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 HKM / HFX cryptosystem is proposed for standardization at the ITU Telecommunication Standardization Sector Study Group 8. It is designed to provide authenticity and confidentiality of FAX messages at a commercial level of security. In addition, the HKM / HFX cryptosystem is designed for unrestricted export.

/pdf/attacks-on-the-hkm-hfx-cryptosystem-3mm55t7kce.pdf

Attacks on the HKM/HFX Cryptosystem

In this paper, we analyze several variants of a simple method for generating prime numbers with fewer random bits. To generate a prime $p$ less than $x$, the basic idea is to fix a constant $q\propto x^{1-\varepsilon}$, pick a uniformly random $a<q$ coprime to $q$, and choose $p$ of the form $a+t\cdot q$, where only $t$ is updated if the primality test fails. We prove that variants of this approach provide prime generation algorithms requiring few random bits and whose output distribution is close to uniform, under less and less expensive assumptions: first a relatively strong conjecture by H.L. Montgomery, made precise by Friedlander and Granville; then the Extended Riemann Hypothesis; and finally fully unconditionally using the Barban-Davenport-Halberstam theorem. We argue that this approach has a number of desirable properties compared to previous algorithms.

Close to Uniform Prime Number Generation With Fewer Random Bits

In this paper we analyze a simple method for generating prime numbers with fewer random bits. Assuming the Extended Riemann Hypothesis, we can prove that our method generates primes according to a distribution that can be made arbitrarily close to uniform. This is unlike the PRIMEINC algorithm studied by Brandt and Damgaard and its many variants implemented in numerous software packages, which reduce the number of random bits used at the price of a distribution easily distinguished from uniform. Our new method is also no more computationally expensive than the ones in current use, and opens up interesting options for prime number generation in constrained environments.

/pdf/close-to-uniform-prime-number-generation-with-fewer-random-3npzwqia2r.pdf

Close to Uniform Prime Number Generation With Fewer Random Bits.

In this paper, we analyze several variants of a simple method for generating prime numbers with fewer random bits. To generate a prime $p$ less than $x$ , the basic idea is to fix a constant $q\propto x^{1- \varepsilon }$ , pick a uniformly random $a coprime to $q$ , and choose $p$ of the form $a+t\cdot q$ , where only $t$ is updated if the primality test fails. We prove that variants of this approach provide prime generation algorithms requiring a few random bits and whose output distribution is close to uniform, under less and less expensive assumptions: first a relatively strong conjecture by H. Montgomery, made precise by Friedlander and Granville; then the Extended Riemann Hypothesis; and finally fully unconditionally using the Barban–Davenport–Halberstam theorem. We argue that this approach has a number of desirable properties compared with the previous algorithms, at least in an asymptotic sense. In particular: 1) it uses much fewer random bits than both the “trivial algorithm” (testing random numbers less than $x$ for primality) and Maurer’s almost uniform prime generation algorithm; 2) the distance of its output distribution to uniform can be made arbitrarily small, unlike algorithms like PRIMEINC (studied by Brandt and Damgard), which we show exhibit significant biases; and 3) all quality measures (number of primality tests, output entropy, randomness, and so on) can be obtained under standard conjectures or even unconditionally, whereas most previous nontrivial algorithms can only be proved based on stronger, less standard assumptions like the Hardy-Littlewood prime tuple conjecture. Note, however, that our analysis involves non-explicit constants, and therefore does not establish the superiority of our approach for concrete parameter sizes.

/pdf/close-to-uniform-prime-number-generation-with-fewer-random-2azn1fhecr.pdf

Many cryptographic algorithms use number theory. They share the problem of generating large primes with a given (fixed) number n of bits. In a series of articles, Brandt, Damgard, Landrock and Pomerance address the problem of optimal use of probabilistic primality proofs for generation of cryptographic primes. Maurer proposed using the Pocklington lemma for generating provable primes. His approach loses efficiency due to involved mechanisms for generating close to uniform distribution of primes. We propose an algorithm which generates provable primes and can be shown to be the most efficient prime generation algorithm up to date. This is possible at the cost of a slight reduction of the set of primes which may be produced by the algorithm. However, the entropy of the primes produced by this algorithm is assymptotically equal to the entropy of primes with random uniform distribution. Primes are sought in arithmetic progressions and proved by recursion. Search in arithmetic progressions allows the use of Eratosthenes sieves, which leads finaly to saving 1/3 of the psuedo prime tests compared to random search.

/pdf/fast-generation-of-provable-primes-using-search-in-2fb613hxd7.pdf

Fast Generation of Provable Primes Using Search in Arithmetic Progressions

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Fast Generation of Provable Primes Using Search in Arithmetic Progressions