The weak password problem: chaos, criticality, and encrypted p-CAPTCHAs

Vulnerabilities related to weak passwords are a pressing global economic and security issue. We report a novel, simple, and effective approach to address the weak password problem. Building upon chaotic dynamics, criticality at phase transitions, CAPTCHA recognition, and computational round-off errors we design an algorithm that strengthens security of passwords. The core idea of our simple method is to split a long and secure password into two components. The first component is memorized by the user. The second component is transformed into a CAPTCHA image and then protected using evolution of a two-dimensional dynamical system close to a phase transition, in such a way that standard brute-force attacks become ineffective. We expect our approach to have wide applications for authentication and encryption technologies. Introduction. – Computer and information security has been subject to intensive research for over 50 years. This included investigation of cryptographic methods, as well as generic security of computing devices, operating systems and networks. However, it is only relatively recently that the importance of the human factor has been given proper attention. Passwords are the common method for authentication and encryption used to secure digital life. Humans have limited capacity to remember passwords and tend to select passwords that are too simple and predictable. Security breaches related to weak passwords are widespread events. Consumers and enterprises around the world are looking for ways to address the weak password problem [1, 2]. In this paper we propose a simple method to address the problem by combining chaotic dynamics, phase transitions, and pattern recognition advantages of the human brain. We do not design a new encryption scheme. Instead we use standard encryption tschemes, and add a littel overhead on top in order to substantially enhance security. A major building block of the proposed algorithm is the dynamic behavior of complex extended non-linear systems, in particular, Hamiltonian lattices close to a phase transition [3, 4]. These systems display non-ergodicity, deterministic chaos [5], and (a)E-mail: [email protected] spontaneous formation of coherent space-time structures. Building upon dynamical chaos and computational roundoff errors and utilizing superiority of the human brain over computers with respect to pattern recognition, our method protects a secret token, which can be used, in combination with a regular password, to derive a secret key for data encryption. It was estimated in 2009 that 86% of US companies use password authentication and encryption [6]. A weak password used with a strong encryption or authentication algorithm potentially makes a computer system vulnerable to brute-force password search attacks. Studies have shown that users will generally address the password complexity problem by using simple predictable passwords [7, 8]. Schneier examined 34,000 MySpace online passwords and concluded that 65% of them contained 8 characters, with most frequently used passwords being “password1”, “abc123”, “myspace1”, and “password” [8]. Other user strategies include using the same password for every account, writing down passwords, storing passwords in files, and reusing or recycling old passwords. Horowitz reported that 15-20% of the users on a regular basis wrote down their password on a Post-it note attached to the computer monitor [8]. Another study found that 66% of users keep password paper records at work and 58% keep passwords in files [8]. p-1 ar X iv :1 10 3. 62 19 v2 [ cs .C R ] 1 J ul 2 01 1 T.V. Laptyeva et al. Vulnerabilities related to weak passwords have significant economic effect globally. Results of a recent study [8,9] revealed that identity fraud affects nearly 5% of consumers, or nearly 10 million people in the USA per year. The total annual cost of identity fraud in the United States was more than $55 billion in 2006 [9]. Vulnerabilities related to weak passwords have significant economic effect globally. Cryptographic science utilizes discrete reversible functions that operate on bit strings and take a secret key as a parameter. As an example, Advanced Encryption Standard (AES) [10] specifies an encryption function approved for use by the US government. AES encrypts data in input/output blocks of 128 bits. The secret key lengths supported by AES are 128, 192, and 256 bits. These long key lengths were selected to make brute-force attacks infeasible. Over the years, a number of more sophisticated cryptanalysis attacks were described for various cryptographic algorithms. Such attacks are usually very technical and algorithm-specific and rely on finding statistical correlations in the cryptographic function to extract information on the cryptographic key. However, an ideal cryptographic function depends on its inputs in a completely random way with no correlations present. Therefore, a brute search attack remains the essential attack used in real world to compromise cryptographic algorithms. For a completely random secret key used with the AES algorithm, a brute-force attack is presently infeasible and will probably remain so in the future. The situation changes dramatically, when the key is limited to a smaller subspace of keys. A common situation is that the key is either a password, memorized by a human, or is derived from a password using a function known to the attacker. A brute search over a small subspace can then be done efficiently. A typical brute-force search attack requires that the attacker is in possession of the encrypted text (Ciphertext) C, and that the true key belongs to a subspace of keys S. The attacker can mount a Ciphertext-Only Attack by iterating through the space S and attempting to decrypt C in each case into a Candidate Plain Text. Now the attacker needs to determine whether it is the True Plain Text. This Recognition Problem is, therefore, a necessary part of Ciphertext-Only Attack, and amounts to designing an efficient algorithm denoted as the Recognition Oracle (RO). Implementations of ROs make use of the block-encryption structure, standard file formats, and correlations in True Plain Text. Proposed scheme. – We assume that a confidential data file (D) is encrypted by a symmetric encryption algorithm, such as AES. We also assume that the encryption and decryption are done by the same person, therefore we do not address vulnerabilities due to messenger capture attacks when transmitting passwords. The encryption key EK is a combination of a reasonable-strength password component, which we denote as Short Password SP and an additional Strong Key SK: EK=SP+SK. The difference between the proposed method and existing cryptographic technologies is that the user is not asked to memorize SK. Instead, the graphical representation of SK is embedded into a two-dimensional Image of Strong Key of a momentary initial state (IS) of a nonlinear Hamiltonian two-dimensional lattice system. This embedding is similar to embeddings used in Completely Automated Public Turing test to tell Computers and Humans Apart (CAPTCHAs) [11–13], therefore, we also coin it password CAPTCHA or p-CAPTCHA. A time evolution of the twodimensional lattice is then performed. The chaotic evolution transforms the p-CAPTCHA into a chaotic final lattice state (FS). Since our Hamiltonian system is close to a phase transition, this chaotic state will contain regularities at various space scales, such as a domain structures. Therefore the level of spatial correlations is the same both for IS and FS. If one encodes lattice site positions and velocities using floating point numbers, these regularities will be manifested in the first half of the digits (the moresignificant bits) of such an encoding. The second half of the digits (the less-significant bits) will have a pseudorandom nature due to the dynamical chaos in the system. at D a D cr pt on e y i