International Association for Cryptologic Research

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2015-02-24
04:17 [Pub][ePrint]

This work extends the line of research on the hidden number problem. Motivated by studying bit security in finite fields, we define the multivariate hidden number problem. Here, the secret and the multiplier are vectors, and partial information about their dot product is given. Using tools from discrete Fourier analysis introduced by Akavia, Goldwasser and Safra, we show that if one can find the significant Fourier coefficients of some function, then one can solve the multivariate hidden number problem for that function. This allows us to generalise the work of Akavia on the hidden number problem with (non-adaptive) chosen multipliers to all finite fields.

We give two further applications of our results, both of which generalise previous works to all (finite) extension fields. The first considers the general (random samples) hidden number problem in F_{p^m} and assumes an advice is given to the algorithm. The second considers a model that allows changing representations, where we show hardness of individual bits for elliptic curve and pairing based functions for elliptic curves over extension fields, as well as hardness of any bit of any component of the Diffie-Hellman secret in F_{p^m} (m>1).

04:17 [Pub][ePrint]

In this paper, we introduce a new functionality for proxy re-encryption (PRE) that we call re-encryption verifiability. In a PRE scheme with re-encryption verifiability (which we simply call verifiable PRE, or VPRE), a receiver of a re-encrypted ciphertext can verify whether the received ciphertext is correctly transformed from an original ciphertext by a proxy, and thus can detect illegal activities of the proxy. We formalize the security model for a VPRE scheme, and show that the single-hop uni-directional PRE scheme by Hanaoka et al. (CT-RSA 2012) can be extended to a secure VPRE scheme.

04:17 [Pub][ePrint]

In typical applications of homomorphic encryption, the first step consists for Alice to encrypt some plaintext m under Bob\'s public key pk and to send the ciphertext c = HE_pk(m) to some third-party evaluator Charlie. This paper specifically considers that first step, i.e. the problem of transmitting c as efficiently as possible from Alice to Charlie. As previously noted, a form of compression is achieved using hybrid encryption. Given a symmetric encryption scheme E, Alice picks a random key k and sends a much smaller ciphertext c′ = (HE_pk(k), E_k(m)) that Charlie decompresses homomorphically into the original c using a decryption circuit.

In this paper, we revisit that paradigm in light of its concrete implementation constraints; in particular E is chosen to be an additive IV-based stream cipher. We propose 2 new designs such that the decryption circuit has very small multiplicative depth, typically between 8 and 12 for 128-bit security. Our first construction of depth 12 is inspired by Trivium and reportedly the current fastest option. Our second construction, based on exponentiation in binary fields, is impractical but sets the lowest depth record to 8 for 128-bit security.

04:17 [Pub][ePrint]

We define ideal functionalities that are weaker than ideal functionalities traditionally used in realizing variable input length (VIL) random oracles (RO) in the indifferentiability or universal-Composability (UC) model. We also show realization of VIL-RO using these weaker ideal functionalities, with applications to proving Fugue and CubeHash hash functions to be VIL-RO. We argue that components of Fugue realize this weaker ideal functionality using techniques employed in proving resistance of Fugue to differential collision-attacks. This should be contrasted with other hash functions that are proven VIL-RO assuming the components are extremely ideal, e.g. random permutations.

04:17 [Pub][ePrint]

Resource constraints in smart devices demand an efficient cryptosystem that allows for low power and memory consumption. This has led to popularity of comparatively efficient Elliptic curve cryptog-raphy (ECC). Prior to this paper, much of ECC is implemented on re-configurable hardware i.e. FPGAs, which are costly and unfavorable as low-cost solutions.

We present comprehensive yet efficient implementations of ECC on fixed-point TMS54xx series of digital signal processors (DSP). 160-bit prime field GF(p) ECC is implemented over a wide range of coordinate choices. This paper also implements windowed recoding technique to provide better execution times. Stalls in the programming are mini-mized by utilization of loop unrolling and by avoiding data dependence. Complete scalar multiplication is achieved within 50 msec in coordinate implementations, which is further reduced till 25 msec for windowed-recoding method. These are the best known results for fixed-point low power digital signal processor to date.

04:17 [Pub][ePrint]

This paper is devoted to the design of a 258-bit multiplier for computing pairings over Barreto-Naehrig (BN) curves at 128-bit security level. The proposed design is optimized for Xilinx ﬁeld programmable gate array (FPGA). Each 258-bit integer is represented as a polynomial with ﬁve, 65 bit signed integer, coefficients. Exploiting this splitting we designed a pipelined 65-bit multiplier based on new Karatsuba- Ofman variant using non-standard splitting to ﬁt to the Xilinx embedded digital signal processor (DSP) blocks. We prototype the coprocessor in two architectures pipelined and serial on a Xilinx Virtex-6 FPGA using around 17000 slices and 11 DSPs in the pipelined design and 7 DSPs in the serial. The pipelined 128-bit pairing is computed in 1. 8 ms running at 225MHz and the serial is performed in 2.2 ms running at 185MHz. To the best of our knowledge, this implementation outperforms all reported hardware designs in term of DSP use.

