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By Alt R., Vignes J.

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5σ 2 2n−τ ±prp Advauth (t , 2σ) + n + n OCB1[E,τ ] (t, σ) ≤ AdvE 2 2 −1 ✷ where t = t + cnσ for some absolute constant c. Propositions 1 and 2 establish that n = 128 and n = 64 satisfy the requirement for unique representations. They also guarantee that there is no representative of 1 within [1 .. 2n/2 ] × {0, 1}. To see this, note that the propositions imply that (0, 0) is the only representative for 1 within a space I1 × I2 that includes [1 .. 2n/2 ] × {0, 1}, and so there can be no representative of 1 within a subspace of I1 × I2 that excludes (0, 0).

M. Bellare, A. Desai, E. Jokipii, and P. Rogaway. A concrete security treatment of symmetric encryption: Analysis of the DES modes of operation. Symposium on Foundations of Computer Science, FOCS ’97, IEEE Computer Society, pp. 394–403, 1997. 2. M. Bellare, J. Kilian, and P. Rogaway. The security of the cipher block chaining message authentication code. Journal of Computer and System Sciences, vol. 61, no. 3, Dec 2000. Earlier version in CRYPTO ’94. 3. M. Bellare, P. Rogaway, and D. Wagner. The EAX Mode of operation.

K ∈ G of bases and a set I1 × · · · × Ik ⊆ Zk of allowed indices. We say that the choice of parameters provides unique representations if for every (i1 , . . , ik ), (j1 , . . , jk ) ∈ I1 × · · · × Ik we have that ✷ α1i1 · · · αkik = α1j1 · · · αkjk implies (i1 , . . , ik ) = (j1 , . . , jk ). In other words, representable points are uniquely representable: any group element α1i1 · · · αkik that can be represented using allowed indices can be represented in only one way (using allowed indices).

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10th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics by Alt R., Vignes J.


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