diff --git a/include/relic_ep.h b/include/relic_ep.h
index 1548afb06..bb7255d09 100644
--- a/include/relic_ep.h
+++ b/include/relic_ep.h
@@ -64,7 +64,7 @@ enum {
     /* Barreto-Lynn-Scott family with embedding degree 12. */
     EP_B12,
     /* New family from Fotiadis-Martindale family with embedding degree 16. */
-    EP_N16,
+    EP_AFG16,
 	/* Fotiadis-Martindale family with embedding degree 16. */
 	EP_FM16,
     /* Kachisa-Schaefer-Scott family with embedding degree 16. */
@@ -161,6 +161,8 @@ enum {
 	K18_P508,
 	/** Barreto-Lynn-Scott curve with embedding degree 24. */
 	B24_P509,
+	/** New family with embeeding degree 16. */
+	AFG16_P510,
 	/** Optimal TNFS-secure curve with embedding degree 8. */
 	OT8_P511,
 	/** Cocks-pinch curve with embedding degree 8. */
@@ -182,7 +184,7 @@ enum {
 	/** Kachisa-Schaefer-Scott with embedding degree 16. */
 	K16_P766,
 	/** New family with embeeding degree 16. */
-	N16_P766,
+	AFG16_P766,
 	/* Fotiadis-Moartindale with embedding degree 18. */
 	FM18_P768,
 	/** Barreto-Lynn-Scott curve with embedding degree 12. */
diff --git a/include/relic_fp.h b/include/relic_fp.h
index 0ecbbac00..38d6d1e9c 100644
--- a/include/relic_fp.h
+++ b/include/relic_fp.h
@@ -140,10 +140,12 @@ enum {
 	B12_446,
 	/** 455-bit prime for BLS curve of embedding degree 12. */
 	B12_455,
-	/** 477-bit prime for BLS curve of embedding degree 24. */
-	B24_509,
 	/** 508-bit prime for KSS16 curve. */
 	K18_508,
+	/** 477-bit prime for BLS curve of embedding degree 24. */
+	B24_509,
+	/** 510-bit prime for new family with embedding degree 16. */
+	AFG16_510,
 	/** Random 544-bit prime for Cocks-Pinch curve with embedding degree 8. */
 	GMT8_544,
 	/** 569-bit prime for SG curve with embedding degree 54. */
@@ -163,7 +165,7 @@ enum {
 	/** 766-bit prime for KSS curve with embedding degree 16. */
 	K16_766,
 	/** 766-bit prime for new family with embedding degree 16. */
-	N16_766,
+	AFG16_766,
 	/** 768-bit prime for FM curve with embedding degree 18. */
 	FM18_768,
 	/** 1024-bit prime for CTIDH. */
diff --git a/include/relic_pc.h b/include/relic_pc.h
index 797b98c9f..f5e317010 100644
--- a/include/relic_pc.h
+++ b/include/relic_pc.h
@@ -59,7 +59,7 @@
 #if FP_PRIME == 575
 #define RLC_G2_LOWER			ep8_
 #define RLC_G2_BASEF(A)			A[0][0][0]
-#elif FP_PRIME == 315 || FP_PRIME == 317 || FP_PRIME == 330 || FP_PRIME == 509 || FP_PRIME == 765 || FP_PRIME == 766
+#elif FP_PRIME == 315 || FP_PRIME == 317 || FP_PRIME == 330 || FP_PRIME == 509 || FP_PRIME == 510 || FP_PRIME == 765 || FP_PRIME == 766
 #define RLC_G2_LOWER			ep4_
 #define RLC_G2_BASEF(A)			A[0][0]
 #elif FP_PRIME == 354 || FP_PRIME == 508 || FP_PRIME == 768 || FP_PRIME == 638 && !defined(FP_QNRES)
@@ -81,7 +81,7 @@
 #elif FP_PRIME == 354 || FP_PRIME == 508 || FP_PRIME == 768 || FP_PRIME == 638 && !defined(FP_QNRES)
 #define RLC_GT_LOWER			fp18_
 #define RLC_GT_EMBED      		18
-#elif FP_PRIME == 330 || FP_PRIME == 765 || FP_PRIME == 766
+#elif FP_PRIME == 330 || FP_PRIME == 510 || FP_PRIME == 765 || FP_PRIME == 766
 #define RLC_GT_LOWER			fp16_
 #define RLC_GT_EMBED      		16
 #elif FP_PRIME == 544
diff --git a/preset/x64-pbc-afg16-510.sh b/preset/x64-pbc-afg16-510.sh
new file mode 100755
index 000000000..2f53dbf3e
--- /dev/null
+++ b/preset/x64-pbc-afg16-510.sh
@@ -0,0 +1,2 @@
+#!/bin/sh
+cmake -DWSIZE=64 -DRAND=UDEV -DSHLIB=OFF -DSTBIN=ON -DTIMER=CYCLE -DCHECK=off -DVERBS=off -DARITH=x64-asm-8l -DFP_PRIME=510 -DFP_METHD="INTEG;INTEG;INTEG;MONTY;JMPDS;JMPDS;SLIDE" -DCFLAGS="-O3 -funroll-loops -fomit-frame-pointer -march=native -mtune=native" -DFP_PMERS=off -DFP_QNRES=off -DFPX_METHD="INTEG;INTEG;LAZYR" -DEP_METHD="JACOB;LWNAF;COMBS;INTER;SWIFT" -DEP_PLAIN=off -DEP_SUPER=off -DPP_METHD="LAZYR;OATEP" -DWITH="ALL" $1
diff --git a/src/ep/relic_ep_curve.c b/src/ep/relic_ep_curve.c
index 236f3d6e8..5c80e6fd2 100644
--- a/src/ep/relic_ep_curve.c
+++ b/src/ep/relic_ep_curve.c
@@ -533,7 +533,7 @@ int ep_curve_embed(void) {
 		case EP_BN:
 		case EP_B12:
 			return 12;
-		case EP_N16:
+		case EP_AFG16:
 		case EP_FM16:
 		case EP_K16:
 			return 16;
diff --git a/src/ep/relic_ep_mul_cof.c b/src/ep/relic_ep_mul_cof.c
index 2101f6ece..a0dd8f5e6 100644
--- a/src/ep/relic_ep_mul_cof.c
+++ b/src/ep/relic_ep_mul_cof.c
@@ -68,7 +68,7 @@ void ep_mul_cof(ep_t r, const ep_t p) {
 				bn_add_dig(k, k, 1);
 				ep_mul_basic(r, p, k);
 				break;
-			case EP_N16:
+			case EP_AFG16:
 				/* if (u % 2) == 0, compute = (u * (u**3+1)/2)*P
     			 * else Compute (u * (u**3+1))*P */
 				bn_sqr(l, k);
diff --git a/src/ep/relic_ep_param.c b/src/ep/relic_ep_param.c
index 5de45b5ad..37709b937 100644
--- a/src/ep/relic_ep_param.c
+++ b/src/ep/relic_ep_param.c
@@ -577,6 +577,20 @@
 /** @} */
 #endif
 
