diff options
Diffstat (limited to 'nss/lib/freebl/ecl/README')
| -rw-r--r-- | nss/lib/freebl/ecl/README | 104 |
1 files changed, 0 insertions, 104 deletions
diff --git a/nss/lib/freebl/ecl/README b/nss/lib/freebl/ecl/README index 04a8b3b..2996822 100644 --- a/nss/lib/freebl/ecl/README +++ b/nss/lib/freebl/ecl/README @@ -90,20 +90,6 @@ the linear coefficient in the curve defining equation). ecp_192.c and ecp_224.c provide optimized field arithmetic. -Point Arithmetic over Binary Polynomial Fields ----------------------------------------------- - -ec2_aff.c provides point arithmetic using affine coordinates. - -ec2_proj.c provides point arithmetic using projective coordinates. -(Projective coordinates represent a point (x, y) as (X, Y, Z), where -x=X/Z, y=Y/Z^2). - -ec2_mont.c provides point multiplication using Montgomery projective -coordinates. - -ec2_163.c, ec2_193.c, and ec2_233.c provide optimized field arithmetic. - Field Arithmetic ---------------- @@ -126,18 +112,6 @@ fields defined by nistp192 and nistp224 primes. ecl_gf.c provides wrappers around the basic field operations. -Binary Polynomial Field Arithmetic ----------------------------------- - -../mpi/mp_gf2m.c provides basic binary polynomial field arithmetic, -including addition, multiplication, squaring, mod, and division, as well -as conversion ob polynomial representations between bitstring and int[]. - -ec2_163.c, ec2_193.c, and ec2_233.c provide optimized field mod, mul, -and sqr operations. - -ecl_gf.c provides wrappers around the basic field operations. - Field Encoding -------------- @@ -187,81 +161,3 @@ arithmetic. Instead, they use basic field arithmetic with their optimized reduction (as in ecp_192.c and ecp_224.c). They use the same point multiplication and simultaneous point multiplication algorithms as other curves over prime fields. - -Curves over binary polynomial fields by default use generic field -arithmetic with montgomery point multiplication and basic kP + lQ -computation (multiply, multiply, and add). (Wiring in function -ECGroup_cons_GF2m in ecl.c.) - -Curves over binary polynomial fields that have optimized field -arithmetic (i.e., any 163-, 193, or 233-bit field) use their optimized -field arithmetic. They use the same point multiplication and -simultaneous point multiplication algorithms as other curves over binary -fields. - -Example -------- - -We provide an example for plugging in an optimized implementation for -the Koblitz curve nistk163. - -Suppose the file ec2_k163.c contains the optimized implementation. In -particular it contains a point multiplication function: - - mp_err ec_GF2m_nistk163_pt_mul(const mp_int *n, const mp_int *px, - const mp_int *py, mp_int *rx, mp_int *ry, const ECGroup *group); - -Since only a pt_mul function is provided, the generic pt_add function -will be used. - -There are two options for handling the optimized field arithmetic used -by the ..._pt_mul function. Say the optimized field arithmetic includes -the following functions: - - mp_err ec_GF2m_nistk163_add(const mp_int *a, const mp_int *b, - mp_int *r, const GFMethod *meth); - mp_err ec_GF2m_nistk163_mul(const mp_int *a, const mp_int *b, - mp_int *r, const GFMethod *meth); - mp_err ec_GF2m_nistk163_sqr(const mp_int *a, const mp_int *b, - mp_int *r, const GFMethod *meth); - mp_err ec_GF2m_nistk163_div(const mp_int *a, const mp_int *b, - mp_int *r, const GFMethod *meth); - -First, the optimized field arithmetic could simply be called directly -by the ..._pt_mul function. This would be accomplished by changing -the ecgroup_fromNameAndHex function in ecl.c to include the following -statements: - - if (name == ECCurve_NIST_K163) { - group = ECGroup_consGF2m(&irr, NULL, &curvea, &curveb, &genx, - &geny, &order, params->cofactor); - if (group == NULL) { res = MP_UNDEF; goto CLEANUP; } - MP_CHECKOK( ec_group_set_nistk163(group) ); - } - -and including in ec2_k163.c the following function: - - mp_err ec_group_set_nistk163(ECGroup *group) { - group->point_mul = &ec_GF2m_nistk163_pt_mul; - return MP_OKAY; - } - -As a result, ec_GF2m_pt_add and similar functions would use the -basic binary polynomial field arithmetic ec_GF2m_add, ec_GF2m_mul, -ec_GF2m_sqr, and ec_GF2m_div. - -Alternatively, the optimized field arithmetic could be wired into the -group's GFMethod. This would be accomplished by putting the following -function in ec2_k163.c: - - mp_err ec_group_set_nistk163(ECGroup *group) { - group->meth->field_add = &ec_GF2m_nistk163_add; - group->meth->field_mul = &ec_GF2m_nistk163_mul; - group->meth->field_sqr = &ec_GF2m_nistk163_sqr; - group->meth->field_div = &ec_GF2m_nistk163_div; - group->point_mul = &ec_GF2m_nistk163_pt_mul; - return MP_OKAY; - } - -For an example of functions that use special field encodings, take a -look at ecp_mont.c. |