### [secdir] secdir review for draft-mcgrew-fundamental-ecc-03

Tina TSOU <tena@huawei.com> Tue, 06 July 2010 02:29 UTC

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Date: Tue, 06 Jul 2010 10:28:54 +0800

From: Tina TSOU <tena@huawei.com>

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Subject: [secdir] secdir review for draft-mcgrew-fundamental-ecc-03

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Hi, I have reviewed this document as part of the security directorate's ongoing effort to review all IETF documents being processed by the IESG. These comments were written primarily for the benefit of the security area directors. Document editors and WG chairs should treat these comments just like any other comments. Abstract 1. First sentence: Should >are< rather be >were< ? Introduction 2. Introduction (p.2): I would insert the word >finite< before >fields<. 3. Introduction (p.4): >ECDH< should be replaced by >Elliptic Curve Diffie-Hellman (ECDH) <. Mathematical Background 4. Mathematical Background (p.1): Should >is< rather be >are< ? The same holds in Sec.~2.2 (p.1). 5. Sec.~2.2 (p.3): The term >g< is undefined. Hence, >g^N< should be replaced by >a^N<. The same holds for >Note that a^M is equal to g^ (M mod R)< in (p.9). 6. Sec.~2.3 (p.2): From this description, it appears to me that all elements in Z_p can perform division operation. However, only non-zero elements, namely elements in the set Z_p^* = Z_p-{0} can perform the division operation. Moreover, all the mathematical operations over Z_p are in the sense of mod p. In addition, a prime number p is called the characteristic of a field, if 1+…+1=0 (add p times); in this case F_q contains the prime field F_p, where q=p^n, n>=1. So I think the definition of the F_p lacks precision. Elliptic Curve Groups 7. Elliptic Curve Groups (p.1): I think the last sentence is too abstract to understand. More precisely, the elliptic curve satisfies the equations, y^2+cy=x^3+ax+b, y^2=x^3+ax^2+bx+c, when the characteristic of the field is 2 and 3, respectively. 8. Elliptic Curve Groups (p.3): The first sentence says that >when both points are the point at Infinity<. Maybe such statement is not accurate enough due to the fundamental fact that each elliptic curve abelian group has only one infinity, i.e., the identity element. 9. Sec.~3.1 (p.2): It seems to me that the projection space representation >x=X/Z mod p , y=Y/Z mod p< is a special case of x=X/Z^{c_1} mod p and y=Y/Z^{c_2} mod p when both c_1 and c_2 are equal to 1. If so, should it be clearly explained ? 10. Sec.~3.3.1: I would simply state the reason for the non-zero discriminant, namely, to ensure that the elliptic curve is chosen to be a non-singular one, i.e., it has no self intersections or cusps. Elliptic Curve Diffie-Hellman (ECDH) 11. Elliptic Curve Groups (p.1): >an arbitrary cyclic group< instead of >an arbitrary mathematical group< ? Elliptic Curve ElGamal Signatures 12. Sec.~5.1 (p.1): Insert >Galois< before >field GF(2^w)<. 13. Sec.~5.3 (p.2): Why not denote the generator >alpha< as >g< for consistency in this draft ? 14. Sec.~5.3.2 (4): As the symbol >*< denotes the scalar multiplication, why use such a symbol in Sec.~2.2 to represent the addition operation in a group ? Needs to be modified ? 15. Sec.~5.3.3 (p.1): Insert >the generator g, the group order q< before >the public key Y< in that these two parameters must know in advance before the signature verification procedure. 16. Sec.~5.3.2 (1): Should >0<s_1<q< be replaced by >s_1 in Z_q< for consistency ? The same holds for >0<s_2<q< and the sentence in Sec.~5.4.3 (1). 17. Sec.~5.3.2 (3): As mentioned above, the symbol >*< in the equation >R'=alpha^{u_1} * Y^{u_2}< represents the addition operation of two points on the elliptic curve; while in >u_2=s_1 * s_2 mod q<, it means the scalar multiplication operation. 18. Sec.~5.6 (p.2): In the equations >A=m< and >m=-r*z+s*k (mod q)<, does the symbol m represent a message digest ? If so, I think m should be replaced by h(m), although the hash function is not necessary here. If not, it should be transformed to an integer since it has been defined to be a bit string in Sec.~5.2. The same holds for the equation >m*s=-r*s*z+k (mod q)<. Converting between integers and octet strings 19. the title >Converting between integers and octet strings<, why not >Converting between Integers and Octet Strings< for consistency ? The same goes for other titles and subtitles. Security Considerations 20. Sec.~10.1 (p.3): I think it is necessary to explain the physical meaning of the cofactor and the reason that a number of attacks are possible against ECDH when the cofactor is not equal to 1. B. R. Tina http://tinatsou.weebly.com/contact.html