+#if defined(EP_ENDOM) && FP_PRIME == 510
+/**
+ * Parameters for a 510-bit pairing-friendly prime curve.
+ */
+/** @{ */
+#define AFG16_P510_A		"1"
+#define AFG16_P510_B		"0"
+#define AFG16_P510_X		"1B28C3BEC45CD9C234F465962ECE64778E165478A23196AB96FDCC96158DB382D54A07059A286B6C1E55B96C4A8C618F47A6A36A26C99E3E1FE8BC25D74E1498"
+#define AFG16_P510_Y		"BA2C88F672B5A4B486E8A86442B9B1A41917DB750072E398FC106020C3ADECC12A87CB01F0D19B1803A97C300D97545941DADE18CB8A648A79F3BB0744F9F8C"
+#define AFG16_P510_R		"E1B262AFF36AB56C7EFDECD784FACE4291A5FFE880A4AAD37C71010000000001"
+#define AFG16_P510_H		"5922DDB02112D02D09E6928213608A7AC1EE7A916706E3DA46FA55988D318CFF"
+/** @} */
+#endif
+
 #if defined(EP_ENDOM) && FP_PRIME == 544
 /**
  * Parameters for the 544-bit Cocks-Pinch curve.
@@ -704,12 +718,12 @@
  * Parameters for a 766-bit pairing-friendly prime curve.
  */
 /** @{ */
-#define N16_P766_A		"1"
-#define N16_P766_B		"0"
-#define N16_P766_X		"177E5E088795AE368F68ADB4938F647BCCB7D0BCB70456E3B3BC0C6EE12FA3D0E1DFC2FD81C215EC25E602DE8BCEE98A7F8FC23E4A296B9DDEF34BB90A27DD4804B90F7783FE2C891A820941DB16535E1FD73E73038A520AAE396F0949D7E46D"
-#define N16_P766_Y		"1CE39931AB952C962CBF6F4E8BE79D6AD3D931B2B100185707032C109C9476305F44D30E1D551E965D44D661327D878EC47ED7A9D1DCDDCA96091E74FB4FF6D42CE809579AB9C72417C55849377E4BA31A0B5F687D840E4CE99E63D583050147"
-#define N16_P766_R		"FFFF7000238FFAF4807374994CF93FE6E28D406881B18D350193FE6E3E533E4073749FEBD2000238FFFFDC0000010001"
-#define N16_P766_H		"3FFFDC0008E3FEBD201CDD26533E4FF9B8A3D019F36C69AB3FF0479FDCFCBD856CEE5D9B2D34778FD7D2F6D2DC004204"
+#define AFG16_P766_A		"1"
+#define AFG16_P766_B		"0"
+#define AFG16_P766_X		"177E5E088795AE368F68ADB4938F647BCCB7D0BCB70456E3B3BC0C6EE12FA3D0E1DFC2FD81C215EC25E602DE8BCEE98A7F8FC23E4A296B9DDEF34BB90A27DD4804B90F7783FE2C891A820941DB16535E1FD73E73038A520AAE396F0949D7E46D"
+#define AFG16_P766_Y		"1CE39931AB952C962CBF6F4E8BE79D6AD3D931B2B100185707032C109C9476305F44D30E1D551E965D44D661327D878EC47ED7A9D1DCDDCA96091E74FB4FF6D42CE809579AB9C72417C55849377E4BA31A0B5F687D840E4CE99E63D583050147"
+#define AFG16_P766_R		"FFFF7000238FFAF4807374994CF93FE6E28D406881B18D350193FE6E3E533E4073749FEBD2000238FFFFDC0000010001"
+#define AFG16_P766_H		"3FFFDC0008E3FEBD201CDD26533E4FF9B8A3D019F36C69AB3FF0479FDCFCBD856CEE5D9B2D34778FD7D2F6D2DC004204"
 /** @} */
 
 #endif
@@ -1143,6 +1157,13 @@ void ep_param_set(int param) {
 				pairf = EP_B24;
 				break;
 #endif
+#if defined(EP_ENDOM) && FP_PRIME == 510
+			case AFG16_P510:
+				ASSIGN(AFG16_P510, AFG16_510);
+				endom = 1;
+				pairf = EP_AFG16;
+				break;
+#endif
 #if defined(EP_PLAIN) && FP_PRIME == 511
 			case CURVE_511187:
 				ASSIGN(CURVE_511187, PRIME_511187);
@@ -1211,10 +1232,10 @@ void ep_param_set(int param) {
 				endom = 1;
 				pairf = EP_K16;
 				break;
-			case N16_P766:
-				ASSIGN(N16_P766, N16_766);
+			case AFG16_P766:
+				ASSIGN(AFG16_P766, AFG16_766);
 				endom = 1;
-				pairf = EP_N16;
+				pairf = EP_AFG16;
 				break;
 #endif
 #if defined(EP_ENDOM) && FP_PRIME == 768
@@ -1290,7 +1311,7 @@ void ep_param_set(int param) {
 					bn_sqr(lamb, lamb);
 					bn_sub_dig(lamb, lamb, 1);
 					break;
-				case EP_N16:
+				case EP_AFG16:
 				case EP_FM16:
 					/* lambda = -u^4. */
 					bn_sqr(lamb, lamb);
@@ -1499,6 +1520,8 @@ int ep_param_set_any_endom(void) {
 	ep_param_set(K18_P508);
 #elif FP_PRIME == 509
 	ep_param_set(B24_P509);
+#elif FP_PRIME == 510
+	ep_param_set(AFG16_P510);
 #elif FP_PRIME == 544
 	ep_param_set(GMT8_P544);
 #elif FP_PRIME == 638
@@ -1512,7 +1535,7 @@ int ep_param_set_any_endom(void) {
 	ep_param_set(FM16_P765);
 #elif FP_PRIME == 766
 	//ep_param_set(K16_P766);
-	ep_param_set(N16_P766);
+	ep_param_set(AFG16_P766);
 #elif FP_PRIME == 768
 	ep_param_set(FM18_P768);
 #elif FP_PRIME == 1150
@@ -1608,6 +1631,10 @@ int ep_param_set_any_pairf(void) {
 	ep_param_set(B24_P509);
 	type = RLC_EP_DTYPE;
 	extension = 4;
+#elif FP_PRIME == 510
+	ep_param_set(AFG16_P510);
+	type = RLC_EP_DTYPE;
+	extension = 4;
 #elif FP_PRIME == 544
 	ep_param_set(GMT8_P544);
 	type = RLC_EP_MTYPE;
@@ -1640,7 +1667,7 @@ int ep_param_set_any_pairf(void) {
 	extension = 4;
 #elif FP_PRIME == 766
 	//ep_param_set(K16_P766);
-	ep_param_set(N16_P766);
+	ep_param_set(AFG16_P766);
 	type = RLC_EP_MTYPE;
 	extension = 4;
 #elif FP_PRIME == 768
@@ -1785,6 +1812,9 @@ void ep_param_print(void) {
 		case B24_P509:
 			util_banner("Curve B24-P509:", 0);
 			break;
+		case AFG16_P510:
+			util_banner("Curve AFG16-P510:", 0);
+			break;
 		case SG54_P569:
 			util_banner("Curve SG54-P569:", 0);
 			break;
@@ -1803,8 +1833,8 @@ void ep_param_print(void) {
 		case SG18_P638:
 			util_banner("Curve SG18-P638:", 0);
 			break;
-		case N16_P766:
-			util_banner("Curve N16-P766:", 0);
+		case AFG16_P766:
+			util_banner("Curve AFG16-P766:", 0);
 			break;
 		case FM16_P765:
 			util_banner("Curve FM16-P765:", 0);
@@ -1872,6 +1902,7 @@ int ep_param_level(void) {
 		case B12_P383:
 		case BN_P446:
 		case B12_P446:
+		case AFG16_P510:
 		case GMT8_P544:
 		case SS_P1536:
 			return 128;
diff --git a/src/epx/relic_ep4_curve.c b/src/epx/relic_ep4_curve.c
index bf0a6c23d..dbb552368 100644
--- a/src/epx/relic_ep4_curve.c
+++ b/src/epx/relic_ep4_curve.c
@@ -130,6 +130,29 @@
 /** @} */
 #endif
 
