explore the results that show secrecy can not be based on imperfect randomness that is not uniform or independent. Thus a line of work attempts to relax notions of secrecy in such a way that they can be constructed with non-perfect sources, and possibly require smaller key sizes. Yet they should match real life applications. An important work in this context is entropic security where the key size could be smaller than the message depending on message distribution. Inspired by this, we propose two relaxed notions of secrecy that are motivated by practical applications. In the first notion, motivated by an application in biometrics authentication, we propose guessing secrecy where the probability of guessing the message for a computational unbounded adversary with the best strategy remains the same when a ciphertext is given or when it is not. We compare the randomness requirements of guessing secrecy with stronger notions and show that in some cases such as key length, the requirements are the same. For key distribution however, we found a family of distributions that provide guessing secrecy but not perfect secrecy. In the second notion, we investigate randomness requirements of multiple message encryption. Considering a natural extension of secrecy definition to multiple messages, we show that independent keys are needed to encrypt each message. We then propose a relaxed notion in which the security of last message is more important than past messages, although the leakage of past messages is bounded using entropic security. By this assumption, we achieve smaller key length compared to indistinguishability, and comparable to key length for entropic security. This notion has applications such as location privacy. In the second part of the thesis, since secrecy crucially depends on perfect randomness, we investigate how perfect randomness can be practically generated, specifically from human game-play. Unlike many random number generators that assume independent or uniform random bits in the random source, we base our work on the realistic model of randomness. Our main observation is that human game-play has an element of randomness coming from the errors in their game-play which is the main entertaining factor of the game. We also observed that this game-play can distinguish among a group of people if the right features are collected from the game-play. We incrementally changed our game design until the distinguishability among a small population is maximized, and then run the experiments required to show the viability of this approach over a larger population. This approach can also provide a hard to delegate authentication property where a human could not emulate the behavior of another human even given statistical information about their game-play.
Random numbers (RNs) have applications in many areas: lottery games, gambling, computer simulation, and, most importantly, cryptography [N. Gisin et al., Rev. Mod. Phys. 74 (2002) 145]. In cryptography theory, the theoretical security of the system calls for high quality RNs. Therefore, developing methods for producing unpredictable RNs with adequate speed is an attractive topic. Early on, despite the lack of theoretical support, pseudo RNs generated by algorithmic methods performed well and satisfied reasonable statistical requirements. However, as implemented, those pseudorandom sequences were completely determined by mathematical formulas and initial seeds, which cannot introduce extra entropy or information. In these cases, “random” bits are generated that are not at all random. Physical random number generators (RNGs), which, in contrast to algorithmic methods, are based on unpredictable physical random phenomena, have attracted considerable research interest. However, the way that we extract random bits from those physical entropy sources has a large influence on the efficiency and performance of the system. In this manuscript, we will review and discuss several randomness extraction schemes that are based on radiation or photon arrival times. We analyze the robustness, post-processing requirements and, in particular, the extraction efficiency of those methods to aid in the construction of efficient, compact and robust physical RNG systems.
In video games, randomness is produced by invisible mechanisms — a seed, a pseudo-random generator, a probability table, a server call — whereas in physical games the draw has a visible, contestable “stage”. As soon as a game becomes a competition, and in esports in particular, this opacity ceases to be a mere design question and becomes a question of integrity: who generated the randomness, when, from which source, under which transformation, and with which verifiable guarantees? This paper argues that competitive games and cyber-physical competitions need an explicit randomness infrastructure, distinct from the statistical quality of the entropy source alone. Using the case study Quantum Tetris — a Tetris written in Rust/Bevy/WebAssembly whose stochastic decisions are delegated to simulated quantum circuits — we show that a good entropy source does not guarantee fairness: the bias of the “T” tetromino, induced by a 3-bit-to 7-piece mapping table, arises in the transformation layer and not in the source. We then decompose competitive randomness into six layers (entropy source, extraction, distribution policy, mapping function, cryptographic receipt, audit journal) and discuss the realistic contributions of quantum randomness (QRNG, certification via Bell-inequality violation) as well as the cryptographic tools of auditability (verifiable random functions, randomness beacons, verifiable delay functions, signed journals). We finally propose an architecture applicable to esports, competitive online games and cyber-physical games such as autonomous drone racing, and we implement its auditability layers in Quantum Tetris — hash-chained receipts and a commit-reveal journal — whose overhead we measure: on the order of a microsecond per draw, i.e. practically free auditability for a game of this class.
In a public-key encryption scheme, if a sender is not concerned about the security of a message and is unwilling to generate costly randomness, the security of the encrypted message can be compromised. In this work, we characterize such lazy parties, who are regraded as honest parties, but are unwilling to perform a costly task when they are not concerned about the security. Specifically, we consider a rather simple setting in which the costly task is to generate randomness used in algorithms, and parties can choose either perfect randomness or a fixed string. We model lazy parties as rational players who behave rationally to maximize their utilities, and define a security game between the parties and an adversary. Since a standard secure encryption scheme does not work in the setting, we provide constructions of secure encryption schemes in various settings.
Cryptographic protocols, though used in a wide range of everyday tasks, are typically built for certain unrealistic ideal conditions in which the user is assumed to work. For example, one such condition that is implicitly assumed is that the user has perfect randomness that she can use as her cryptographic secret key. Another commonly made assumption is that the user runs her cryptographic tasks (such as encryption) on a device that is perfectly secure; that is, its internals are not tampered with or even observed by an adversary.
In this thesis, we focus on designing cryptographic techniques that are secure under less-than-ideal conditions. In order to remove the assumption that users share perfectly random secret keys, we study the problem of privacy amplification: key agreement between two parties who both know a weak secret w, such as a password. The goal of the protocol is to convert this non-uniform secret w into a uniformly distributed string R that is fully secret from the adversary. R may then be used as a key for running symmetric cryptographic protocols (such as encryption or authentication). Because we make no computational assumptions, the entropy in R can come only from w. Thus such a protocol must minimize the entropy loss during its execution, so that R is as long as possible. In this thesis, we present the first protocol for information-theoretic key agreement that has entropy loss linear in the security parameter. The result is optimal up to constant factors. We also extend our results to the case where the users share correlated secrets w and w' . This setting occurs, for example, when the secrets are biometric readings taken at different points of time and is more generally known as information-reconciliation.
There has been much recent progress in constructing cryptosystems that maintain their security without requiring uniform randomness and perfect secrecy. These schemes are motivated by a diverse set of problems such as providing resilience to side-channel leakage, using weak physical sources of randomness as secret keys, and allowing deterministic encryption for high-entropy messages. Nevertheless, despite this progress, some basic and seemingly achievable security properties have eluded our reach. For example, we are unable to prove the security of basic tools for manipulating weak/leaky random sources, such as as pseudo-entropy generators and seed-dependent computational condensers. We also do not know how to prove leakage-resilient security of any cryptosystem with a uniquely determined secret key. In the context of deterministic encryption we do not have a standard-model constructions achieving the strongest notion of security proposed by Bellare, Boldyreva and O'Neill (CRYPTO '07), that would allow us to encrypt arbitrarily correlated messages of sufficiently large individual entropy.