Handbook of Applied Cryptography

Menezes, Alfred; Oorschot, Paul C. van; Vanstone, Scott A.

doi:10.1201/9781439821916

Cited by 2,380 publications

(531 citation statements)

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“…As the problem of finding the shortest addition chain is NPcomplete [17], practical algorithms for exponentiation without a division operation have been studied such as the binary method, the m-ary method, window methods [31,34,41,52], exponent-folding methods [33,49], and precomputation methods [7,32]. For a group where the inversion operation is efficient like elliptic curve cryptosystems [30,35], an addition-subtraction chain can yield a good performance [38].…”

Section: Introductionmentioning

confidence: 99%

Fast batch modular exponentiation with common-multiplicand multiplication

Seo

Park

2018

Information Processing Letters

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Section: Introductionmentioning

confidence: 99%

Fast batch modular exponentiation with common-multiplicand multiplication

Seo

Park

2018

Information Processing Letters

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“…-Encryption requires only two exponentiations (and not three), because most of the work done to compute V r can be reused to compute V r/π(B) , regardless of the exponentiation algorithm used (whether straight double-and-add, or one of the many efficient window methods; cf., e.g., [30]). -Decryption can similarly be performed in about a single exponentiation (instead of two), by computingC π(B) asD π(B)·Sk , which uses the same generator asD Sk and thus shares the same intermediate powers.…”

Section: Operational Efficiencymentioning

confidence: 99%

Miniature CCA2 PK Encryption: Tight Security Without Redundancy

Boyen¹

Advances in Cryptology – ASIACRYPT 2007

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Abstract. We present a minimalist public-key cryptosystem, as compact as ElGamal, but with adaptive chosen-ciphertext security under the gap Diffie-Hellman assumption in the random oracle model. The novelty is a dual-hash device that provides tight redundancy-free implicit validation. Compared to previous constructions, ours features a tight security reduction, both in efficacy and efficiency, to a classic and essentially non-interactive complexity assumption, and without resorting to asymmetric/symmetric-key hybrid constructions. The system is very compact: on elliptic curves with 80-bit security, a 160-bit plaintext becomes a 320-bit ciphertext. It is also very simple and has a number of practical advantages, and we hope to see it adopted widely.

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“…Now the standard continuation is to use the method of multi-exponentiation combined with the Frobenius [12], so that the final exponentiation is the calculation of…”

Section: Final Exponentiationmentioning

confidence: 99%

“…We made the choice of multiplication and squaring algorithms based on the exhaustive testing described in [10]. Karatsuba Chung-Hasan SQR2 F p 12 Karatsuba Complex…”

Section: Finite Field Arithmeticmentioning

confidence: 99%

Implementing Cryptographic Pairings over Barreto-Naehrig Curves

Devegili

Scott

Dahab

Pairing-Based Cryptography – Pairing 2007

111

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Abstract. In this paper we describe an efficient implementation of the Tate and Ate pairings using Barreto-Naehrig pairing-friendly curves, on both a standard 32-bit PC and on a 32-bit smartcard. First we introduce a sub-family of such curves with a particularly simple representation. Next we consider the issues that arise in the efficient implementation of field arithmetic in F p 12 , which is crucial to good performance. Various optimisations are suggested, including a novel approach to the 'final exponentiation', which is faster and requires less memory than the methods previously recommended.

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Handbook of Applied Cryptography

Cited by 2,380 publications

References 0 publications

Fast batch modular exponentiation with common-multiplicand multiplication

Fast batch modular exponentiation with common-multiplicand multiplication

Miniature CCA2 PK Encryption: Tight Security Without Redundancy

Implementing Cryptographic Pairings over Barreto-Naehrig Curves

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