+#if defined(EP_ENDOM) && FP_PRIME == 510
+/** @{ */
+#define AFG16_P510_A0		"0"
+#define AFG16_P510_A1		"0"
+#define AFG16_P510_A2		"0"
+#define AFG16_P510_A3		"13E5E7C71142B9DC2408FB30DBAAEBDDE145A72D66379DC2D4B10355A1D8584917372EB11F4AB5569F6FDC8A937BB4D34A18BF84721822098BBFC11A4134E6CD"
+#define AFG16_P510_B0		"0"
+#define AFG16_P510_B1		"0"
+#define AFG16_P510_B2		"0"
+#define AFG16_P510_B3		"0"
+#define AFG16_P510_X0		"2EA0D837F9505A1BD454082C2B8B728CD8C403B17932782BD070620535AFA442A9CE24AD9F2963DB2A4D5E7BDC022C4FA4F2AB2B55D6DD0BCBB9857923109CD4"
+#define AFG16_P510_X1		"232FE02EC19D4540C57E8CB2B2ED780FAB2725E9CF7AE8925696B98EDF91F3190B1B2AD86D2D8B341F6B94AADAC1FBFE652D09AE648ED001A89108B8AF4294B2"
+#define AFG16_P510_X2		"32F92073C40562819F5328FB42392C407193B90F23A908806D96A3AB6DB2873638ADE6F3482ECEAA64BC28FC97B786B08F68F3843E385D860757F4E12CF5572"
+#define AFG16_P510_X3		"DE1B564F45550ECBF18AE6C4AD5D33230E7D0FC3748BC740B983658867DE2EC6AE414CAB17A1E0AD2C46A375C8E8BF55E5A3069FB24C24AADC15074867F6DAE"
+#define AFG16_P510_Y0		"1191E5FF4B39DCA47B9AAD66C34FF0804EB111F1812E724A57E360DFEE99F6B02B61BAACB913F60B651958A81E8866D95F53B9EB6DE67745A7E728E99B89C4B4"
+#define AFG16_P510_Y1		"D679B3985E3E8059FFD648A42F8A0469FC407E18A60E5C43F44D7DE80E6C88C6F08E6DB68F12807AA4E5B9146F1916A6F55DC205A28B43D97E9FEF4BEB8CCF6"
+#define AFG16_P510_Y2		"F9EC59C51A0659B345BBC667995C7CE7E0B634650695F10DBF5DC6939C8C01EB6300D4CFE588F2688AC62321E0680781EC762F7BC15188A6402D6A8385E2ACE"
+#define AFG16_P510_Y3		"548143A57CCE97D112AE4E7F508666844FA738024B39CA491CE95DA900B80FF2825CD1C29D31D2B65AF808206B44543F963290FD53346A21C1985D1D7D79C03"
+#define AFG16_P510_R		"E1B262AFF36AB56C7EFDECD784FACE4291A5FFE880A4AAD37C71010000000001"
+#define AFG16_P510_H		"452D1EFAAFB1078C06C4761679A4108402FC0F525F80ACCFC87584691797A9AD719B7AC94460FB954747B6F7C620A2541331D0D613001C5218AF53F0D5A5D056B3EBDAAC432A488D849F1F2B3FC5A4FE5AD308B8BEBB37F25FA43EC06A7436AEB728AAE611014434A0CEB65D43DE1C46722886DB8B870792912A24099077382"
+/** @} */
+#endif
+
 #if defined(EP_ENDOM) && FP_PRIME == 765
 /** @{ */
 #define FM16_P765_A0	"0"
@@ -178,24 +201,24 @@
 
