zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Efficient elliptic curve scalar multiplication algorithms resistant to power analysis. (English) Zbl 1111.94013
Summary: This paper presents four algorithms for securing elliptic curve scalar multiplication against power analysis. The highest-weight binary form (HBF) of scalars and randomization are applied to resist power analysis. By using a special method to recode the scalars, the proposed algorithms do not suffer from simple power analysis (SPA). With the randomization of the secret scalar or base point, three of the four algorithms are secure against differential power analysis (DPA), refined power analysis (RPA) and zero-value point attacks (ZPA). The countermeasures are also immune to the doubling attack. Fast Shamir’s method is used in order to improve the efficiency of parallel scalar multiplication. Compared with previous countermeasures, the new countermeasures achieve higher security and do not impact overall performance.

14G50Applications of algebraic geometry to coding theory and cryptography
Full Text: DOI
[1] Akishita, T.; Takagi, T.: Zero-value point attacks on elliptic curve cryptosystem. Lncs 2851, 218-233 (2003) · Zbl 1255.94052
[2] Coron, J.: Resistance against differential power analysis for elliptic curve cryptosystem. Lncs 1717, 292-302 (1999) · Zbl 0955.94009
[3] Chevallier-Mames, B.; Ciet, M.; Joye, M.: Low-cost solutions for preventing simple side-channel analysis: side-channel atomicity. IEEE trans. Comput. 53, No. 6, 760-768 (2004) · Zbl 1300.94045
[4] Clavier, C.; Joye, M.: Universal exponentiation algorithm -- a first step towards provable SPA-resistance. Lncs 2162, 300-308 (2001) · Zbl 1007.68995
[5] Ciet, M.; Joye, M.: (Virtually) free randomization technique for elliptic curve cryptography. Lncs 2836, 348-359 (2003) · Zbl 1300.94047
[6] W. Fischer, C. Giraud, E.W. Knudsen, J.P. Seifert, Parallel scalar multiplication on general elliptic curves over Fp hedged against non-differential side-channel attacks. Cryptology ePrint Archive, Report 2002/007, IACR, January 2002. Available from: <http://eprint.iacr.org/2002/007/>.
[7] Fouque, P. A.; Valette, F.: The doubling attack-why upwards is better than downwards. Lncs 2779, 269-280 (2003) · Zbl 1274.94066
[8] Izu, T.; Takagi, T.: A fast parallel elliptic curve multiplication resistant against side channel attacks. Lncs 2274, 280-296 (2002) · Zbl 1055.94516
[9] Itoh, T.; Izu, T.; Takenaka, M.: Address-bit differential power analysis of cryptographic schemes OK-ECDH and OK-ECDSA. Lncs 2523, 129-143 (2003) · Zbl 1019.68557
[10] Izu, T.; Takagi, T.: Fast elliptic curve multiplications resistant against side channel attacks. IEICE trans. 88A, No. 1, 161-171 (2005)
[11] Joye, M.; Tymen, C.: Protections against differential analysis for elliptic curve cryptosystem. Lncs 2162, 377-390 (2001) · Zbl 1012.94550
[12] Joye, M.; Yen, S. M.: The Montgomery powering ladder. Lncs 2523, 291-302 (2003) · Zbl 1020.11500
[13] Koblitz, N.: Elliptic curve cryptosystems. Math. comput. 48, 203-209 (1987) · Zbl 0622.94015
[14] Kocher, P.: Timing attacks on implementations of diffie-hellman, RSA, DSS, and other system. Lncs 1109, 104-113 (1996) · Zbl 06507372
[15] Kocher, P.; Jaffe, J.; Jun, B.: Differential power analysis. Lncs 1666, 388-397 (1999) · Zbl 0942.94501
[16] Lim, Ch.: A new method for securing elliptic scalar multiplication against side channel attacks. Lncs 3108, 289-300 (2004) · Zbl 1098.94623
[17] Goubin, L.: A refined power-analysis attack on elliptic curve cryptosystems. Lncs 2567, 199-210 (2003) · Zbl 1033.94526
[18] Miller, V.: Use of elliptic curves in cryptography. Lncs 218, 417-426 (1986)
[19] Muoller, B.: Securing elliptic curve point multiplication against side-channel attacks. Lncs 2200, 324-334 (2001) · Zbl 1042.68585
[20] Mamiya, H.; Miyaji, A.; Morimoto, H.: Efficient countermeasure against RPA, DPA, and SPA. Lncs 3156, 343-356 (2004) · Zbl 1104.68488
[21] J. Solinas, Low-weight binary representation for pairs of integers, Avaliable from <http://www.cacr.math.uwaterloo.ca/techreports/2001/corr2001-41.ps>.
[22] Smart, N.: An analysis of goubins refined power analysis attack. Lncs 2779, 281-290 (2003) · Zbl 1274.94116
[23] K. Shim, S. Woo, Cryptanalysis of tripartite and multiparty authenticated key agreement protocols Inform. Sci., 2006, doi:10.1016/j.ins.2006.07.034. · Zbl 1130.94329
[24] L. Wang, Z. Cao, X. Li, H.Qian, Simulatability and security of certificateless threshold signatures, Inform. Sci. 2006, doi:10.1016/j.ins.2006.08.008. · Zbl 1125.94039