Efficient Algorithms for Pairing-Based Cryptosystems

By Paulo L. Barreto, Hae Yong Kim, Ben Lynn, Michael Scott. Annual International Cryptology Conference, 2002

1,139 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Information Systems

View Paper: https://www.semanticscholar.org/paper/751cf0dd2237bc8243b9bef842e4a722ff6abb39

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Citations in the corpus

Multipurpose Identity-Based Signcryption (A Swiss Army Knife for Identity-Based Cryptography) (2003, methodology): “It is based on an elliptic-curve implementation of the BDH parameter generator G, which we describe following [2,14] as recently generalized in [6].”
An Identity-Based Signature from Gap Diffie-Hellman Groups (2003, methodology): “(Very recently, an efficient implementation of Tate pairing over an elliptic curve with odd characteristic was announced in [BKS02].”
A One Round Protocol for Tripartite Diffie–Hellman (2000, background): “Of course, in that case, speed is of the essence and recent results show that it is possible to improve upon Miller’s algorithm by using numerous tricks (see [13] and [4]).”
Enhanced Privacy ID from Bilinear Pairing for Hardware Authentication and Attestation (2010, methodology): “1 Admissible Bilinear Map from the Tate Pairing We first review the description of an admissible bilinear map [5, 31, 36] from the Tate pairing.”
Faster Explicit Formulas for Computing Pairings over Ordinary Curves (2011, methodology): “When generalizing the denominator-free version [21] of Miller's Algorithm for computing the pairing aopt with the set of implementationfriendly parameters suggested by [10] at the 128-bit security level, we obtain Algorithm 1.”
Certificate-Based Encryption and the Certificate Revocation Problem (2003, neutral): “57 ms to compute on a Pentium III 1 GHz [3], a single PC can easily handle the computation.”
Identity-Based Encryption from the Weil Pairing (2001, neutral): “We note that both encryption and decryption in FullIdent can be made faster by using the Tate pairing on elliptic curves rather than the Weil pairing [19, 1].”
Certificateless Public Key Cryptography (2003, neutral): “We refer to [3, 6, 7, 12] for a more comprehensive description of how these groups, pairings and other parameters should be selected in practice for efficiency and security.”
Hierarchical ID-Based Cryptography (2002, background): “We note that the Weil and Tate pairings associated with supersingular elliptic curves or abelian varieties can be modified to create such bilinear maps, as in [13, 5, 7]; see also [14, 2].”
Location-based compromise-tolerant security mechanisms for wireless sensor networks (2006, methodology): “We refer to [19], [20] for a more comprehensive description of how these pairing parameters should be selected in practice for efficiency and security.”
Anonymous Hierarchical Identity-Based Encryption (Without Random Oracles) (2006, background): “One can also exploit the fact that all the k··· are fixed for a given recipient to perform advantageous pre-computations [3].”
Succinct Non-Interactive Zero Knowledge for a von Neumann Architecture (2014, background): “The instantiation of G1 and G2 depends on the choice of e; typically, G1 is instantiated as an order-r subgroup of E(Fq), while, for efficiency reasons [7, 8], G2 as an orderr subgroup of E ′(Fk/d) where E ′ is a d-th twist of E.”
An Efficient Conditional Privacy-Preserving Authentication Scheme for Vehicular Sensor Networks Without Pairings (2016, neutral): “Since the computation cost of one pairing operation is three or more times that of a one point multiplication operation [12], [28], Shim’s scheme requires heavy computation cost in the signature verification phase, where three multiplication point operations and three”
New Software Speed Records for Cryptographic Pairings (2010, methodology): “Since the introduction of Miller’s algorithm [28, 29] for computing pairings on elliptic curves, a lot of research has been devoted to finding the most efficient Tate-pairing variants for different security levels by constructing suitable pairingfriendly elliptic curves [20] and by making specific c”
A Taxonomy of Pairing-Friendly Elliptic Curves (2010, methodology): “The second method, due to Kachisa, Schaefer, and Scott [38] is to ﬁnd a non-cyclotomic polynomial r ( x ) such that K = Q [ x ] / ( r ( x )) is isomorphic to the cy-clotomic ﬁeld Q ( ζ ‘ ).”