By Yiming Jing, Gail-Joon Ahn, Hongxin Hu (auth.), Goichiro Hanaoka, Toshihiro Yamauchi (eds.)

This publication constitutes the refereed lawsuits of the seventh overseas Workshop on safety, IWSEC 2012, held in Fukuoka, Japan, in November 2012. The sixteen revised chosen papers offered during this quantity have been rigorously reviewed and chosen from fifty three submissions. they're prepared in topical sections named: implementation; encryption and key trade; cryptanalysis; and safe protocols.

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M (or M−1 ) induces a group isomorphism between E(Fp ) and Edd . Example 2 (embedding degree 16). 3: 1 (2x5 + 41x + 35), 35 r(x) = x8 + 48x4 + 625, 1 (x10 + 2x9 + 5x8 + 48x6 + 152x5 + 240x4 + 625x2 + 2398x + 3125). 250, which is minimal. We choose parameters of 160-bit security level, and thus, r(x) is 321( 320) bits. We have a parameter (t, r, p) from this family: t =94214916718141455091342235761227844718201546014893892748927714, r =2292694845382374047698454660181934086354941621399707011613780070// 697827842713365290625541067244113 (321-bit), p =27738907913157391241888841689555045766744968140788405824011445844// 78218136859751438675039143383901154081701677760538397710213 (411-bit).

EUROCRYPT 2006. LNCS, vol. 4004, pp. 445–464. Springer, Heidelberg (2006) 24. : The Eta Pairing Revisited. IEEE Transactions on Information Theory 52, 4595–4602 (2006) 25. : Twisted Edwards Curves Revisited. In: Pieprzyk, J. ) ASIACRYPT 2008. LNCS, vol. 5350, pp. 326–343. Springer, Heidelberg (2008) 26. : Another Approach to Pairing Computation in Edwards Coordinates. , Das, A. ) INDOCRYPT 2008. LNCS, vol. 5365, pp. 400–413. Springer, Heidelberg (2008) 27. : Constructing Brezing-Weng PairingFriendly Elliptic Curves Using Elements in the Cyclotomic Field.

1 In the remainder of the paper we refer to instruction cycles as cycles. -N. Chen et al. (a) Software simulator (b) In-circuit emulator (c) Target board Fig. 1. 1 Montgomery Multiplication Montgomery multiplication introduced by Peter Montgomery is commonly used in modular arithmetic. It computes (A × B × 2−nt mod M) instead of (A × B mod M) to avoid expensive modular operations (divisions). Figure 2 provides the typical Montgomery multiplication, where A and B are the two operands, M is the modulus, A[], B[], M[] are their (2t )-ary representation, m = (−M[0])−1 mod 2t , and 0 ≤ A, B, M < 2nt as well as 0 ≤ A[i], B[i], M[i] ≤ 2t − 1 for all 0 ≤ i ≤ n − 1.

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