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This paper discusses several Montgomery multiplication algorithms, two of which h a ve been proposed before. We describe three additional algorithms, and analyze in detail the space and time requirements of all ve methods. These algorithms have been implemented in C and in assembler. The analyses and actual performance results indicate that the Coarsely… (More)

We initiate a provable-security treatment of cryptographic agility. A primitive (for example PRFs, authenticated encryption schemes or digital signatures) is agile when multiple, individually secure schemes can securely share the same key. We provide a surprising connection between two seemingly unrelated but challenging questions. The first, new to this… (More)

- C K Ko, T Acar
- 1998

We show that the multiplication operation c = a br ,1 in the eld GF2 k can be implemented signiicantly faster in software than the standard multiplication, where r is a special xed element of the eld. This operation is the nite eld analogue of the Montgomery multiplication for modular multiplication of integers. We give the bit-level and word-level… (More)

We present a new algorithm for computing a e where a 2 GF2 k and e is a positive integer. The proposed algorithm is more suitable for implementation in software , and relies on the Montgomery multiplication in GF2 k. The speed of the exponentiation algorithm largely depends on the availability of a fast method for multiplying two polynomials of length w… (More)

This paper introduces and formalizes homomorphic proofs that allow 'adding' proofs and proof statements to get a new proof of the 'sum' statement. Additionally, we introduce a construction of ho-momorphic proofs, and show an accumulator scheme with delegatable non-membership proofs (ADNMP) as one of its applications with prov-able security. Finally, the… (More)

We report on relative performance numbers for affine and projective pairings on a dual-core Cortex A9 ARM processor. Using a fast inversion in the base field and doing inversion in extension fields by using the norm map to reduce to inversions in smaller fields, we find a very low ratio of inversion-to-multiplication costs. In our implementation , this… (More)

This work introduces the most efficient universal accumula-tor known today. For the first time, we have an accumulator which does not depend on hidden order groups, does not require any exponentia-tions in the target group associated with the pairing function, and only requires two pairings to verify a proof-of-knowledge of a witness. We present… (More)

- Tolga Acar
- 1997

approved: C etin K. Ko c Computer and network security systems rely on the privacy and authenticity of information, which requires implementation of cryptographic functions. Software implementations of these functions are often desired because of their exibility and cost eeec-tiveness. In this study, w e concentrate on developing high-speed and area-eecient… (More)