XOR Leak

Known Plaintext Recovers

Known plaintext A recovers plaintext B in this toy reused-keystream example.

highlighted = computed this step

Known plaintext turns the leak into recovery

If plaintext A is known, then plaintext A XOR ciphertext A XOR ciphertext B recovers plaintext B.

known plaintext A=1\text{known plaintext A}=1
Known plaintext recovers BKnowing plaintext A lets the toy leak recover plaintext B.Plaintext A48 bits / 6 bytes0x7061793d3130byte 0byte 1byte 2byte 301110000011000010111100100111101byte 4byte 50011000100110000byte-00x70byte-10x61byte-20x79byte-30x3dbyte-40x31byte-50x30Ciphertext A48 bits / 6 bytes0x7f7f54017a6abyte 0byte 1byte 2byte 301111111011111110101010000000001byte 4byte 50111101001101010byte-00x7fbyte-10x7fbyte-20x54byte-30x01byte-40x7abyte-50x6aCiphertext B48 bits / 6 bytes0x7f7f5401726abyte 0byte 1byte 2byte 301111111011111110101010000000001byte 4byte 50111001001101010byte-00x7fbyte-10x7fbyte-20x54byte-30x01byte-40x72byte-50x6aRecovered B48 bits / 6 bytes0x7061793d3930byte 0byte 1byte 2byte 301110000011000010111100100111101byte 4byte 50011100100110000byte-00x70byte-10x61byte-20x79byte-30x3dbyte-40x39byte-50x30

The recovered bytes

The recovered plaintext B is 0x7061793d3930.

recovered B=0x7061793d3930\text{recovered B}=0x7061793d3930
Known plaintext recovers BKnowing plaintext A lets the toy leak recover plaintext B.Plaintext A48 bits / 6 bytes0x7061793d3130byte 0byte 1byte 2byte 301110000011000010111100100111101byte 4byte 50011000100110000byte-00x70byte-10x61byte-20x79byte-30x3dbyte-40x31byte-50x30Ciphertext A48 bits / 6 bytes0x7f7f54017a6abyte 0byte 1byte 2byte 301111111011111110101010000000001byte 4byte 50111101001101010byte-00x7fbyte-10x7fbyte-20x54byte-30x01byte-40x7abyte-50x6aCiphertext B48 bits / 6 bytes0x7f7f5401726abyte 0byte 1byte 2byte 301111111011111110101010000000001byte 4byte 50111001001101010byte-00x7fbyte-10x7fbyte-20x54byte-30x01byte-40x72byte-50x6aRecovered B48 bits / 6 bytes0x7061793d3930byte 0byte 1byte 2byte 301110000011000010111100100111101byte 4byte 50011100100110000byte-00x70byte-10x61byte-20x79byte-30x3dbyte-40x39byte-50x30

It matches the second message

At the toy text level, the recovered message says pay equals 90.

pay B=90\text{pay B}=90
Known plaintext recovers BKnowing plaintext A lets the toy leak recover plaintext B.Plaintext A48 bits / 6 bytes0x7061793d3130byte 0byte 1byte 2byte 301110000011000010111100100111101byte 4byte 50011000100110000byte-00x70byte-10x61byte-20x79byte-30x3dbyte-40x31byte-50x30Ciphertext A48 bits / 6 bytes0x7f7f54017a6abyte 0byte 1byte 2byte 301111111011111110101010000000001byte 4byte 50111101001101010byte-00x7fbyte-10x7fbyte-20x54byte-30x01byte-40x7abyte-50x6aCiphertext B48 bits / 6 bytes0x7f7f5401726abyte 0byte 1byte 2byte 301111111011111110101010000000001byte 4byte 50111001001101010byte-00x7fbyte-10x7fbyte-20x54byte-30x01byte-40x72byte-50x6aRecovered B48 bits / 6 bytes0x7061793d3930byte 0byte 1byte 2byte 301110000011000010111100100111101byte 4byte 50011100100110000byte-00x70byte-10x61byte-20x79byte-30x3dbyte-40x39byte-50x30

Summary

One known plaintext plus two ciphertexts is enough to recover the other toy plaintext.

recovered bytes=6\text{recovered bytes}=6
Known plaintext recovers BKnowing plaintext A lets the toy leak recover plaintext B.Plaintext A48 bits / 6 bytes0x7061793d3130byte 0byte 1byte 2byte 301110000011000010111100100111101byte 4byte 50011000100110000byte-00x70byte-10x61byte-20x79byte-30x3dbyte-40x31byte-50x30Ciphertext A48 bits / 6 bytes0x7f7f54017a6abyte 0byte 1byte 2byte 301111111011111110101010000000001byte 4byte 50111101001101010byte-00x7fbyte-10x7fbyte-20x54byte-30x01byte-40x7abyte-50x6aCiphertext B48 bits / 6 bytes0x7f7f5401726abyte 0byte 1byte 2byte 301111111011111110101010000000001byte 4byte 50111001001101010byte-00x7fbyte-10x7fbyte-20x54byte-30x01byte-40x72byte-50x6aRecovered B48 bits / 6 bytes0x7061793d3930byte 0byte 1byte 2byte 301110000011000010111100100111101byte 4byte 50011100100110000byte-00x70byte-10x61byte-20x79byte-30x3dbyte-40x39byte-50x30