 #if defined(EP_ENDOM) && FP_PRIME == 766
 /** @{ */
-#define N16_P766_A0		"0"
-#define N16_P766_A1		"0"
-#define N16_P766_A2		"1"
-#define N16_P766_A3		"0"
-#define N16_P766_B0		"0"
-#define N16_P766_B1		"0"
-#define N16_P766_B2		"0"
-#define N16_P766_B3		"0"
-#define N16_P766_X0		"36097A5BDF2276730FCAC23EA21B0C85D46B013D5A33B2D403BD82155F681BC3A1213F7AD40BFD5B64409C6B909A44F1AC391DE4222B56C55CC74DCB5DCEC23696575F80C402A1256C267F9D1CA325558C3357B116AC85CF856E51590FE7C34F"
-#define N16_P766_X1		"17CC3006229289EEC6AAA00FD81F17F26CECDE216E03B5DF64B61FEBA6DFF9D3F032642D66F8E5D4DE44934FB1CB99AFB0A6A939ADAFDA1E6197A474C3BBDDBA71E6120B3AAFE1007A8D0F360651B316312F902B1EB346DD2B276FEEE75ABDD1"
-#define N16_P766_X2		"2B79EC9BDF7F80A86DD7F3CE18A3D1FAAEAEDE9312797735EA7F090760B4730CEE401EF9CAB0978C14E967FCE1CEEF5660DFA40F367F698D0CDE9C0F0EF361D70E186EA991CD0F6DB63FE88C45EC5909DFC866862C7B1D1DE6A04843761E5E3"
-#define N16_P766_X3		"2005908CF374B24B1C7CF8C5CE656D04515082E61F3088C28D58B9E0249CA864AF1773F479D3272C567311FB287E579547743E8CA51A9D4B45FF5D3D6B4A2BB1865B6E4FB045953D716C68A73095A74CCDDAD5AFCEA74E676D37452916B5CB24"
-#define N16_P766_Y0		"137A898DDF4399F2ABB29920707790495F645B373F419C4E2A96DA05B90488BED334F2B8A44AF71C92D947009618358A14F8DE18F0D777F0DE4F98625C4024DBEB8EA858A7AEFAEC093EA12ED7A7C70142AE3583D27982B26AFD75FB441A4B66"
-#define N16_P766_Y1		"4D0ADEC5B4B77DFBEB78227FC664F7520A469DBEA674C845F64B537ABFB808F9857EEFBDE088D0422C919ECD562D7C668A42F6C2DAB0B26D7C4D4C3B835CBEA2A843CD3A449B44F0D6D4026512670C3600B02CEFDF9BBF21975B596DD732C13"
-#define N16_P766_Y2		"2FCE7D8564D037E95317C3110542BB780D8824436B6F3626C8A4BF1D1C1FB7C1FDF12E7BC52D9F19914404EF71873EFB36C95AF0C6635329D556431A902BA01186D968C0D4BF55F17F7FED3072D77D9DE8D151135952C6EE7855E8F6176B4D66"
-#define N16_P766_Y3		"2BAD268ACF32E9D617EC80588A3F1063C5565008B9DF82E8E9B8451F874C36157A280057EF467E0BFCA1FE7AF5C79CDCD055011B2F0F14764B8F1C97BEA256BD5A40FC8020486507E52413A11B70F8D6A3ACF396D5F0D8902950A3E3821B4C64"
-#define N16_P766_R		"FFFF7000238FFAF4807374994CF93FE6E28D406881B18D350193FE6E3E533E4073749FEBD2000238FFFFDC0000010001"
-#define N16_P766_H		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
+#define AFG16_P766_A0		"0"
+#define AFG16_P766_A1		"0"
+#define AFG16_P766_A2		"1"
+#define AFG16_P766_A3		"0"
+#define AFG16_P766_B0		"0"
+#define AFG16_P766_B1		"0"
+#define AFG16_P766_B2		"0"
+#define AFG16_P766_B3		"0"
+#define AFG16_P766_X0		"36097A5BDF2276730FCAC23EA21B0C85D46B013D5A33B2D403BD82155F681BC3A1213F7AD40BFD5B64409C6B909A44F1AC391DE4222B56C55CC74DCB5DCEC23696575F80C402A1256C267F9D1CA325558C3357B116AC85CF856E51590FE7C34F"
+#define AFG16_P766_X1		"17CC3006229289EEC6AAA00FD81F17F26CECDE216E03B5DF64B61FEBA6DFF9D3F032642D66F8E5D4DE44934FB1CB99AFB0A6A939ADAFDA1E6197A474C3BBDDBA71E6120B3AAFE1007A8D0F360651B316312F902B1EB346DD2B276FEEE75ABDD1"
+#define AFG16_P766_X2		"2B79EC9BDF7F80A86DD7F3CE18A3D1FAAEAEDE9312797735EA7F090760B4730CEE401EF9CAB0978C14E967FCE1CEEF5660DFA40F367F698D0CDE9C0F0EF361D70E186EA991CD0F6DB63FE88C45EC5909DFC866862C7B1D1DE6A04843761E5E3"
+#define AFG16_P766_X3		"2005908CF374B24B1C7CF8C5CE656D04515082E61F3088C28D58B9E0249CA864AF1773F479D3272C567311FB287E579547743E8CA51A9D4B45FF5D3D6B4A2BB1865B6E4FB045953D716C68A73095A74CCDDAD5AFCEA74E676D37452916B5CB24"
+#define AFG16_P766_Y0		"137A898DDF4399F2ABB29920707790495F645B373F419C4E2A96DA05B90488BED334F2B8A44AF71C92D947009618358A14F8DE18F0D777F0DE4F98625C4024DBEB8EA858A7AEFAEC093EA12ED7A7C70142AE3583D27982B26AFD75FB441A4B66"
+#define AFG16_P766_Y1		"4D0ADEC5B4B77DFBEB78227FC664F7520A469DBEA674C845F64B537ABFB808F9857EEFBDE088D0422C919ECD562D7C668A42F6C2DAB0B26D7C4D4C3B835CBEA2A843CD3A449B44F0D6D4026512670C3600B02CEFDF9BBF21975B596DD732C13"
+#define AFG16_P766_Y2		"2FCE7D8564D037E95317C3110542BB780D8824436B6F3626C8A4BF1D1C1FB7C1FDF12E7BC52D9F19914404EF71873EFB36C95AF0C6635329D556431A902BA01186D968C0D4BF55F17F7FED3072D77D9DE8D151135952C6EE7855E8F6176B4D66"
+#define AFG16_P766_Y3		"2BAD268ACF32E9D617EC80588A3F1063C5565008B9DF82E8E9B8451F874C36157A280057EF467E0BFCA1FE7AF5C79CDCD055011B2F0F14764B8F1C97BEA256BD5A40FC8020486507E52413A11B70F8D6A3ACF396D5F0D8902950A3E3821B4C64"
+#define AFG16_P766_R		"FFFF7000238FFAF4807374994CF93FE6E28D406881B18D350193FE6E3E533E4073749FEBD2000238FFFFDC0000010001"
+#define AFG16_P766_H		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
 /** @} */
 #endif
 
