From the Publisher:
A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.

Handbook of Applied Cryptography

The well-studied task of learning a linear function with errors is a seemingly hard problem and the basis for several cryptographic schemes. Here we demonstrate additional applications that enjoy strong security properties and a high level of efficiency. Namely, we construct: 1 Public-key and symmetric-key cryptosystems that provide security for key-dependent messages and enjoy circular security. Our schemes are highly efficient: in both cases the ciphertext is only a constant factor larger than the plaintext, and the cost of encryption and decryption is only n·polylog(n) bit operations per message symbol in the public-key case, and polylog(n) bit operations in the symmetric-case.
1 Two efficient pseudorandom objects: a "weak randomized pseudorandom function" -- a relaxation of standard PRF -- that can be computed obliviously via a simple protocol, and a length-doubling pseudorandom generator that can be computed by a circuit of n ·polylog(n) size. The complexity of our pseudorandom generator almost matches the complexity of the fastest known construction (Applebaum et al., RANDOM 2006), which runs in linear time at the expense of relying on a nonstandard intractability assumption.


Our constructions and security proofs are simple and natural, and involve new techniques that may be of independent interest. In addition, by combining our constructions with prior ones, we get fast implementations of several other primitives and protocols.

/pdf/fast-cryptographic-primitives-and-circular-secure-encryption-4puhqs7pwg.pdf

Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems

Our main result is a construction of a lattice-based digital signature scheme that represents an improvement, both in theory and in practice, over today’s most efficient lattice schemes. The novel scheme is obtained as a result of a modification of the rejection sampling algorithm that is at the heart of Lyubashevsky’s signature scheme (Eurocrypt, 2012) and several other lattice primitives. Our new rejection sampling algorithm which samples from a bimodal Gaussian distribution, combined with a modified scheme instantiation, ends up reducing the standard deviation of the resulting signatures by a factor that is asymptotically square root in the security parameter. The implementations of our signature scheme for security levels of 128, 160, and 192 bits compare very favorably to existing schemes such as RSA and ECDSA in terms of efficiency. In addition, the new scheme has shorter signature and public key sizes than all previously proposed lattice signature schemes.

/pdf/lattice-signatures-and-bimodal-gaussians-3dj8x434mh.pdf

Lattice Signatures and Bimodal Gaussians

Nearly all of the currently used and well-tested signature schemes (e.g. RSA or DSA) are based either on the factoring assumption or the presumed intractability of the discrete logarithm problem. Further algorithmic advances on these problems may lead to the unpleasant situation that a large number of schemes have to be replaced with alternatives. In this work we present such an alternative --- a signature scheme whose security is derived from the hardness of lattice problems. It is based on recent theoretical advances in lattice-based cryptography and is highly optimized for practicability and use in embedded systems. The public and secret keys are roughly 12000 and 2000 bits long, while the signature size is approximately 9000 bits for a security level of around 100 bits. The implementation results on reconfigurable hardware (Spartan/Virtex 6) are very promising and show that the scheme is scalable, has low area consumption, and even outperforms some classical schemes.

/pdf/practical-lattice-based-cryptography-a-signature-scheme-for-10d8ddh0k8.pdf

Practical lattice-based cryptography: a signature scheme for embedded systems

We study the pseudorandomness of bounded knapsack functions over arbitrary finite abelian groups. Previous works consider only specific families of finite abelian groups and 0-1 coefficients. The main technical contribution of our work is a new, general theorem that provides sufficient conditions under which pseudorandomness of bounded knapsack functions follows directly from their one-wayness. Our results generalize and substantially extend previous work of Impagliazzo and Naor (J. Cryptology 1996).

As an application of the new theorem, we give sample preserving search-to-decision reductions for the Learning With Errors (LWE) problem, introduced by (Regev, STOC 2005) and widely used in lattice-based cryptography. Concretely, we show that, for a wide range of parameters, m LWE samples can be proved indistinguishable from random just under the hypothesis that search LWE is a one-way function for the same number m of samples.

/pdf/pseudorandom-knapsacks-and-the-sample-complexity-of-lwe-4gd4qq2g1f.pdf

Pseudorandom knapsacks and the sample complexity of LWE search-to-decision reductions

We show a simple and efficient construction of a pseudo-random generator based on the intractability of an NP-complete problem from the area of error-correcting codes. The generalor is proved as secure as a hard instance of the syndrome decoding problem. Each application of the scheme generates a linear amount of bits in only quadratic computing time.

/pdf/an-efficient-pseudo-random-generator-provably-as-secure-as-3omddl4p4y.pdf

Jean-Bernard Fischer

Papers

An efficient pseudo-random generator provably as secure as syndrome decoding