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  • Authors: Shacham, Hovav (2005)

  • Digital signatures provide authenticity and nonrepudiation. They are a standard crypto¬graphic primitive with many applications in higher-level protocols. Groups featuring a com¬putable bilinear map are particularly well suited for signature-related primitives. For some signature variants the only construction known uses bilinear maps. Where constructions based on, e.g., RSA are known.. bilinear-map-based constructions are simpler, more efficient. and yield shorter signatures. We describe several constructions that support this claim. First, we present the Boneh-Lynn-Shacham (BLS) short signature scheme. BLS signa¬tures with 1024-bit security are 160 bits long, the shortest of any scheme based on standard assumptions. Second, we present Boneh-Gentry-Lynn-Shacham (BGLS) aggregate s...

  • Thesis


  • Authors: Ulrich, James L (2005)

  • Motivated by a desire to test the security of the pubic key exchange protocol of I. Anshel, M. Anshel, and D. Goldfeld, (“An Algebraic Method for Public-Key Cryptography”, Mathematical Research Letters, vol. 6, pp. 1-5, 1999), we study algorithmic approaches to the simple commutator decision and promise problems (SCDP/SCPP) for the braid groups Bn. We take as our point of departure a seminal paper of O. Ore, (“Some Remarks on Commutators”, Proceedings of the American Mathematical Society, Vol. 2, No. 2, pp.307-314, 1951), which studies the SCPP for the symmetric groups. Our results build on the work of H. Cejtin and I. Rivin, (“A Property of Alternating Groups”, arXiv:math.GR/0303036). We extract, from their proof that any element of the alternating subgroup of Sn can be written as...