@@ -354,7 +377,7 @@ void ep4_curve_mul_a(fp4_t c, const fp4_t a) {
 		}
 		fp4_mul_art(c, c);
 	} else {
-		switch (ctx->ep8_opt_a) {
+		switch (ctx->ep4_opt_a) {
 			case RLC_ZERO:
 				fp4_zero(c);
 				break;
@@ -481,6 +504,10 @@ void ep4_curve_set_twist(int type) {
 			case B24_P509:
 				ASSIGN(B24_P509);
 				break;
+#elif FP_PRIME == 510
+			case AFG16_P510:
+				ASSIGN(AFG16_P510);
+				break;
 #elif FP_PRIME == 765
 			case FM16_P765:
 				ASSIGN(FM16_P765);
@@ -489,8 +516,8 @@ void ep4_curve_set_twist(int type) {
 			case K16_P766:
 				ASSIGN(K16_P766);
 				break;
-			case N16_P766:
-				ASSIGN(N16_P766);
+			case AFG16_P766:
+				ASSIGN(AFG16_P766);
 				break;
 #endif
 			default:
@@ -514,16 +541,21 @@ void ep4_curve_set_twist(int type) {
 		bn_copy(&(ctx->ep4_h), h);
 
 		if (ep4_curve_opt_b() == RLC_ZERO) {
-			fp2_zero(a[0]);
-			fp_copy(a[1][0], ctx->fp2_p2[1][0]);
-			fp_copy(a[1][1], ctx->fp2_p2[1][1]);
-			fp4_inv(a, a);
-			fp_copy(ctx->fp4_p1[0], a[1][0]);
-			fp_copy(ctx->fp4_p1[1], a[1][1]);
-			if (fp2_is_zero(a[1])) {
-				ctx->frb4 = 0;
+			if (type == RLC_EP_MTYPE) {
+				fp2_zero(a[0]);
+				fp_copy(a[1][0], ctx->fp2_p2[1][0]);
+				fp_copy(a[1][1], ctx->fp2_p2[1][1]);
+				fp4_inv(a, a);
+				fp_copy(ctx->fp4_p1[0], a[1][0]);
+				fp_copy(ctx->fp4_p1[1], a[1][1]);
+				if (fp2_is_zero(a[1])) {
+					ctx->frb4 = 0;
+				} else {
+					ctx->frb4 = 1;
+				}
 			} else {
-				ctx->frb4 = 1;
+				fp_copy(ctx->fp4_p1[0], ctx->fp2_p2[1][0]);
+				fp_copy(ctx->fp4_p1[1], ctx->fp2_p2[1][1]);
 			}
 		} else {
 			if (type == RLC_EP_MTYPE) {
diff --git a/src/epx/relic_ep4_mul.c b/src/epx/relic_ep4_mul.c
index fa092228a..1ee6fd59e 100644
--- a/src/epx/relic_ep4_mul.c
+++ b/src/epx/relic_ep4_mul.c
@@ -60,7 +60,7 @@ static void ep4_psi(ep4_t r, const ep4_t p) {
 				ep4_dbl(r, r);
 				ep4_sub(r, r, q);
 				break;
-			case EP_N16:
+			case EP_AFG16:
 				/* u = -p^5 mod r */
 				ep4_frb(r, p, 5);
 				ep4_neg(r, r);
@@ -122,7 +122,7 @@ static void ep4_mul_gls_imp(ep4_t r, const ep4_t p, const bn_t k) {
 		}
 		ep4_tab(t[0], q, RLC_WIDTH);
 
-		if (ep_curve_is_pairf() == EP_K16 || ep_curve_is_pairf() == EP_N16) {
+		if (ep_curve_is_pairf() == EP_K16 || ep_curve_is_pairf() == EP_AFG16) {
 			/* Minimize use of endomorphism when it's expensive. */
 			for (size_t i = 1; i < 8; i++) {
 				ep4_psi(q, t[i - 1][0]);
diff --git a/src/epx/relic_ep4_mul_cof.c b/src/epx/relic_ep4_mul_cof.c
index 459a64f87..cb6801815 100644
--- a/src/epx/relic_ep4_mul_cof.c
+++ b/src/epx/relic_ep4_mul_cof.c
@@ -132,7 +132,7 @@ static void ep4_mul_cof_k16(ep4_t r, const ep4_t p) {
  * @param[out] r			- the result.
  * @param[in] p				- the point to multiply.
  */
-static void ep4_mul_cof_n16(ep4_t r, const ep4_t p) {
+static void ep4_mul_cof_afg16(ep4_t r, const ep4_t p) {
 	bn_t x;
 	ep4_t t0, t1, t2, t3, t4, t5;
 
@@ -357,8 +357,8 @@ void ep4_mul_cof(ep4_t r, const ep4_t p) {
 			case EP_K16:
 				ep4_mul_cof_k16(r, p);
 				break;
-			case EP_N16:
-				ep4_mul_cof_n16(r, p);
+			case EP_AFG16:
+				ep4_mul_cof_afg16(r, p);
 				break;
 			case EP_FM16:
 				ep4_mul_cof_fm16(r, p);
diff --git a/src/fp/relic_fp_param.c b/src/fp/relic_fp_param.c
index 136899c52..fe01a4744 100644
--- a/src/fp/relic_fp_param.c
+++ b/src/fp/relic_fp_param.c
@@ -475,6 +475,17 @@ void fp_param_set(int param) {
 				bn_neg(t0, t0);
 				fp_prime_set_pairf(t0, EP_B24);
 				break;
+#elif FP_PRIME == 510
+			case AFG16_510:
+				/* x = 2^32-2^26+2^10+2^5. */
+				bn_set_2b(t0, 32);
+				bn_set_2b(t1, 26);
+				bn_sub(t0, t0, t1);
+				bn_set_2b(t1, 10);
+				bn_add(t0, t0, t1);
+				bn_add_dig(t0, t0, 32);
+				fp_prime_set_pairf(t0, EP_AFG16);
+				break;
 #elif FP_PRIME == 511
 			case CTIDH_511:
 				bn_read_str(p, STR_P511, strlen(STR_P511), 16);
@@ -605,7 +616,7 @@ void fp_param_set(int param) {
 				bn_add_dig(t0, t0, 1);
 				fp_prime_set_pairf(t0, EP_K16);
 				break;
-			case N16_766:
+			case AFG16_766:
 				/* u = 2^48-2^28-2^25+2^2 */
 				bn_set_2b(t0, 48);
 				bn_set_2b(t1, 28);
@@ -613,7 +624,7 @@ void fp_param_set(int param) {
 				bn_set_2b(t1, 25);
 				bn_sub(t0, t0, t1);
 				bn_add_dig(t0, t0, 4);
-				fp_prime_set_pairf(t0, EP_N16);
+				fp_prime_set_pairf(t0, EP_AFG16);
 				break;
 #elif FP_PRIME == 768
 			case FM18_768:
@@ -823,6 +834,8 @@ int fp_param_set_any_tower(void) {
 	fp_param_set(K18_508);
 #elif FP_PRIME == 509
 	fp_param_set(B24_509);
+#elif FP_PRIME == 510
+	fp_param_set(AFG16_510);
 #elif FP_PRIME == 511
 	fp_param_set(CTIDH_511);
 #elif FP_PRIME == 544
@@ -842,7 +855,7 @@ int fp_param_set_any_tower(void) {
 #elif FP_PRIME == 765
 	fp_param_set(FM16_765);
 #elif FP_PRIME == 766
-	fp_param_set(N16_766);
+	fp_param_set(AFG16_766);
 	//fp_param_set(K16_766);
 #elif FP_PRIME == 768
 	fp_param_set(FM18_768);
diff --git a/src/fp/relic_fp_prime.c b/src/fp/relic_fp_prime.c
index a44c2ccab..240d03024 100644
--- a/src/fp/relic_fp_prime.c
+++ b/src/fp/relic_fp_prime.c
@@ -414,7 +414,7 @@ void fp_prime_set_pairf(const bn_t x, int pairf) {
 				bn_add(p, p, t0);
 				fp_prime_set_dense(p);
 				break;
-			case EP_N16:
+			case EP_AFG16:
 				/* p = (x^16 + 2*x^13 + x^10 + 5*x^8 + 6*x^5 + x^2 + 4)/4 */
 				bn_sqr(p, t0);
 				bn_mul(p, p, t0);
diff --git a/src/fpx/relic_fp16_mul.c b/src/fpx/relic_fp16_mul.c
index d2ce1447a..a51997a5f 100644
--- a/src/fpx/relic_fp16_mul.c
+++ b/src/fpx/relic_fp16_mul.c
@@ -94,16 +94,28 @@ void fp16_mul_dxs_basic(fp16_t c, const fp16_t a, const fp16_t b) {
 
