- Ciphers which can change the fundamental word size used.
There are a few of these: Keccak can work with 64-bit, 32-bit, or even 16-bit words (or smaller, but there isn’t any real security with going below 16 bits). RadioGatún, Keccak’s predecessor, also allowed any word length between one bit and 64 bits. RC5 and RC6 can work with either 32-bit or 64-bit words (but are, alas, patented until at least 2015). The stream cipher ISAAC exists in 32-bit and 64-bit variants.
But, besides those, there really aren’t that many cryptographic primitives with word size flexibility, which is a disappointment right now, since 32-bit and 64-bit systems are currently very common.
I’m not the only one hungering for this; observe halfskein.js, which is an unofficial Skein variant using 32-bit words (Skein normally uses 64-bit words). I should also point out that LUX has both a 32-bit and a 64-bit mode (unfortunately the original LUX specification was broken; hopefully the revised version will not be.)
- A block cipher with a 2048-bit or larger block size.
The largest block size out there in an unbroken cipher is Threefish, which includes a version with a 1024-bit block size. There was Mercy, with a 4096-bit (512-byte) block size, but that was unfortunately broken. XXTEA, which also allowed really large blocks has also been broken; and the Hasty Pudding Cipher has also this ability, but I remember reading somewhere that HPC doesn’t pass standard randomness tests, and weaknesses with the key schedule have been found with this cipher (it was also criticized by Brian Gladman as being difficult to implement).
Yes, it is possible to make, say, an AES variant using 128-bit sized words and a 2048-bit block size, but it hasn’t been officially proposed as a block cipher. It should also not be too difficult to make a Skein variant with 2048-bit blocks (or 1024-bit blocks when using 32-bit words), but again this has not been done.
A 2048-bit cipher, for example, would be useful for making a Cryptographic sponge with a 1024-bit rate and 1024-bit capacity, which could be used for either a stream cipher or for a 512-bit cryptographic hash primitive.
- More tweakable block ciphers. There is only one unbroken block cipher primitive with a tweakable core out there: Threefish. The only other tweakable block cipher is the original: Hasty Pudding Cipher (as discussed above); unfortunately, HPC appears to be broken (or at least have weaknesses)
- A cipher using playing cards with no known weaknesses.
The strongest cipher designed specifically to be implemented using a deck of cards is the Solitaire cipher; but it has some bias in its PRNG. There has been proposed Mirdek, which is broken, as well as John Savard’s playing card cipher, which also is broken.
The most secure playing card cipher out there appears to be a RC4 variant using playing cards.
So, hey, if you’re one of the very few people in the world with the intelligence and chops to make a strong cryptographic primitive, this is my wishlist! And, yes, I really appreciate that most cryptographic primitives out there are public domain. AES was perfect when I was making a secure random number generator for MaraDNS 1.x, and RadioGatún was perfect (tiny, able to easily compress entropy from various sources with variable amounts of entropy-per-bit, fast, 32-bit compatible and easily adapted to 64-bit environments, and derived from PANAMA with a proven record as a secure stream cipher) for my needs when I originally designed Deadwood back in 2007.