412 |
- verify: check that the revealed RNs hashes to right hash in public key - |
- verify: check that the revealed RNs hashes to right hash in public key - |
413 |
calculate `$b$` hashes |
calculate `$b$` hashes |
414 |
|
|
415 |
|
Octuplet: `$(1, b, bh, 2bh, h, 2b, 0, b)$` |
416 |
|
|
417 |
|
|
418 |
Merkle (?) |
Merkle (?) |
419 |
---------- |
---------- |
420 |
|
|
435 |
|
|
436 |
- verify: |
- verify: |
437 |
|
|
438 |
|
Octuplet: `$(1, b, h(b+\\lceil \\log{2} b \\rceil), h, h, |
439 |
|
b+\\lceil \\log{2} b \\rceil + 1, 0, |
440 |
|
\\le b+\\lceil \\log{2} b \\rceil$` |
441 |
|
|
442 |
|
|
443 |
Merkle-Winternitz |
Merkle-Winternitz |
444 |
----------------- |
----------------- |
445 |
|
|
474 |
Verification requires `$k2^n + 1$` invocations |
Verification requires `$k2^n + 1$` invocations |
475 |
of the hash function. |
of the hash function. |
476 |
|
|
477 |
|
Octuplet: `$(1, b, \\frac{bh}{n}+h, h, h, |
478 |
|
2\\frac{b}{n}(2^n-1)+1, \\frac{b}{n}(2^n-1)+1, |
479 |
|
\\frac{b}{n}(2^n-1)+1)$` |
480 |
|
|
481 |
|
|
482 |
BiBa |
BiBa |
483 |
---- |
---- |
484 |
|
|
502 |
into the same bin; verify that the balls match the public key |
into the same bin; verify that the balls match the public key |
503 |
(i.e., that the public key contains their hashes). |
(i.e., that the public key contains their hashes). |
504 |
|
|
505 |
|
Octuplet: `$(q, b, th, wh, h, t, ?+wh, w)$` |
506 |
|
|
507 |
|
|
508 |
Reyzin |
Reyzin |
509 |
------ |
------ |
531 |
|
|
532 |
? |
? |
533 |
|
|
534 |
|
Octuplet: `$(1, b, kh, th, h, t, 1, 1+k)$` |
535 |
|
|
536 |
|
|
537 |
Bleichenbacher-Maurer |
Bleichenbacher-Maurer |
538 |
--------------------- |
--------------------- |
539 |
|
|
555 |
- verify: check that right nodes revealed, and that tree computes right |
- verify: check that right nodes revealed, and that tree computes right |
556 |
public key - calculate some less than `$9n+2$` hashes |
public key - calculate some less than `$9n+2$` hashes |
557 |
|
|
558 |
|
Octuplet: `$(1, \\lfloor\\eta n\\rfloor, |
559 |
|
3(n+1)h, h, h, 9n+2, 0, 9n+2)$` |
560 |
|
|
561 |
|
|
562 |
Merkle hash trees |
Merkle hash trees |
563 |
----------------- |
----------------- |
564 |
|
|
587 |
|
|
588 |
- verify: verify signature with new public key, verify hash chain. |
- verify: verify signature with new public key, verify hash chain. |
589 |
|
|
590 |
|
Octuplet: `$({2^n}q', b, 2s'+r'+hn, h, h, |
591 |
|
({2^n}+1)c_0'+c_s' + 2^{n+1}-1, c_s', 2c_v'+n$` |
592 |
|
|
593 |
Efficiency of key boosting |
Efficiency of key boosting |
594 |
========================== |
========================== |
600 |
|
|
601 |
- maybe recommendations |
- maybe recommendations |
602 |
|
|
603 |
|
Octuplet: `${q'}^N, b, N(r'+s'), r', h, |
604 |
|
c_0', N(c_0'+c_s'), Nc_v)$` |
605 |
|
|
606 |
|
|
607 |
Tradeoffs in deterministic key boosting |
Tradeoffs in deterministic key boosting |
608 |
--------------------------------------- |
--------------------------------------- |
609 |
|
|