 		/* Karatsuba algorithm. */
 
-		/* t0 = a_0 * b_0. */
-		fp8_mul(t0, a[0], b[0]);
-
-		/* t1 = a_1 * b_1. */
-		fp4_mul(t1[0], a[1][1], b[1][1]);
-		fp4_add(t1[1], a[1][0], a[1][1]);
-		fp4_mul(t1[1], t1[1], b[1][1]);
-		fp4_sub(t1[1], t1[1], t1[0]);
-		fp4_mul_art(t1[0], t1[0]);
-
+		if (fp4_is_zero(b[1][0])) {
+			/* t0 = a_0 * b_0. */
+			fp8_mul(t0, a[0], b[0]);
+
+			/* t1 = a_1 * b_1. */
+			fp4_mul(t1[0], a[1][1], b[1][1]);
+			fp4_add(t1[1], a[1][0], a[1][1]);
+			fp4_mul(t1[1], t1[1], b[1][1]);
+			fp4_sub(t1[1], t1[1], t1[0]);
+			fp4_mul_art(t1[0], t1[0]);
+		} else {
+			/* t0 = a_0 * b_0. */
+			for (int i = 0; i < 2; i++) {
+				for (int j = 0; j < 2; j++) {
+					for (int k = 0; k < 2; k++) {
+						fp_mul(t0[i][j][k], a[0][i][j][k], b[0][0][0][0]);
+					}
+				}
+			}
+			/* t1 = a_1 * b_1. */
+			fp8_mul(t1, a[1], b[1]);
+		}
 		/* t4 = b_0 + b_1. */
 		fp8_add(t4, b[0], b[1]);
 
@@ -240,43 +252,56 @@ void fp16_mul_dxs_lazyr(fp16_t c, const fp16_t a, const fp16_t b) {
 
