A General Analysis of the Security of Elastic Block Ciphers

We analyze the security of elastic block ciphers in general to show that an attack on an elastic version of block cipher implies a polynomial time related attack on the fixed-length version of the block cipher. We relate the security of the elastic version of a block cipher to the fixed-length version by forming a reduction between the versions. Our method is independent of the specific block cipher used. The results imply that if the fixed-length version of a block cipher is secure against attacks which attempt key recovery then the elastic version is also secure against such attacks

Elastic Block Ciphers: Method, Security and Instantiations

We introduce the concept of an elastic block cipher which refers to stretching the supported block size of a block cipher to any length up to twice the original block size while incurring a computational workload that is proportional to the block size. Our method uses the round function of an existing block cipher as a black box and inserts it into a substitution- permutation network. Our method is designed to enable us to form a reduction between the elastic and the original versions of the cipher. Using this reduction, we prove that the elastic version of a cipher is secure against key-recovery attacks if the original cipher is secure against such attacks. We note that while reduction-based proofs of security are a cornerstone of cryptographic analysis, they are typical when complete components are used as sub-components in a larger design. We are not aware of the use of such techniques in the case of concrete block cipher designs. We demonstrate the general applicability of the elastic block cipher method by constructing examples from existing block ciphers: AES, Camellia, MISTY1, and RC6. We compare the performance of the elastic versions to that of the original versions and evaluate the elastic versions using statistical tests measuring the randomness of the ciphertext. We also use our examples to demonstrate the concept of a generic key schedule for block ciphers

Elastic Block Ciphers in Practice: Constructions and Modes of Encryption

We demonstrate the general applicability of the elastic block cipher method by constructing examples from existing block ciphers: AES, Camellia, MISTY1 and RC6. An elastic block cipher is a variable-length block cipher created from an existing fixed-length block cipher. The elastic version supports any block size between one and two times that of the original block size. We compare the performance of the elastic versions to that of the original versions and evaluate the elastic versions using statistical tests measuring the randomness of the ciphertext. The benefit, in terms of an increased rate of encryption, of using an elastic block cipher varies based on the specific block cipher and implementation. In most cases, there is an advantage to using an elastic block cipher to encrypt blocks that are a few bytes longer than the original block length. The statistical test results indicate no obvious flaws in the method for constructing elastic block ciphers. We also use our examples to demonstrate the concept of a generic key schedule for block ciphers. In addition, we present ideas for new modes of encryption using the elastic block cipher construction

Methods for Linear and Differential Cryptanalysis of Elastic Block Ciphers

The elastic block cipher design employs the round function of a given, b-bit block cipher in a black box fashion, embedding it in a network structure to construct a family of ciphers in a uniform manner. The family is parameterized by block size, for any size between b and 2b. The design assures that the overall workload for encryption is proportional to the block size. When considering the approach taken in elastic block ciphers, the question arises as to whether cryptanalysis results, including methods of analysis and bounds on security, for the original fixed-sized cipher are lost or, since original components of the cipher are used, whether previous analysis can be applied or reused in some manner. With this question in mind, we analyze elastic block ciphers and consider the security against two basic types of attacks, linear and differential cryptanalysis. We show how they can be related to the corresponding security of the fixed-length version of the cipher. Concretely, we develop techniques that take advantage of relationships between the structure of the elastic network and the original version of the cipher, independently of the cipher. This approach demonstrates how one can build upon existing components to allow cryptanalysis within an extended structure (a topic which may be of general interest outside of elastic block ciphers). We show that any linear attack on an elastic block cipher can be converted efficiently into a linear attack on the fixed-length version of the cipher by converting the equations used to attack the elastic version to equations for the fixed-length version. We extend the result to any algebraic attack. We then define a general method for deriving the differential characteristic bound of an elastic block cipher using the differential bound on a single round of the fixed-length version of the cipher. The structure of elastic block ciphers allows us to use a state transition method to compute differentials for the elastic version from differentials of the round function of the original cipher

The Security of Elastic Block Ciphers Against Key-Recovery Attacks

We analyze the security of elastic block ciphers against key-recovery attacks. An elastic version of a fixed-length block cipher is a variable-length block cipher that supports any block size in the range of one to two times the length of the original block. Our method for creating an elastic block cipher involves inserting the round function of the original cipher into a substitution-permutation network. In this paper, we form a polynomial-time reduction between the elastic and original versions of the cipher by exploiting the underlying network structure. We prove that the elastic version of a cipher is secure against a given key-recovery attack if the original cipher is secure against such an attack. Our analysis is based on the general structure of elastic block ciphers (i.e., the network‘s structure, the composition methods between rounds in the network and the keying methodology) and is independent of the specific cipher

Best Effort and Practice Activation Codes

Activation Codes are used in many different digital services and known by many different names including voucher, e-coupon and discount code. In this paper we focus on a specific class of ACs that are short, human-readable, fixed-length and represent value. Even though this class of codes is extensively used there are no general guidelines for the design of Activation Code schemes. We discuss different methods that are used in practice and propose BEPAC, a new Activation Code scheme that provides both authenticity and confidentiality. The small message space of activation codes introduces some problems that are illustrated by an adaptive chosen-plaintext attack (CPA-2) on a general 3-round Feis- tel network of size 2^(2n) . This attack recovers the complete permutation from at most 2^(n+2) plaintext-ciphertext pairs. For this reason, BEPAC is designed in such a way that authenticity and confidentiality are in- dependent properties, i.e. loss of confidentiality does not imply loss of authenticity.Comment: 15 pages, 3 figures, TrustBus 201

Constructing Variable-Length PRPs and SPRPs from Fixed-Length PRPs

We create variable-length pseudorandom permutations (PRPs) and strong PRPs (SPRPs) accepting any input length chosen from the range of b to 2b bits from fixed-length, b-bit PRPs. We utilize the elastic network that underlies the recently introduced concrete design of elastic block ciphers, exploiting it as a network of PRPs. We prove that three and four-round elastic networks are variable-length PRPs and five-round elastic networks are variable-length SPRPs, accepting any input length that is fixed in the range of b to 2b bits, when the round functions are independently chosen fixed-length PRPs on b bits. We also prove that these are the minimum number of rounds required

Computational and Energy Costs of Cryptographic Algorithms on Handheld Devices

Networks are evolving toward a ubiquitous model in which heterogeneous devices are interconnected. Cryptographic algorithms are required for developing security solutions that protect network activity. However, the computational and energy limitations of network devices jeopardize the actual implementation of such mechanisms. In this paper, we perform a wide analysis on the expenses of launching symmetric and asymmetric cryptographic algorithms, hash chain functions, elliptic curves cryptography and pairing based cryptography on personal agendas, and compare them with the costs of basic operating system functions. Results show that although cryptographic power costs are high and such operations shall be restricted in time, they are not the main limiting factor of the autonomy of a device

Elastic Block Ciphers: The Basic Design

We introduce the concept of an elastic block cipher, which refers to stretching the supported block size of a block cipher to any length up to twice the original block size while incurring a computational workload that is proportional to the block size. We define a method for converting any existing block cipher into an elastic block cipher and mention our analysis of the construction