Tethered Downgrade

Tethered Downgrades are downgrades which in someway flash an unsigned iOS Version but require some way to meet iTunes' requirements to do a restore. This process is most commonly used on A4 Devices (such as an iPhone 4) because of the bootrom exploit known as "Limera1n". If no attempt is done to fix the signature of the LLB, locking will result in adisplay failure which can only be fixed by restoring to a signed iOS version.

Installing a firmware version using this method (without valid SHSH blobs) is incompatible with an untethered jailbreak. Each time the device boots, the bootrom validates the SHSH blobs for LLB, LLB for iBoot, and so on. Therefore, the image validation function must be patched or bypassed with an appropriate bootrom exploit payload on every boot or the device will be forced into DFU mode.

Dead LCD Bug

Locking a device with an unsigned bootchain (speficially the LLB) while on battery power causes iOS to disable the LCD. A restore to the latest iOS is needed to fix this.

LCD Incompatibility

Some iOS versions (such as iOS 5) cannot boot when the device has a counterfeit display. A workaround for this has been found.

Method

Name	LCD Fix	Description
Bluefreeze	Yes?	Bluefreeze, a tool written by a group called The Private Dev Team, modifies the firmware version (and firmware checksum) in the iFaith certificate file, so that this check gets disabled. By doing so, you can install any firmware version on your device, even without having saved the SHSH files. The problem by doing so is that you actually install a firmware without signatures, with all consequences.
GeekGrade Beta 1	Partial	IPSWs made via Sn0wbreeze, ramdisk modified to have BlackGeek's logo, and preinstalled with mobile substrate and a deep sleep disabler. Once the device is running, the device will not go into deep sleep, causing severe battery draining. This workaround avoids the display failure issue but locking via safe mode will cause the display to fail.
ＲＥＡＬＬＹ ＢＡＤ ＭＥＴＨＯＤ™	NO	Grab someone's blobs and make an IPSW with iFaith. Then restore with it when in PWNDFU. basically what Bluefreeze does. Don't do this method or I'll laugh at you.
GeekGrade 1.0	Yes	Instead of making the IPSW via sn0wbreeze, it's made via iFaith. The ramdisk is modified to remove iH8sn0w's iFaith logo and to replace it with BlackGeek's logo. It also sets FlashNOR to false in option.plist. This last modification allows the bootchain to stay signed (if it was signed prior to restore). This method fixes the display failure bug (no longer possible unless bootchain somehow becomes unsigned O.o). Device is sent to recovery mode (instead of DFU) because the bootchain is signed but fails to load iOS.
Sund0wn	Yes	Sund0wn is a downgrade utility which allows tether and untether downgroades for iOS 6.0-7.1.2 for the iPhone 4. It is for the Windows family of operating systems written by iSuns9. It works on all iPhone 4 models. This is useful if you want to use older iOS versions. Even if Apple doesn't sign that firmware anymore, sund0wn creates a restoreable IPSW so that you can install the firmware and tether boot after.

Purpose

With this method you can install a firmware for which you don't have SHSH saved for some tests, for example if you're a software developer and need to do some tests on a specific version or if you prefer older iOS versions.

Alternative

You have to patch a firmware file (IPSW) which is signed by Apple exactly when you want to perform the downgrade.

1. Patch out the signature check in iBSS and iBEC and apply another patch to iBEC (some lines of code before the patch the string "debug-enabled" is loaded into a register and some lines after the patch the string "development-cert" is loaded. Look at a patched iBEC from an iFaith IPSW for details).
2. Patch the boot-args in iBEC to "rd=md0 amfi=0xff cs_enforcement_disable=1 pio-error=0" and do an iBEC patch that injects the boot-args.
3. Patch asr to return "Image passed signature verification" where it would usually return "Image failed signature verification".
4. Update the page hashes of asr with ldid.
5. Grow the ramdisk to original size + size of asr (better some bytes larger).
6. Rename the original asr and add the patched asr.
7. chmod asr to 100755
8. Replace the root file system dmg with the decrypted root file system dmg of the older firmware you want to downgrade to. (take care that the decrypted dmg has the format UDZO!)
9. Enter pwned DFU Mode.
10. Use an old iTunes version that allows downgrades on your iOS device and restore to your patched IPSW.
11. To start up your device you will have to boot tethered (depending on iOS version redsn0w or opensn0w).