 		/* Karatsuba algorithm. */
 
-		/* u0 = a_0 * b_0. */
-		fp8_mul_unr(u0, a[0], b[0]);
-
-		/* u1 = a_1 * b_1. */
-		fp4_mul_unr(u1[0], a[1][1], b[1][1]);
-		fp4_add(t1[0], a[1][0], a[1][1]);
-		fp4_mul_unr(u1[1], t1[0], b[1][1]);
-		fp2_subc_low(u2[1][0], u1[1][0], u1[0][0]);
-		fp2_subc_low(u2[1][1], u1[1][1], u1[0][1]);
-		fp2_nord_low(u2[0][0], u1[0][1]);
-		dv_copy(u2[0][1][0], u1[0][0][0], 2 * RLC_FP_DIGS);
-		dv_copy(u2[0][1][1], u1[0][0][1], 2 * RLC_FP_DIGS);
-
+		if (fp4_is_zero(b[1][0])) {
+			/* u0 = a_0 * b_0. */
+			fp8_mul_unr(u0, a[0], b[0]);
+
+			/* u1 = a_1 * b_1. */
+			fp4_mul_unr(u2[0], a[1][1], b[1][1]);
+			fp4_add(t1[0], a[1][0], a[1][1]);
+			fp4_mul_unr(u2[1], t1[0], b[1][1]);
+			fp2_subc_low(u1[1][0], u2[1][0], u2[0][0]);
+			fp2_subc_low(u1[1][1], u2[1][1], u2[0][1]);
+			fp2_nord_low(u1[0][0], u2[0][1]);
+			dv_copy(u1[0][1][0], u2[0][0][0], 2 * RLC_FP_DIGS);
+			dv_copy(u1[0][1][1], u2[0][0][1], 2 * RLC_FP_DIGS);
+		} else {
+			/* u0 = a_0 * b_0. */
+			for (int i = 0; i < 2; i++) {
+				for (int j = 0; j < 2; j++) {
+					for (int k = 0; k < 2; k++) {
+						fp_muln_low(u0[i][j][k], a[0][i][j][k], b[0][0][0][0]);
+					}
+				}
+			}
+			/* u1 = a_1 * b_1. */
+			fp8_mul_unr(u1, a[1], b[1]);
+		}
 		/* t1 = a_0 + a_1. */
 		fp8_add(t0, a[0], a[1]);
 		/* t0 = b_0 + b_1. */
 		fp8_add(t1, b[0], b[1]);
 		/* u2 = (a_0 + a_1) * (b_0 + b_1) */
-		fp8_mul_unr(u1, t0, t1);
+		fp8_mul_unr(u2, t0, t1);
+
 		/* c_1 = u2 - a_0b_0 - a_1b_1. */
 		for (int i = 0; i < 2; i++) {
 			for (int j = 0; j < 2; j++) {
-				fp2_subc_low(t[1][i][j], u1[i][j], u0[i][j]);
-				fp2_subc_low(t[1][i][j], t[1][i][j], u2[i][j]);
+				fp2_subc_low(t[1][i][j], u2[i][j], u0[i][j]);
+				fp2_subc_low(t[1][i][j], t[1][i][j], u1[i][j]);
 			}
 		}
 		/* c_0 = a_0b_0 + v * a_1b_1. */
-		fp2_nord_low(u1[0][0], u2[1][1]);
-		dv_copy(u1[0][1][0], u2[1][0][0], 2 * RLC_FP_DIGS);
-		dv_copy(u1[0][1][1], u2[1][0][1], 2 * RLC_FP_DIGS);
-		dv_copy(u1[1][0][0], u2[0][0][0], 2 * RLC_FP_DIGS);
-		dv_copy(u1[1][0][1], u2[0][0][1], 2 * RLC_FP_DIGS);
-		dv_copy(u1[1][1][0], u2[0][1][0], 2 * RLC_FP_DIGS);
-		dv_copy(u1[1][1][1], u2[0][1][1], 2 * RLC_FP_DIGS);
+		fp2_nord_low(u2[0][0], u1[1][1]);
+		dv_copy(u2[0][1][0], u1[1][0][0], 2 * RLC_FP_DIGS);
+		dv_copy(u2[0][1][1], u1[1][0][1], 2 * RLC_FP_DIGS);
+		dv_copy(u2[1][0][0], u1[0][0][0], 2 * RLC_FP_DIGS);
+		dv_copy(u2[1][0][1], u1[0][0][1], 2 * RLC_FP_DIGS);
+		dv_copy(u2[1][1][0], u1[0][1][0], 2 * RLC_FP_DIGS);
+		dv_copy(u2[1][1][1], u1[0][1][1], 2 * RLC_FP_DIGS);
 		for (int i = 0; i < 2; i++) {
 			for (int j = 0; j < 2; j++) {
-				fp2_addc_low(t[0][i][j], u0[i][j], u1[i][j]);
+				fp2_addc_low(t[0][i][j], u0[i][j], u2[i][j]);
 			}
 		}
 		for (int i = 0; i < 2; i++) {
diff --git a/src/low/x64-asm-8l/macro.s b/src/low/x64-asm-8l/macro.s
index f17329514..2073e5b6e 100644
--- a/src/low/x64-asm-8l/macro.s
+++ b/src/low/x64-asm-8l/macro.s
@@ -42,6 +42,16 @@
 #define P6	0x555955557955572A
 #define P7	0x0000000000000055
 #define U0	0x4B3EF8137F4017FD
+#elif FP_PRIME == 510
+#define P0	0xDD5F62C1A3044101
+#define P1	0x393DDECB1D3C5517
+#define P2	0x8E97A75A70B54410
+#define P3	0xBA09F4BACE3AC558
+#define P4	0x13BA8856149CDCB6
+#define P5	0xB32E21F17F8B0A67
+#define P6	0x5A1673FA252B4DAA
+#define P7	0X31BEC371AB26D0A6
+#define U0	0x766D29254B8340FF
 #elif FP_PRIME == 511
 #define P0	0x84DD401C8E4AB001
 #define P1	0x98707BD8B8D7F1F5
@@ -52,7 +62,7 @@
 #define P6	0x0000031F8F000000
 #define P7	0x4000000000156000
 #define U0	0xDF085042554AAFFF
-#else
+#else /* B24_P509 */
 #define P0	0xA13D118DB8BFD2AB
 #define P1	0xEE63BD076E8D9300
 #define P2	0xCFCB5C6071BAD3D2
diff --git a/src/pc/relic_pc_exp.c b/src/pc/relic_pc_exp.c
index a86e0f54a..0b6334bd8 100644
--- a/src/pc/relic_pc_exp.c
+++ b/src/pc/relic_pc_exp.c
@@ -58,7 +58,7 @@ static void gt_psi(gt_t c, const gt_t a) {
 				gt_inv(b, b);
 				gt_mul(c, c, b);
 				break;
-			case EP_N16:
+			case EP_AFG16:
 				/* u = -p^5 mod r */
 				gt_frb(c, a, 5);
 				gt_inv(c, c);
@@ -175,7 +175,7 @@ void gt_exp_gls_naf(gt_t c, const gt_t a, const bn_t b, size_t f) {
 			l = RLC_MAX(l, _l[i]);
 		}
 
-		if (ep_curve_is_pairf() == EP_K16 || ep_curve_is_pairf() == EP_N16 ||
+		if (ep_curve_is_pairf() == EP_K16 || ep_curve_is_pairf() == EP_AFG16 ||
 				ep_curve_embed() == 18) {
 			gt_copy(t[0], a);
 			for (size_t i = 1; i < f; i++) {
diff --git a/src/pc/relic_pc_util.c b/src/pc/relic_pc_util.c
index 414c34a62..f8d33abc3 100644
--- a/src/pc/relic_pc_util.c
+++ b/src/pc/relic_pc_util.c
@@ -54,7 +54,7 @@ void gt_rand(gt_t a) {
 	pp_exp_k48(a, a);
 #elif FP_PRIME == 315 || FP_PRIME == 317 || FP_PRIME == 509
 	pp_exp_k24(a, a);
-#elif FP_PRIME == 330 || FP_PRIME == 765 || FP_PRIME == 766
+#elif FP_PRIME == 330 || FP_PRIME == 510 || FP_PRIME == 765 || FP_PRIME == 766
 	pp_exp_k16(a, a);
 #elif FP_PRIME == 354 || FP_PRIME == 508 || FP_PRIME == 768 || FP_PRIME == 638 && !defined(FP_QNRES)
 	pp_exp_k18(a, a);
@@ -131,7 +131,7 @@ int g1_is_valid(const g1_t a) {
 					break;
 				/* if (u % 2) == 0, check (u**4)*\psi(P) == P
     		 	* else check (u**4-1)//2 * (\psi(P) - P) == P */
-				case EP_N16:
+				case EP_AFG16:
 					bn_sqr(n, n);
 					bn_sqr(n, n);
 					ep_psi(u, a);
@@ -333,7 +333,7 @@ int g2_is_valid(const g2_t a) {
 				break;
 			/* If u is even, check that [u*p^3]P = P
 			 * else check [p^5]P = [u]P. */
-			case EP_N16:
+			case EP_AFG16:
 				g2_mul_any(u, a, n);
 				if (bn_is_even(n)) {
 					g2_frb(v, u, 3);
@@ -532,7 +532,7 @@ int gt_is_valid(const gt_t a) {
 				break;
 			/* If u is even, check that [u*p^3]P = P
 			 * else check [p^5]P = [u]P. */
-			case EP_N16:
+			case EP_AFG16:
 				fp_prime_get_par(n);
 				gt_exp(u, a, n);
 				if (bn_is_even(n)) {
diff --git a/src/pp/relic_pp_exp_k16.c b/src/pp/relic_pp_exp_k16.c
index 6f64ef199..7f7cf8e89 100644
--- a/src/pp/relic_pp_exp_k16.c
+++ b/src/pp/relic_pp_exp_k16.c
@@ -213,12 +213,12 @@ static void pp_exp_kss(fp16_t c, fp16_t a) {
 }
 