Keywords-

04:17 [Pub][ePrint]

Hardcore lemmas are results in complexity theory which state that average-case hardness must have a very hard kernel\'\', that is a subset of instances where the given problem is extremely hard. They find important applications in hardness amplification. In this paper we revisit the following two fundamental results:

\\begin{enumerate}[(a)]

\\item The hardcore lemma for unpredictability, due to Impagliazzo (FOCS \'95). It states that if a boolean function $f$ is moderately\'\' hard to predict on average, then there must be a set of noticeable size on which $f$ is extremely\'\' hard to predict.

\\item The hardcore lemma for indistinguishability, proved by Maurer and Tessaro (TCC\'10), states that for two random variables $X$ and $Y$ which are $\\epsilon$-computationally close, there are events $A$ and $B$ of probability $1-\\epsilon$ such that the distributions of $X|A$ and $Y|B$ are computationally\'\' identical.

\\end{enumerate}

Using only the standard min-max theorem and some basic facts about convex approximations in $L_p$ spaces, we provide alternative modular proofs and some generalizations of these results in the nonuniform setting, achieving best possible bounds for (a) and slightly improving the known bounds for (b). As an interesting application, we show a strengthening of the transformation between two most popular pseudoentropy variants: HILL and Metric Entropy, and apply it to show how to extract pseudorandomness from a sequence of metric-entropy sources of poor quality. In this case we significantly improve security parameters, comparing to the best known techniques.

04:17 [Pub][ePrint]

In this paper, we introduce and study a new cryptographic primitive that we call \"puncturable key encapsulation mechanism\" (PKEM), which is a special class of KEMs that satisfy some functional and security requirements that, combined together, imply chosen ciphertext security (CCA security). The purpose of introducing this primitive is to capture certain common patterns in the security proofs of the several existing CCA secure public key encryption (PKE) schemes and KEMs based on general cryptographic primitives which (explicitly or implicitly) use the ideas and techniques of the Dolev-Dwork-Naor (DDN) construction (STOC\'91), and \"break down\" the proofs into smaller steps, so that each small step is easier to work with/verify/understand than directly tackling CCA security.

To see the usefulness of PKEM, we show (1) how several existing constructions of CCA secure PKE/KEM constructed based on general cryptographic primitives can be captured as a PKEM, which enables us to understand these constructions via a unified framework, (2) its connection to detectable CCA security (Hohenberger et al. EUROCRYPT\'12), and (3) a new security proof for a KEM-analogue of the DDN construction from a set of assumptions: \"sender non-committing encryption\" (SNCE) and non-interactive witness indistinguishable proofs.

Then, as our main technical result, we show how to construct a PKEM satisfying our requirements (and thus a CCA secure KEM) from a new set of general cryptographic primitives: \"SNCE\" and \"symmetric key encryption secure for key-dependent messages\" (KDM secure SKE). Our construction realizes the \"decrypt-then-re-encrypt\"-style validity check of a ciphertext which is powerful but in general has a problem of the circularity between a plaintext and a randomness.We show how SNCE and KDM secure SKE can be used together to overcome the circularity. We believe that the connection among three seemingly unrelated notions of encryption primitives, i.e. CCA security, the sender non-committing property, and KDM security, to be of theoretical interest.

2015-02-23
22:17 [Pub][ePrint]

Secure transmission of message was the concern of early men. Several techniques have been developed ever since to assure that the message is understandable only by the sender and the receiver while it would be meaningless to others. In this century, cryptography has gained much significance. This paper proposes a scheme to generate a Dynamic Key-dependent S-Box for the SubBytes Transformation used in Cryptographic Techniques.

22:17 [Pub][ePrint]

Linear and differential cryptanalysis and their generalizations are the most important tools in ststistical analysis of symmetric ciphers.

These attacks make use of linear and differential properties of Sboxes and component functions of symmetric ciphers. In this

article, we investigate generalized statistical properties for Sboxes. We justify the application of linear, differential and differential-linear

cryptanalysis from the mathematical viewpoint. We verify some well-known Sboxes and vectotial Boolean functions by the proposed

criteria and show that these functions have larger biases compared with previous criteria presentesd up to now.

22:17 [Pub][ePrint]

This paper presents several methods for reducing the number of bit operations for multiplication of polynomials over the binary field. First, a modified Bernstein\'s 3-way algorithm is introduced, followed by a new 5-way algorithm. Next, a new 3-way algorithm that improves asymptotic arithmetic complexity compared to Bernstein\'s 3-way algorithm is introduced. This new algorithm uses three multiplications of one-third size polynomials over the binary field and one multiplication of one-third size polynomials over the finite field with four elements. Unlike Bernstein\'s algorithm, which has a linear delay complexity with respect to input size, the delay complexity of the new algorithm is logarithmic. The number of bit operations for the multiplication of polynomials over the finite field with four elements is also computed. Finally, all these new results are combined to obtain improved complexities.