 /**
- * Computes the final exponentiation of a pairing defined over a KSS curve.
+ * Computes the final exponentiation of a pairing defined over an AFG16 curve.
  *
  * @param[out] c			- the result.
  * @param[in] a				- the extension field element to exponentiate.
  */
-static void pp_exp_new(fp16_t c, fp16_t a) {
+static void pp_exp_afg16(fp16_t c, fp16_t a) {
 	fp16_t t0, t1, t2, t3, t4;
 	bn_t x, x_;
 
@@ -438,8 +438,8 @@ void pp_exp_k16(fp16_t c, fp16_t a) {
 		case EP_K16:
 			pp_exp_kss(c, a);
 			break;
-		case EP_N16:
-			pp_exp_new(c, a);
+		case EP_AFG16:
+			pp_exp_afg16(c, a);
 			break;
 		case EP_FM16:
 			pp_exp_fm16(c, a);
diff --git a/src/pp/relic_pp_map_k16.c b/src/pp/relic_pp_map_k16.c
index 6ab261f85..66d13ab23 100644
--- a/src/pp/relic_pp_map_k16.c
+++ b/src/pp/relic_pp_map_k16.c
@@ -499,7 +499,7 @@ void pp_map_oatep_k16(fp16_t r, const ep_t p, const ep4_t q) {
 		if (!ep_is_infty(_p[0]) && !ep4_is_infty(_q[0])) {
 			switch (ep_curve_is_pairf()) {
 				case EP_FM16:
-				case EP_N16:
+				case EP_AFG16:
 					/* r = f_{|a|,Q}(P). */
 					pp_mil_k16(r, t, _q, _p, 1, a);
 					if (bn_sign(a) == RLC_NEG) {
@@ -570,7 +570,7 @@ void pp_map_sim_oatep_k16(fp16_t r, const ep_t *p, const ep4_t *q, int m) {
 		if (j > 0) {
 			switch (ep_curve_is_pairf()) {
 				case EP_FM16:
-				case EP_N16:
+				case EP_AFG16:
 					/* r = f_{|a|,Q}(P). */
 					pp_mil_k16(r, t, _q, _p, j, a);
 					if (bn_sign(a) == RLC_NEG) {
diff --git a/test/test_fpx.c b/test/test_fpx.c
index fb2109442..241e07247 100644
--- a/test/test_fpx.c
+++ b/test/test_fpx.c
@@ -778,7 +778,7 @@ static int square_root2(void) {
 		fp2_new(a);
 		fp2_new(b);
 		fp2_new(c);
-#if 0
+
 		TEST_CASE("quadratic residuosity test is correct") {
 			fp2_zero(a);
 			TEST_ASSERT(fp2_is_sqr(a) == 1, end);
@@ -791,7 +791,6 @@ static int square_root2(void) {
 			TEST_ASSERT(fp2_is_sqr(a) == 0, end);
 		}
 		TEST_END;
-#endif
 
 		TEST_CASE("square root extraction is correct") {
 			fp2_zero(a);
@@ -799,15 +798,11 @@ static int square_root2(void) {
 			r = fp2_srt(b, c);
 			TEST_ASSERT(r, end);
 			TEST_ASSERT(fp2_cmp(b, a) == RLC_EQ, end);
-#if 0
 			fp_rand(a[0]);
 			fp_zero(a[1]);
 			fp2_sqr(c, a);
 			r = fp2_srt(b, c);
 			fp2_neg(c, b);
-			fp2_print(a);
-			fp2_print(b);
-			fp2_print(c);
 			TEST_ASSERT(r, end);
 			TEST_ASSERT(fp2_cmp(b, a) == RLC_EQ ||
 					fp2_cmp(c, a) == RLC_EQ, end);
@@ -820,7 +815,6 @@ static int square_root2(void) {
 			TEST_ASSERT(r, end);
 			TEST_ASSERT(fp2_cmp(b, a) == RLC_EQ ||
 					fp2_cmp(c, a) == RLC_EQ, end);
-#endif
 			fp2_rand(a);
 			fp2_sqr(c, a);
 			r = fp2_srt(b, c);
@@ -5023,7 +5017,7 @@ static int util16(void) {
 	return code;
 }
 
-static int addition16(void) {
+static int additioAFG16(void) {
 	int code = RLC_ERR;
 	fp16_t a, b, c, d, e;
 
@@ -5087,7 +5081,7 @@ static int addition16(void) {
 	return code;
 }
 
-static int subtraction16(void) {
+static int subtractioAFG16(void) {
 	int code = RLC_ERR;
 	fp16_t a, b, c, d;
 
@@ -5172,7 +5166,7 @@ static int doubling16(void) {
 	return code;
 }
 
-static int multiplication16(void) {
+static int multiplicatioAFG16(void) {
 	int code = RLC_ERR;
 	fp16_t a, b, c, d, e, f;
 
@@ -5426,7 +5420,7 @@ static int cyclotomic16(void) {
 	return code;
 }
 
-static int inversion16(void) {
+static int inversioAFG16(void) {
 	int code = RLC_ERR;
 	fp16_t a, b, c, d[2];
 
@@ -5490,7 +5484,7 @@ static int inversion16(void) {
 	return code;
 }
 
-static int exponentiation16(void) {
+static int exponentiatioAFG16(void) {
 	int code = RLC_ERR;
 	fp16_t a, b, c;
 	bn_t d;
@@ -9065,12 +9059,12 @@ int main(void) {
 
 		util_banner("Arithmetic:", 1);
 
-		if (addition16() != RLC_OK) {
+		if (additioAFG16() != RLC_OK) {
 			core_clean();
 			return 1;
 		}
 
-		if (subtraction16() != RLC_OK) {
+		if (subtractioAFG16() != RLC_OK) {
 			core_clean();
 			return 1;
 		}
@@ -9080,7 +9074,7 @@ int main(void) {
 			return 1;
 		}
 
-		if (multiplication16() != RLC_OK) {
+		if (multiplicatioAFG16() != RLC_OK) {
 			core_clean();
 			return 1;
 		}
@@ -9095,12 +9089,12 @@ int main(void) {
 			return 1;
 		}
 
-		if (inversion16() != RLC_OK) {
+		if (inversioAFG16() != RLC_OK) {
 			core_clean();
 			return 1;
 		}
 
-		if (exponentiation16() != RLC_OK) {
+		if (exponentiatioAFG16() != RLC_OK) {
 			core_clean();
 			return 1;
 		}